\hypertarget{group__float}{}\section{Simple Interface -\/ Single Real}
\label{group__float}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsection*{Functions}
\begin{DoxyCompactItemize}
\item 
int \hyperlink{group__float_ga32d664987f7932446c6a1a039e314fc8_ga32d664987f7932446c6a1a039e314fc8}{P\+L\+A\+S\+M\+A\+\_\+sgeadd} (P\+L\+A\+S\+M\+A\+\_\+enum trans, int M, int N, float alpha, float $\ast$A, int L\+D\+A, float beta, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga5a8eb1ec5b7f9a24c45ad5250100c4d5_ga5a8eb1ec5b7f9a24c45ad5250100c4d5}{P\+L\+A\+S\+M\+A\+\_\+sgebrd} (P\+L\+A\+S\+M\+A\+\_\+enum jobq, P\+L\+A\+S\+M\+A\+\_\+enum jobp, int M, int N, float $\ast$A, int L\+D\+A, float $\ast$D, float $\ast$E, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q, float $\ast$P, int L\+D\+P)
\item 
int \hyperlink{group__float_gacf47b4a9669e8566884a9f25a6b9a6b5_gacf47b4a9669e8566884a9f25a6b9a6b5}{P\+L\+A\+S\+M\+A\+\_\+sgecfi} (int m, int n, float $\ast$A, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+in, int imb, int inb, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+out, int omb, int onb)
\item 
int \hyperlink{group__float_ga13c9384aa848ed668f4964fee57fccc3_ga13c9384aa848ed668f4964fee57fccc3}{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async} (int m, int n, float $\ast$A, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+in, int imb, int inb, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+out, int omb, int onb, \hyperlink{structplasma__sequence__t}{P\+L\+A\+S\+M\+A\+\_\+sequence} $\ast$sequence, \hyperlink{structplasma__request__t}{P\+L\+A\+S\+M\+A\+\_\+request} $\ast$request)
\item 
int \hyperlink{group__float_ga23012d51cf74d10f924e8dad2d56ba52_ga23012d51cf74d10f924e8dad2d56ba52}{P\+L\+A\+S\+M\+A\+\_\+sgecon} (P\+L\+A\+S\+M\+A\+\_\+enum norm, int N, float $\ast$A, int L\+D\+A, float Anorm, float $\ast$rcond)
\item 
int \hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\+L\+A\+S\+M\+A\+\_\+sgelqf} (int M, int N, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T)
\item 
int \hyperlink{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}{P\+L\+A\+S\+M\+A\+\_\+sgelqs} (int M, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga2bbab59e86acca698a73c5bc8023e5c3_ga2bbab59e86acca698a73c5bc8023e5c3}{P\+L\+A\+S\+M\+A\+\_\+sgels} (P\+L\+A\+S\+M\+A\+\_\+enum trans, int M, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gace4e6452ba3ffb8cef11be1987091382_gace4e6452ba3ffb8cef11be1987091382}{P\+L\+A\+S\+M\+A\+\_\+sgemm} (P\+L\+A\+S\+M\+A\+\_\+enum trans\+A, P\+L\+A\+S\+M\+A\+\_\+enum trans\+B, int M, int N, int K, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B, float beta, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_ga06922daf59255d12c1fc228cecd6aaa0_ga06922daf59255d12c1fc228cecd6aaa0}{P\+L\+A\+S\+M\+A\+\_\+sgeqp3} (int M, int N, float $\ast$A, int L\+D\+A, int $\ast$jpvt, float $\ast$tau, float $\ast$work, float $\ast$rwork)
\item 
int \hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf} (int M, int N, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T)
\item 
int \hyperlink{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}{P\+L\+A\+S\+M\+A\+\_\+sgeqrs} (int M, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gad5f1778952268ef575d41e6bfcc7c7b4_gad5f1778952268ef575d41e6bfcc7c7b4}{P\+L\+A\+S\+M\+A\+\_\+sgesdd} (P\+L\+A\+S\+M\+A\+\_\+enum jobu, P\+L\+A\+S\+M\+A\+\_\+enum jobvt, int M, int N, float $\ast$A, int L\+D\+A, float $\ast$S, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$U, int L\+D\+U, float $\ast$V\+T, int L\+D\+V\+T)
\item 
int \hyperlink{group__float_ga39018420f926f77ef11c50c82f66da77_ga39018420f926f77ef11c50c82f66da77}{P\+L\+A\+S\+M\+A\+\_\+sgesv} (int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, int $\ast$I\+P\+I\+V, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gab9dab6c3f22b6cf8dad0fa2f1b563988_gab9dab6c3f22b6cf8dad0fa2f1b563988}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv} (int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+L, int $\ast$I\+P\+I\+V, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gabaf1acf98c5bbd242f4e603c2bbfffb1_gabaf1acf98c5bbd242f4e603c2bbfffb1}{P\+L\+A\+S\+M\+A\+\_\+sgesvd} (P\+L\+A\+S\+M\+A\+\_\+enum jobu, P\+L\+A\+S\+M\+A\+\_\+enum jobvt, int M, int N, float $\ast$A, int L\+D\+A, float $\ast$S, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$U, int L\+D\+U, float $\ast$V\+T, int L\+D\+V\+T)
\item 
int \hyperlink{group__float_ga51861b9bdc9c8058822c32807a78fca7_ga51861b9bdc9c8058822c32807a78fca7}{P\+L\+A\+S\+M\+A\+\_\+sgetmi} (int m, int n, float $\ast$A, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+in, int imb, int inb)
\item 
int \hyperlink{group__float_gaa35042844f1c885bc26a5f47293e3d45_gaa35042844f1c885bc26a5f47293e3d45}{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async} (int m, int n, float $\ast$A, P\+L\+A\+S\+M\+A\+\_\+enum f\+\_\+in, int mb, int nb, \hyperlink{structplasma__sequence__t}{P\+L\+A\+S\+M\+A\+\_\+sequence} $\ast$sequence, \hyperlink{structplasma__request__t}{P\+L\+A\+S\+M\+A\+\_\+request} $\ast$request)
\item 
int \hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} (int M, int N, float $\ast$A, int L\+D\+A, int $\ast$I\+P\+I\+V)
\item 
int \hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv} (int M, int N, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+L, int $\ast$I\+P\+I\+V)
\item 
int \hyperlink{group__float_ga1c9ced92c5818ef3a6af88e6545ba1e6_ga1c9ced92c5818ef3a6af88e6545ba1e6}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv} (int M, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_ga4a519bbf13b7a335ca2dd079693f9edc_ga4a519bbf13b7a335ca2dd079693f9edc}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv} (int M, int N, float $\ast$A, int L\+D\+A, int $\ast$I\+P\+I\+V)
\item 
int \hyperlink{group__float_gadb78715cdd99791aa77c2640f1325f8e_gadb78715cdd99791aa77c2640f1325f8e}{P\+L\+A\+S\+M\+A\+\_\+sgetri} (int N, float $\ast$A, int L\+D\+A, int $\ast$I\+P\+I\+V)
\item 
int \hyperlink{group__float_ga655cb742ac1c78e5ce86070f4ce1271b_ga655cb742ac1c78e5ce86070f4ce1271b}{P\+L\+A\+S\+M\+A\+\_\+sgetrs} (P\+L\+A\+S\+M\+A\+\_\+enum trans, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, const int $\ast$I\+P\+I\+V, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gae593ed2d7e164acc75c4e6efdca4d95a_gae593ed2d7e164acc75c4e6efdca4d95a}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv} (P\+L\+A\+S\+M\+A\+\_\+enum trans, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+L, const int $\ast$I\+P\+I\+V, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga2ae5e8cc7cf6222bf521a6decd6c27a1_ga2ae5e8cc7cf6222bf521a6decd6c27a1}{P\+L\+A\+S\+M\+A\+\_\+slacpy} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int M, int N, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
float \hyperlink{group__float_gaf12ff85306bc548593674ce694d5e5be_gaf12ff85306bc548593674ce694d5e5be}{P\+L\+A\+S\+M\+A\+\_\+slange} (P\+L\+A\+S\+M\+A\+\_\+enum norm, int M, int N, float $\ast$A, int L\+D\+A)
\item 
float \hyperlink{group__float_gaad7d8cac5c5334f8cc144f36050bbdc3_gaad7d8cac5c5334f8cc144f36050bbdc3}{P\+L\+A\+S\+M\+A\+\_\+slansy} (P\+L\+A\+S\+M\+A\+\_\+enum norm, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A)
\item 
float \hyperlink{group__float_gac89a3f7eb1600d358791d38d2e662cb1_gac89a3f7eb1600d358791d38d2e662cb1}{P\+L\+A\+S\+M\+A\+\_\+slantr} (P\+L\+A\+S\+M\+A\+\_\+enum norm, P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum diag, int M, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_ga70bbb11d008076ce34d89399a31d5ca2_ga70bbb11d008076ce34d89399a31d5ca2}{P\+L\+A\+S\+M\+A\+\_\+slascal} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int M, int N, float alpha, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}{P\+L\+A\+S\+M\+A\+\_\+slaset} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int M, int N, float alpha, float beta, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_gaa20663314d5fd0c31c8a8a2fd6efc7e5_gaa20663314d5fd0c31c8a8a2fd6efc7e5}{P\+L\+A\+S\+M\+A\+\_\+slaswp} (int N, float $\ast$A, int L\+D\+A, int K1, int K2, const int $\ast$I\+P\+I\+V, int I\+N\+C\+X)
\item 
int \hyperlink{group__float_ga044b505b0a887de1be5636328ebe60ab_ga044b505b0a887de1be5636328ebe60ab}{P\+L\+A\+S\+M\+A\+\_\+slaswpc} (int N, float $\ast$A, int L\+D\+A, int K1, int K2, const int $\ast$I\+P\+I\+V, int I\+N\+C\+X)
\item 
int \hyperlink{group__float_gaafb49f230a9c4dbdc635144f46f680f6_gaafb49f230a9c4dbdc635144f46f680f6}{P\+L\+A\+S\+M\+A\+\_\+slauum} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_ga2f8b6c06f4346761e024c9fa00427a61_ga2f8b6c06f4346761e024c9fa00427a61}{P\+L\+A\+S\+M\+A\+\_\+sorglq} (int M, int N, int K, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga4b6a6aa9e5da7961424f3afb62a69562_ga4b6a6aa9e5da7961424f3afb62a69562}{P\+L\+A\+S\+M\+A\+\_\+sorgqr} (int M, int N, int K, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga4f42eb41e34bdf290b36fe5ce8e576b7_ga4f42eb41e34bdf290b36fe5ce8e576b7}{P\+L\+A\+S\+M\+A\+\_\+sormlq} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum trans, int M, int N, int K, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_ga3d2c263d860db4a6d63fd13156262bd2_ga3d2c263d860db4a6d63fd13156262bd2}{P\+L\+A\+S\+M\+A\+\_\+sormqr} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum trans, int M, int N, int K, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\+L\+A\+S\+M\+A\+\_\+splgsy} (float bump, int N, float $\ast$A, int L\+D\+A, unsigned long long int seed)
\item 
int \hyperlink{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}{P\+L\+A\+S\+M\+A\+\_\+splrnt} (int M, int N, float $\ast$A, int L\+D\+A, unsigned long long int seed)
\item 
int \hyperlink{group__float_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1}{P\+L\+A\+S\+M\+A\+\_\+spltmg} (P\+L\+A\+S\+M\+A\+\_\+enum mtxtype, int M, int N, float $\ast$A, int L\+D\+A, unsigned long long int seed)
\item 
int \hyperlink{group__float_gae4ca020dbb8fa3516e2e4c89a6b60b1a_gae4ca020dbb8fa3516e2e4c89a6b60b1a}{P\+L\+A\+S\+M\+A\+\_\+spocon} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float Anorm, float $\ast$rcond)
\item 
int \hyperlink{group__float_ga113c09b4a9f41fc4c19358a52477d685_ga113c09b4a9f41fc4c19358a52477d685}{P\+L\+A\+S\+M\+A\+\_\+sposv} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\+L\+A\+S\+M\+A\+\_\+spotrf} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{P\+L\+A\+S\+M\+A\+\_\+spotri} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}{P\+L\+A\+S\+M\+A\+\_\+spotrs} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{P\+L\+A\+S\+M\+A\+\_\+ssyev} (P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$W, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga71305bb114c063946ddd9003bea058bf_ga71305bb114c063946ddd9003bea058bf}{P\+L\+A\+S\+M\+A\+\_\+ssyevd} (P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$W, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga850dfaa20a85559bd1ef0042e4218ecd_ga850dfaa20a85559bd1ef0042e4218ecd}{P\+L\+A\+S\+M\+A\+\_\+ssyevr} (P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum range, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float vl, float vu, int il, int iu, float abstol, int $\ast$nbcomputedeig, float $\ast$W, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga66b77c0de44f80760c4184756250e75e_ga66b77c0de44f80760c4184756250e75e}{P\+L\+A\+S\+M\+A\+\_\+ssygst} (P\+L\+A\+S\+M\+A\+\_\+enum itype, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gaa5deb8e85d037eff767d9a9e5e99fad9_gaa5deb8e85d037eff767d9a9e5e99fad9}{P\+L\+A\+S\+M\+A\+\_\+ssygv} (P\+L\+A\+S\+M\+A\+\_\+enum itype, P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B, float $\ast$W, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga366bd2466847e2b9f29bd39a9d699fb9_ga366bd2466847e2b9f29bd39a9d699fb9}{P\+L\+A\+S\+M\+A\+\_\+ssygvd} (P\+L\+A\+S\+M\+A\+\_\+enum itype, P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B, float $\ast$W, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_gaaffcd386f207f3e3a3073a803e27e3f1_gaaffcd386f207f3e3a3073a803e27e3f1}{P\+L\+A\+S\+M\+A\+\_\+ssymm} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int M, int N, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B, float beta, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_gafac964a38a7c62696c3b95d35108ad9b_gafac964a38a7c62696c3b95d35108ad9b}{P\+L\+A\+S\+M\+A\+\_\+ssyr2k} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans, int N, int K, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B, float beta, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_gae83f0347570d23dc62dd8b298eb14ad6_gae83f0347570d23dc62dd8b298eb14ad6}{P\+L\+A\+S\+M\+A\+\_\+ssyrk} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans, int N, int K, float alpha, float $\ast$A, int L\+D\+A, float beta, float $\ast$C, int L\+D\+C)
\item 
int \hyperlink{group__float_gadfee26871dee9a24b201bc329fccd81b_gadfee26871dee9a24b201bc329fccd81b}{P\+L\+A\+S\+M\+A\+\_\+ssytrd} (P\+L\+A\+S\+M\+A\+\_\+enum jobz, P\+L\+A\+S\+M\+A\+\_\+enum uplo, int N, float $\ast$A, int L\+D\+A, float $\ast$D, float $\ast$E, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+T, float $\ast$Q, int L\+D\+Q)
\item 
int \hyperlink{group__float_ga5395fb5a2b6c3f123e3fc7e5fba0dc56_ga5395fb5a2b6c3f123e3fc7e5fba0dc56}{P\+L\+A\+S\+M\+A\+\_\+stradd} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans, int M, int N, float alpha, float $\ast$A, int L\+D\+A, float beta, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gabbc2cf7c018815bd2c1ce8a6623b2813_gabbc2cf7c018815bd2c1ce8a6623b2813}{P\+L\+A\+S\+M\+A\+\_\+strmm} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans\+A, P\+L\+A\+S\+M\+A\+\_\+enum diag, int N, int N\+R\+H\+S, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga572e80d04d4e9701bf3dd73d1f96d54c_ga572e80d04d4e9701bf3dd73d1f96d54c}{P\+L\+A\+S\+M\+A\+\_\+strsm} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans\+A, P\+L\+A\+S\+M\+A\+\_\+enum diag, int N, int N\+R\+H\+S, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga245da4f8540c426fde27a50eff39b64a_ga245da4f8540c426fde27a50eff39b64a}{P\+L\+A\+S\+M\+A\+\_\+strsmpl} (int N, int N\+R\+H\+S, float $\ast$A, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$desc\+L, const int $\ast$I\+P\+I\+V, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_ga7713151eac0c0ff54c5a6aac1957b5e0_ga7713151eac0c0ff54c5a6aac1957b5e0}{P\+L\+A\+S\+M\+A\+\_\+strsmrv} (P\+L\+A\+S\+M\+A\+\_\+enum side, P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum trans\+A, P\+L\+A\+S\+M\+A\+\_\+enum diag, int N, int N\+R\+H\+S, float alpha, float $\ast$A, int L\+D\+A, float $\ast$B, int L\+D\+B)
\item 
int \hyperlink{group__float_gaaf0df7b8ff03a270a25da71b9f133abb_gaaf0df7b8ff03a270a25da71b9f133abb}{P\+L\+A\+S\+M\+A\+\_\+strtri} (P\+L\+A\+S\+M\+A\+\_\+enum uplo, P\+L\+A\+S\+M\+A\+\_\+enum diag, int N, float $\ast$A, int L\+D\+A)
\item 
int \hyperlink{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile} (float $\ast$Af77, int L\+D\+A, \hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$A)
\item 
int \hyperlink{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack} (\hyperlink{structplasma__desc__t}{P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$A, float $\ast$Af77, int L\+D\+A)
\end{DoxyCompactItemize}


\subsection{Detailed Description}
This is the group of single real functions using the simple user interface. 

\subsection{Function Documentation}
\hypertarget{group__float_ga32d664987f7932446c6a1a039e314fc8_ga32d664987f7932446c6a1a039e314fc8}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgeadd@{P\+L\+A\+S\+M\+A\+\_\+sgeadd}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgeadd@{P\+L\+A\+S\+M\+A\+\_\+sgeadd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgeadd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgeadd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{beta, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga32d664987f7932446c6a1a039e314fc8_ga32d664987f7932446c6a1a039e314fc8}
P\+L\+A\+S\+M\+A\+\_\+sgeadd -\/ Performs a matrix addition similarly to the psgeadd() function from the P\+B\+L\+A\+S library\+:

\[ C = \alpha op( A ) + \beta B \],

where op( X ) is one of

op( X ) = X or op( X ) = X\textquotesingle{} or op( X ) = g( X\textquotesingle{} )

alpha and beta are scalars, and A, and B are matrices, with op( A ) and B two m by n matrices.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em M} & M specifies the number of rows of the matrix op( A ) and of the matrix B. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the number of columns of the matrix op( A ) and of the matrix B. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is N when trans = Plasma\+No\+Trans, and is M otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+K), where K is M when trans = Plasma\+No\+Trans, and is N when otherwise.\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em B} & B is a L\+D\+B-\/by-\/\+N matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga87d12ba559572c6fe86af294f5cfb3a3_ga87d12ba559572c6fe86af294f5cfb3a3}{P\+L\+A\+S\+M\+A\+\_\+sgeadd\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_gabe6af489e627824777d1428f1ab586c0_gabe6af489e627824777d1428f1ab586c0}{P\+L\+A\+S\+M\+A\+\_\+cgeadd} 

\hyperlink{group__double_gaf337216ce367c98b6e78e15f05ca928b_gaf337216ce367c98b6e78e15f05ca928b}{P\+L\+A\+S\+M\+A\+\_\+dgeadd} 

\hyperlink{group__float_ga32d664987f7932446c6a1a039e314fc8_ga32d664987f7932446c6a1a039e314fc8}{P\+L\+A\+S\+M\+A\+\_\+sgeadd} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga5a8eb1ec5b7f9a24c45ad5250100c4d5_ga5a8eb1ec5b7f9a24c45ad5250100c4d5}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgebrd@{P\+L\+A\+S\+M\+A\+\_\+sgebrd}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgebrd@{P\+L\+A\+S\+M\+A\+\_\+sgebrd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgebrd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgebrd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobq, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobp, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{D, }
\item[{float $\ast$}]{E, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q, }
\item[{float $\ast$}]{P, }
\item[{int}]{L\+D\+P}
\end{DoxyParamCaption}
)}\label{group__float_ga5a8eb1ec5b7f9a24c45ad5250100c4d5_ga5a8eb1ec5b7f9a24c45ad5250100c4d5}
P\+L\+A\+S\+M\+A\+\_\+sgebrd -\/ reduces a general complex M-\/by-\/\+N matrix A to upper or lower bidiagonal form B using a two-\/stage approach First stage\+: reduction to band bidiagonal form (orthogonal matrices Q1 and P1); Second stage\+: reduction from band to bidiagonal form (orthogonal matrices Q2 and P2). Let Q = Q1 $\ast$ Q2 be the global left unitary transformation; Let P = P1 $\ast$ P2 be the global right unitary transformation; Q$\ast$$\ast$\+T $\ast$ A $\ast$ P = B. If M $>$= N, B is upper bidiagonal; if M $<$ N, B is lower bidiagonal. Not L\+A\+P\+A\+C\+K Compliant for now! Note\+: T is incomplete and contains only the block reflectors of the first stage. Therefore, Q and P can not be built completely.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobq} & Specifies options for computing all or part of the matrix Q. Intended usage\+: = Plasma\+Vec\+: all M columns of Q are returned in array Q; = Plasma\+No\+Vec\+: not referenced.\\
\hline
\mbox{\tt in}  & {\em jobp} & Specifies options for computing all or part of the matrix V$\ast$$\ast$\+T. Intended usage\+: = Plasma\+Vec\+: all N columns of P are returned in array P; = Plasma\+No\+Vec\+: not referenced.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, if M $>$= N, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array T, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array T, represent the unitary matrix P as a product of elementary reflectors; if M $<$ N, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array T, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array T, represent the unitary matrix P as a product of elementary reflectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em D} & On exit, the diagonal elements of the bidiagonal matrix\+: D(i) = A(i,i). Dimension (min(\+M,\+N)).\\
\hline
\mbox{\tt out}  & {\em E} & On exit, the off-\/diagonal elements of the bidiagonal matrix\+: if M $>$= N, E(i) = A(i,i+1) for i = 1,2,...,N-\/1; if M $<$ N, E(i) = A(i+1,i) for i = 1,2,...,M-\/1. Dimension (min(\+M,\+N)-\/1).\\
\hline
\mbox{\tt out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+sgebrd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec, then if return value = 0, Q contains the M-\/by-\/\+M unitary matrix Q. If jobz = Plasma\+No\+Vec, then it is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= M.\\
\hline
\mbox{\tt out}  & {\em P} & On exit, if jobz = Plasma\+Vec, then if return value = 0, P contains the N-\/by-\/\+N unitary matrix P. If jobz = Plasma\+No\+Vec, then it is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+P} & The leading dimension of the array P. L\+D\+P $>$= N.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gac1da440c28ae9d970489d4523956f3dd_gac1da440c28ae9d970489d4523956f3dd}{P\+L\+A\+S\+M\+A\+\_\+sgebrd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gae67c2111c450820663dc20c933c2703f_gae67c2111c450820663dc20c933c2703f}{P\+L\+A\+S\+M\+A\+\_\+sgebrd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga2b35d07a5ac3eb2f953372b16416aeab_ga2b35d07a5ac3eb2f953372b16416aeab}{P\+L\+A\+S\+M\+A\+\_\+cgebrd} 

\hyperlink{group__double_gaabe52f420c4ae6d1db03f9fb37b8045f_gaabe52f420c4ae6d1db03f9fb37b8045f}{P\+L\+A\+S\+M\+A\+\_\+dgebrd} 

\hyperlink{group__float_ga5a8eb1ec5b7f9a24c45ad5250100c4d5_ga5a8eb1ec5b7f9a24c45ad5250100c4d5}{P\+L\+A\+S\+M\+A\+\_\+sgebrd} 
\end{DoxySeeAlso}
\hypertarget{group__float_gacf47b4a9669e8566884a9f25a6b9a6b5_gacf47b4a9669e8566884a9f25a6b9a6b5}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgecfi@{P\+L\+A\+S\+M\+A\+\_\+sgecfi}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgecfi@{P\+L\+A\+S\+M\+A\+\_\+sgecfi}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgecfi}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgecfi (
\begin{DoxyParamCaption}
\item[{int}]{m, }
\item[{int}]{n, }
\item[{float $\ast$}]{A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+in, }
\item[{int}]{imb, }
\item[{int}]{inb, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+out, }
\item[{int}]{omb, }
\item[{int}]{onb}
\end{DoxyParamCaption}
)}\label{group__float_gacf47b4a9669e8566884a9f25a6b9a6b5_gacf47b4a9669e8566884a9f25a6b9a6b5}
P\+L\+A\+S\+M\+A\+\_\+sgecfi convert the matrice A in place from format f\+\_\+in to format f\+\_\+out


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em m} & Number of rows of matrix A\\
\hline
\mbox{\tt in}  & {\em n} & Number of columns of matrix A\\
\hline
\mbox{\tt in,out}  & {\em A} & Matrix of size m$\ast$n\\
\hline
\mbox{\tt in}  & {\em f\+\_\+in} & Original layout of the matrix A. Must be part of\+: Plasma\+C\+M\+: if A is stored in Column Major, Plasma\+R\+M\+: if A is stored in Row Major, Plasma\+C\+C\+R\+B\+: if A is stored in Column Column Rectangular Block layout, Plasma\+C\+R\+R\+B\+: if A is stored in Column Row Rectangular Block layout, Plasma\+R\+C\+R\+B\+: if A is stored in Row Column Rectangular Block layout, Plasma\+R\+R\+R\+B\+: if A is stored in Row Row Rectangular Block layout; where the first Column/\+Row stand for the order in which tiles are sorted, and the secon Column/\+Row stand for the layout inside each tile.\\
\hline
\mbox{\tt in}  & {\em imb} & Number of rows of each block in original format\\
\hline
\mbox{\tt in}  & {\em inb} & Number of columns of each block in original format\\
\hline
\mbox{\tt in}  & {\em f\+\_\+out} & Format requested for the matrix A. Must be part of (Plasma\+C\+M, Plasma\+R\+M, Plasma\+C\+C\+R\+B, Plasma\+C\+R\+R\+B, Plasma\+R\+C\+R\+B, Plasma\+R\+R\+R\+B)\\
\hline
\mbox{\tt in}  & {\em omb} & Number of rows of each block in requested format\\
\hline
\mbox{\tt in}  & {\em onb} & Number of columns of each block in requested format\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float_ga13c9384aa848ed668f4964fee57fccc3_ga13c9384aa848ed668f4964fee57fccc3}{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga13c9384aa848ed668f4964fee57fccc3_ga13c9384aa848ed668f4964fee57fccc3}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async@{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async@{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async (
\begin{DoxyParamCaption}
\item[{int}]{m, }
\item[{int}]{n, }
\item[{float $\ast$}]{A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+in, }
\item[{int}]{imb, }
\item[{int}]{inb, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+out, }
\item[{int}]{omb, }
\item[{int}]{onb, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+sequence} $\ast$}]{sequence, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+request} $\ast$}]{request}
\end{DoxyParamCaption}
)}\label{group__float_ga13c9384aa848ed668f4964fee57fccc3_ga13c9384aa848ed668f4964fee57fccc3}
P\+L\+A\+S\+M\+A\+\_\+sgecfi\+\_\+\+Async convert the matrice A in place from format f\+\_\+in to format f\+\_\+out


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em m} & Number of rows of matrix A\\
\hline
\mbox{\tt in}  & {\em n} & Number of columns of matrix A\\
\hline
\mbox{\tt in,out}  & {\em A} & Matrix of size L$\ast$m$\ast$n\\
\hline
\mbox{\tt in}  & {\em f\+\_\+in} & Original format of the matrix A. Must be part of (Plasma\+C\+M, Plasma\+R\+M, Plasma\+C\+C\+R\+B, Plasma\+C\+R\+R\+B, Plasma\+R\+C\+R\+B, Plasma\+R\+R\+R\+B)\\
\hline
\mbox{\tt in}  & {\em imb} & Number of rows of each block in original format\\
\hline
\mbox{\tt in}  & {\em inb} & Number of columns of each block in original format\\
\hline
\mbox{\tt in}  & {\em f\+\_\+out} & Format requested for the matrix A. Must be part of (Plasma\+C\+M, Plasma\+R\+M, Plasma\+C\+C\+R\+B, Plasma\+C\+R\+R\+B, Plasma\+R\+C\+R\+B, Plasma\+R\+R\+R\+B)\\
\hline
\mbox{\tt in}  & {\em omb} & Number of rows of each block in requested format\\
\hline
\mbox{\tt in}  & {\em onb} & Number of columns of each block in requested format\\
\hline
\mbox{\tt in}  & {\em sequence} & Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).\\
\hline
\mbox{\tt out}  & {\em request} & Identifies this function call (for exception handling purposes).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float_gacf47b4a9669e8566884a9f25a6b9a6b5_gacf47b4a9669e8566884a9f25a6b9a6b5}{P\+L\+A\+S\+M\+A\+\_\+sgecfi} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga23012d51cf74d10f924e8dad2d56ba52_ga23012d51cf74d10f924e8dad2d56ba52}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgecon@{P\+L\+A\+S\+M\+A\+\_\+sgecon}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgecon@{P\+L\+A\+S\+M\+A\+\_\+sgecon}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgecon}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgecon (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{norm, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{Anorm, }
\item[{float $\ast$}]{rcond}
\end{DoxyParamCaption}
)}\label{group__float_ga23012d51cf74d10f924e8dad2d56ba52_ga23012d51cf74d10f924e8dad2d56ba52}
P\+L\+A\+S\+M\+A\+\_\+sgecon -\/ estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-\/norm or the infinity-\/norm, using the L\+U factorization computed by \hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf()}.

An estimate is obtained for norm(inv(\+A)), and the reciprocal of the condition number is computed as

\[ rcond = \frac{1}{\|\|A\-\| \times \-\|A^{-1}\|\|} \]


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & Specifies whether the 1-\/norm condition number or the infinity-\/norm condition number is required\+: = Plasma\+One\+Norm\+: One norm = Plasma\+Inf\+Norm\+: Infinity norm\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\+N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em Anorm} & If norm = Plasma\+One\+Norm, the 1-\/norm of the original matrix A. If norm = Plasma\+Inf\+Norm, the infinity-\/norm of the original matrix A.\\
\hline
\mbox{\tt out}  & {\em rcond} & The reciprocal of the condition number of the matrix A, computed as stated above.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga2f84d657dbd1d672faf0251081facaf6_ga2f84d657dbd1d672faf0251081facaf6}{P\+L\+A\+S\+M\+A\+\_\+sgecon\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaaa8291aabe6b837154fba55481a8fdd1_gaaa8291aabe6b837154fba55481a8fdd1}{P\+L\+A\+S\+M\+A\+\_\+sgecon\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga59c8cdc7aee5dab4baa2059b6d508b84_ga59c8cdc7aee5dab4baa2059b6d508b84}{P\+L\+A\+S\+M\+A\+\_\+cgecon} 

\hyperlink{group__double_gaffb6839f6bec9ca91ddba211efecb14c_gaffb6839f6bec9ca91ddba211efecb14c}{P\+L\+A\+S\+M\+A\+\_\+dgecon} 

\hyperlink{group__float_ga23012d51cf74d10f924e8dad2d56ba52_ga23012d51cf74d10f924e8dad2d56ba52}{P\+L\+A\+S\+M\+A\+\_\+sgecon} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgelqf@{P\+L\+A\+S\+M\+A\+\_\+sgelqf}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgelqf@{P\+L\+A\+S\+M\+A\+\_\+sgelqf}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgelqf}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgelqf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T}
\end{DoxyParamCaption}
)}\label{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}
P\+L\+A\+S\+M\+A\+\_\+sgelqf -\/ Computes the tile L\+Q factorization of a complex M-\/by-\/\+N matrix A\+: A = L $\ast$ Q.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, the elements on and below the diagonal of the array contain the m-\/by-\/min(M,N) lower trapezoidal matrix L (L is lower triangular if M $<$= N); the elements above the diagonal represent the unitary matrix Q as a product of elementary reflectors, stored by tiles.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em desc\+T} & On exit, auxiliary factorization data, required by P\+L\+A\+S\+M\+A\+\_\+sgelqs to solve the system of equations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga4360b93a339b6fff6aa98a6427224395_ga4360b93a339b6fff6aa98a6427224395}{P\+L\+A\+S\+M\+A\+\_\+sgelqf\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga66c68c7a249b7528c5cf086a44f27586_ga66c68c7a249b7528c5cf086a44f27586}{P\+L\+A\+S\+M\+A\+\_\+sgelqf\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gadab1e78967134c5e784bb80d03760b25_gadab1e78967134c5e784bb80d03760b25}{P\+L\+A\+S\+M\+A\+\_\+cgelqf} 

\hyperlink{group__double_ga60fffe07485af5c38c0447efccf8ccfe_ga60fffe07485af5c38c0447efccf8ccfe}{P\+L\+A\+S\+M\+A\+\_\+dgelqf} 

\hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\+L\+A\+S\+M\+A\+\_\+sgelqf} 

\hyperlink{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}{P\+L\+A\+S\+M\+A\+\_\+sgelqs} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgelqs@{P\+L\+A\+S\+M\+A\+\_\+sgelqs}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgelqs@{P\+L\+A\+S\+M\+A\+\_\+sgelqs}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgelqs}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgelqs (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}
P\+L\+A\+S\+M\+A\+\_\+sgelqs -\/ Compute a minimum-\/norm solution min $\vert$$\vert$ A$\ast$\+X -\/ B $\vert$$\vert$ using the L\+Q factorization A = L$\ast$\+Q computed by P\+L\+A\+S\+M\+A\+\_\+sgelqf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of columns of B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & Details of the L\+Q factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgelqf. Remark\+: If out-\/of-\/place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= M.\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the M-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= N.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga1b602ea68c4e9eb0fba8f890231b2a57_ga1b602ea68c4e9eb0fba8f890231b2a57}{P\+L\+A\+S\+M\+A\+\_\+sgelqs\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga3163bc7f3ca8713217401f54956768c2_ga3163bc7f3ca8713217401f54956768c2}{P\+L\+A\+S\+M\+A\+\_\+sgelqs\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gab6c2a5892b81e8ee9740268d06adf9b1_gab6c2a5892b81e8ee9740268d06adf9b1}{P\+L\+A\+S\+M\+A\+\_\+cgelqs} 

\hyperlink{group__double_ga092545f106c9fae67b82eb65f11ca4ab_ga092545f106c9fae67b82eb65f11ca4ab}{P\+L\+A\+S\+M\+A\+\_\+dgelqs} 

\hyperlink{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}{P\+L\+A\+S\+M\+A\+\_\+sgelqs} 

\hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\+L\+A\+S\+M\+A\+\_\+sgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga2bbab59e86acca698a73c5bc8023e5c3_ga2bbab59e86acca698a73c5bc8023e5c3}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgels@{P\+L\+A\+S\+M\+A\+\_\+sgels}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgels@{P\+L\+A\+S\+M\+A\+\_\+sgels}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgels}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgels (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga2bbab59e86acca698a73c5bc8023e5c3_ga2bbab59e86acca698a73c5bc8023e5c3}
P\+L\+A\+S\+M\+A\+\_\+sgels -\/ solves overdetermined or underdetermined linear systems involving an M-\/by-\/\+N matrix A using the Q\+R or the L\+Q factorization of A. It is assumed that A has full rank. The following options are provided\+:

\subsection*{trans = Plasma\+No\+Trans and M $>$= N\+: find the least squares solution of an}

overdetermined system, i.\+e., solve the least squares problem\+: minimize $\vert$$\vert$ B -\/ A$\ast$\+X $\vert$$\vert$.

\subsection*{trans = Plasma\+No\+Trans and M $<$ N\+: find the minimum norm solution of an}

underdetermined system A $\ast$ X = B.

Several right hand side vectors B and solution vectors X can be handled in a single call; they are stored as the columns of the M-\/by-\/\+N\+R\+H\+S right hand side matrix B and the N-\/by-\/\+N\+R\+H\+S solution matrix X.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended usage\+: = Plasma\+No\+Trans\+: the linear system involves A; = Plasma\+Trans\+: the linear system involves A$\ast$$\ast$\+T. Currently only Plasma\+No\+Trans is supported.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrices B and X. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, if M $>$= N, A is overwritten by details of its Q\+R factorization as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf; if M $<$ N, A is overwritten by details of its L\+Q factorization as returned by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em desc\+T} & On exit, auxiliary factorization data.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the M-\/by-\/\+N\+R\+H\+S matrix B of right hand side vectors, stored columnwise; On exit, if return value = 0, B is overwritten by the solution vectors, stored columnwise\+: if M $>$= N, rows 1 to N of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if M $<$ N, rows 1 to N of B contain the minimum norm solution vectors;\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= M\+A\+X(1,\+M,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga887751384d11e2b2324e15eb59aeb58d_ga887751384d11e2b2324e15eb59aeb58d}{P\+L\+A\+S\+M\+A\+\_\+sgels\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gae5517496f2ab1a5c3c35705384454eb7_gae5517496f2ab1a5c3c35705384454eb7}{P\+L\+A\+S\+M\+A\+\_\+sgels\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga047c51e0c630ac15b2679b8352013f7b_ga047c51e0c630ac15b2679b8352013f7b}{P\+L\+A\+S\+M\+A\+\_\+cgels} 

\hyperlink{group__double_ga4bfc0cdaf567c26828f484e54d457d92_ga4bfc0cdaf567c26828f484e54d457d92}{P\+L\+A\+S\+M\+A\+\_\+dgels} 

\hyperlink{group__float_ga2bbab59e86acca698a73c5bc8023e5c3_ga2bbab59e86acca698a73c5bc8023e5c3}{P\+L\+A\+S\+M\+A\+\_\+sgels} 
\end{DoxySeeAlso}
\hypertarget{group__float_gace4e6452ba3ffb8cef11be1987091382_gace4e6452ba3ffb8cef11be1987091382}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgemm@{P\+L\+A\+S\+M\+A\+\_\+sgemm}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgemm@{P\+L\+A\+S\+M\+A\+\_\+sgemm}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgemm}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgemm (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans\+A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans\+B, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B, }
\item[{float}]{beta, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_gace4e6452ba3ffb8cef11be1987091382_gace4e6452ba3ffb8cef11be1987091382}
P\+L\+A\+S\+M\+A\+\_\+sgemm -\/ Performs one of the matrix-\/matrix operations

\[ C = \alpha [op( A )\times op( B )] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = X\textquotesingle{} or op( X ) = g( X\textquotesingle{} )

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans\+A} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em trans\+B} & Specifies whether the matrix B is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: B is not transposed; = Plasma\+Trans\+: B is transposed; = Plasma\+Trans\+: B is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em M} & M specifies the number of rows of the matrix op( A ) and of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the number of columns of the matrix op( B ) and of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is K when trans\+A = Plasma\+No\+Trans, and is M otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\+D\+B-\/by-\/kb matrix, where kb is N when trans\+B = Plasma\+No\+Trans, and is K otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\+D\+C-\/by-\/\+N matrix. On exit, the array is overwritten by the M by N matrix ( alpha$\ast$op( A )$\ast$op( B ) + beta$\ast$\+C )\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga6d536762bed042f104f5b730b82fa49b_ga6d536762bed042f104f5b730b82fa49b}{P\+L\+A\+S\+M\+A\+\_\+sgemm\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga5505cdf8794ea00c9160d656d2a00ec9_ga5505cdf8794ea00c9160d656d2a00ec9}{P\+L\+A\+S\+M\+A\+\_\+cgemm} 

\hyperlink{group__double_ga5c560bea8139857be91339582ba830ef_ga5c560bea8139857be91339582ba830ef}{P\+L\+A\+S\+M\+A\+\_\+dgemm} 

\hyperlink{group__float_gace4e6452ba3ffb8cef11be1987091382_gace4e6452ba3ffb8cef11be1987091382}{P\+L\+A\+S\+M\+A\+\_\+sgemm} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga06922daf59255d12c1fc228cecd6aaa0_ga06922daf59255d12c1fc228cecd6aaa0}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgeqp3@{P\+L\+A\+S\+M\+A\+\_\+sgeqp3}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgeqp3@{P\+L\+A\+S\+M\+A\+\_\+sgeqp3}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgeqp3}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgeqp3 (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int $\ast$}]{jpvt, }
\item[{float $\ast$}]{tau, }
\item[{float $\ast$}]{work, }
\item[{float $\ast$}]{rwork}
\end{DoxyParamCaption}
)}\label{group__float_ga06922daf59255d12c1fc228cecd6aaa0_ga06922daf59255d12c1fc228cecd6aaa0}
P\+L\+A\+S\+M\+A\+\_\+sgeqp3 -\/ Computes the Q\+R factorization with column pivoting of a complex M-\/by-\/\+N matrix A\+: A$\ast$\+P = Q$\ast$\+R.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, the elements on and above the diagonal of the array contain the min(\+M,\+N)-\/by-\/\+N upper trapezoidal matrix R (R is upper triangular if M $>$= N); the elements below the diagonal represent the unitary matrix Q as a product of elementary reflectors stored by tiles.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in,out}  & {\em jpvt} & Integer array of dimension N. On exit, if jpvt(j)=k, then the j-\/th column of A$\ast$\+P was the k-\/th column of A. Uses 1-\/based indexing for Fortran compatability.\\
\hline
\mbox{\tt out}  & {\em tau} & On exit, scalars that define Householder reflectors, size n.\\
\hline
\mbox{\tt out}  & {\em work} & Workspace of size (n + 1)$\ast$nb.\\
\hline
\mbox{\tt out}  & {\em rwork} & Workspace of size 2$\ast$n.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga5947ee719bb85214b3347d6c0066f413_ga5947ee719bb85214b3347d6c0066f413}{P\+L\+A\+S\+M\+A\+\_\+sgeqp3\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gad7f0d63f6ee3f7398131d0d8c9ee5eb4_gad7f0d63f6ee3f7398131d0d8c9ee5eb4}{P\+L\+A\+S\+M\+A\+\_\+sgeqp3\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga1702f0732bb5432db6f3eb07200b1c1c_ga1702f0732bb5432db6f3eb07200b1c1c}{P\+L\+A\+S\+M\+A\+\_\+cgeqp3} 

\hyperlink{group__double_ga9d11b150328fa64daa7c9f798baf3ea1_ga9d11b150328fa64daa7c9f798baf3ea1}{P\+L\+A\+S\+M\+A\+\_\+dgeqp3} 

\hyperlink{group__float_ga06922daf59255d12c1fc228cecd6aaa0_ga06922daf59255d12c1fc228cecd6aaa0}{P\+L\+A\+S\+M\+A\+\_\+sgeqp3} 
\end{DoxySeeAlso}
\hypertarget{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgeqrf@{P\+L\+A\+S\+M\+A\+\_\+sgeqrf}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgeqrf@{P\+L\+A\+S\+M\+A\+\_\+sgeqrf}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgeqrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgeqrf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T}
\end{DoxyParamCaption}
)}\label{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}
P\+L\+A\+S\+M\+A\+\_\+sgeqrf -\/ Computes the tile Q\+R factorization of a complex M-\/by-\/\+N matrix A\+: A = Q $\ast$ R.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, the elements on and above the diagonal of the array contain the min(\+M,\+N)-\/by-\/\+N upper trapezoidal matrix R (R is upper triangular if M $>$= N); the elements below the diagonal represent the unitary matrix Q as a product of elementary reflectors stored by tiles.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em desc\+T} & On exit, auxiliary factorization data, required by P\+L\+A\+S\+M\+A\+\_\+sgeqrs to solve the system of equations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga7c5ef5b73dada9d9560e8fbed71971c9_ga7c5ef5b73dada9d9560e8fbed71971c9}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga494b58b8d9bfb2c9c9edb0dcde0ace11_ga494b58b8d9bfb2c9c9edb0dcde0ace11}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gae8490d9c587725716adbb347d85537b2_gae8490d9c587725716adbb347d85537b2}{P\+L\+A\+S\+M\+A\+\_\+cgeqrf} 

\hyperlink{group__double_gaad8136b3520b4bda7261d3f921c8a740_gaad8136b3520b4bda7261d3f921c8a740}{P\+L\+A\+S\+M\+A\+\_\+dgeqrf} 

\hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf} 

\hyperlink{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}{P\+L\+A\+S\+M\+A\+\_\+sgeqrs} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgeqrs@{P\+L\+A\+S\+M\+A\+\_\+sgeqrs}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgeqrs@{P\+L\+A\+S\+M\+A\+\_\+sgeqrs}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgeqrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgeqrs (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}
P\+L\+A\+S\+M\+A\+\_\+sgeqrs -\/ Compute a minimum-\/norm solution min $\vert$$\vert$ A$\ast$\+X -\/ B $\vert$$\vert$ using the Q\+R factorization A = Q$\ast$\+R computed by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of columns of B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & Details of the Q\+R factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf. Remark\+: If out-\/of-\/place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= M.\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the m-\/by-\/nrhs right hand side matrix B. On exit, the n-\/by-\/nrhs solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga9f069cadfcd63ff8013e2e25079830d0_ga9f069cadfcd63ff8013e2e25079830d0}{P\+L\+A\+S\+M\+A\+\_\+sgeqrs\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga481b8b15be614dc287fb42b0f6a71141_ga481b8b15be614dc287fb42b0f6a71141}{P\+L\+A\+S\+M\+A\+\_\+sgeqrs\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga961a4dfc433c5086670b813e5fa53bbf_ga961a4dfc433c5086670b813e5fa53bbf}{P\+L\+A\+S\+M\+A\+\_\+cgeqrs} 

\hyperlink{group__double_gaa133b69ef592ef01466fd93b6ac7689d_gaa133b69ef592ef01466fd93b6ac7689d}{P\+L\+A\+S\+M\+A\+\_\+dgeqrs} 

\hyperlink{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}{P\+L\+A\+S\+M\+A\+\_\+sgeqrs} 

\hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_gad5f1778952268ef575d41e6bfcc7c7b4_gad5f1778952268ef575d41e6bfcc7c7b4}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgesdd@{P\+L\+A\+S\+M\+A\+\_\+sgesdd}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgesdd@{P\+L\+A\+S\+M\+A\+\_\+sgesdd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgesdd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgesdd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobu, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobvt, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{S, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{U, }
\item[{int}]{L\+D\+U, }
\item[{float $\ast$}]{V\+T, }
\item[{int}]{L\+D\+V\+T}
\end{DoxyParamCaption}
)}\label{group__float_gad5f1778952268ef575d41e6bfcc7c7b4_gad5f1778952268ef575d41e6bfcc7c7b4}
P\+L\+A\+S\+M\+A\+\_\+sgesdd -\/ computes the singular value decomposition (S\+V\+D) of a complex M-\/by-\/\+N matrix A, optionally computing the left and/or right singular vectors, by using divide-\/and-\/conquer method. The S\+V\+D is written \begin{DoxyVerb} A = U * SIGMA * ugate-transpose(V)
\end{DoxyVerb}


where S\+I\+G\+M\+A is an M-\/by-\/\+N matrix which is zero except for its min(m,n) diagonal elements, U is an M-\/by-\/\+M unitary matrix, and V is an N-\/by-\/\+N unitary matrix. The diagonal elements of S\+I\+G\+M\+A are the singular values of A; they are real and non-\/negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns V\+T = V$\ast$$\ast$\+T, not V.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-\/\+M\+P, Cray Y-\/\+M\+P, Cray C-\/90, or Cray-\/2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

N\+O\+T\+E that the input parameter of this function differ from the L\+A\+P\+A\+C\+K S\+G\+E\+S\+D\+D. We have jobu and jobvt instead of only jobz first to be consistent with S\+G\+E\+S\+V\+D and second to allow a computation of only U or V\+T.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobu} & Specifies options for computing all or part of the matrix U. Intended usage\+: = Plasma\+Vec = \textquotesingle{}A\textquotesingle{}(lapack)\+: all M columns of U are returned in array U; = Plasma\+No\+Vec = \textquotesingle{}N\textquotesingle{}\+: no columns of U (no left singular vectors) are computed. = Plasma\+S\+Vec = \textquotesingle{}S\textquotesingle{}\+: the first min(m,n) columns of U (the left singular vectors) are returned in the array U; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T = Plasma\+O\+Vec = \textquotesingle{}O\textquotesingle{}\+: the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T\\
\hline
\mbox{\tt in}  & {\em jobvt} & Specifies options for computing all or part of the matrix V$\ast$$\ast$\+T. Intended usage\+: = Plasma\+Vec = \textquotesingle{}A\textquotesingle{}(lapack)\+: all N rows of V$\ast$$\ast$\+T are returned in the array V\+T; = Plasma\+No\+Vec = \textquotesingle{}N\textquotesingle{}\+: no rows of V$\ast$$\ast$\+T (no right singular vectors) are computed. = Plasma\+S\+Vec = \textquotesingle{}S\textquotesingle{}\+: the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors) are returned in the array V\+T; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T = Plasma\+O\+Vec = \textquotesingle{}O\textquotesingle{}\+: the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors) are overwritten on the array A; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T\\
\hline
\end{DoxyParams}
Note\+: jobu and jobvt cannot both be Plasma\+O\+Vec.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, if J\+O\+B\+U = \textquotesingle{}O\textquotesingle{}, A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\+O\+B\+V\+T = \textquotesingle{}O\textquotesingle{}, A is overwritten with the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors, stored rowwise); if J\+O\+B\+U .ne. \textquotesingle{}O\textquotesingle{} and J\+O\+B\+V\+T .ne. \textquotesingle{}O\textquotesingle{}, the contents of A are destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em S} & The real singular values of A, sorted so that S(i) $>$= S(i+1).\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+sgesdd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em U} & (L\+D\+U,M) if J\+O\+B\+U = \textquotesingle{}A\textquotesingle{} or (L\+D\+U,min(\+M,\+N)) if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{}. If J\+O\+B\+U = \textquotesingle{}A\textquotesingle{}, U contains the M-\/by-\/\+M unitary matrix U; if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{}, U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\+O\+B\+U = \textquotesingle{}N\textquotesingle{} or \textquotesingle{}O\textquotesingle{}, U is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+U} & The leading dimension of the array U. L\+D\+U $>$= 1; if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{} or \textquotesingle{}A\textquotesingle{}, L\+D\+U $>$= M.\\
\hline
\mbox{\tt out}  & {\em V\+T} & If J\+O\+B\+V\+T = \textquotesingle{}A\textquotesingle{}, V\+T contains the N-\/by-\/\+N unitary matrix V$\ast$$\ast$\+T; if J\+O\+B\+V\+T = \textquotesingle{}S\textquotesingle{}, V\+T contains the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors, stored rowwise); if J\+O\+B\+V\+T = \textquotesingle{}N\textquotesingle{} or \textquotesingle{}O\textquotesingle{}, V\+T is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+V\+T} & The leading dimension of the array V\+T. L\+D\+V\+T $>$= 1; if J\+O\+B\+V\+T = \textquotesingle{}A\textquotesingle{}, L\+D\+V\+T $>$= N; if J\+O\+B\+V\+T = \textquotesingle{}S\textquotesingle{}, L\+D\+V\+T $>$= min(\+M,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga7468a0b96b97ae0eef8975c7e9e05a68_ga7468a0b96b97ae0eef8975c7e9e05a68}{P\+L\+A\+S\+M\+A\+\_\+sgesdd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga31cc8a5cc51ffb0ad6f46c39711392b3_ga31cc8a5cc51ffb0ad6f46c39711392b3}{P\+L\+A\+S\+M\+A\+\_\+sgesdd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gafee4a25fd8dad584ec50f1718a319a8b_gafee4a25fd8dad584ec50f1718a319a8b}{P\+L\+A\+S\+M\+A\+\_\+cgesdd} 

\hyperlink{group__double_ga90d8245b7c9b7124c35c485f0e4f63b7_ga90d8245b7c9b7124c35c485f0e4f63b7}{P\+L\+A\+S\+M\+A\+\_\+dgesdd} 

\hyperlink{group__float_gad5f1778952268ef575d41e6bfcc7c7b4_gad5f1778952268ef575d41e6bfcc7c7b4}{P\+L\+A\+S\+M\+A\+\_\+sgesdd} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga39018420f926f77ef11c50c82f66da77_ga39018420f926f77ef11c50c82f66da77}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgesv@{P\+L\+A\+S\+M\+A\+\_\+sgesv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgesv@{P\+L\+A\+S\+M\+A\+\_\+sgesv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgesv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgesv (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int $\ast$}]{I\+P\+I\+V, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga39018420f926f77ef11c50c82f66da77_ga39018420f926f77ef11c50c82f66da77}
P\+L\+A\+S\+M\+A\+\_\+sgesv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\+N matrix and X and B are N-\/by-\/\+N\+R\+H\+S matrices. The tile L\+U decomposition with partial tile pivoting and row interchanges is used to factor A. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\+e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the N-\/by-\/\+N coefficient matrix A. On exit, the tile L and U factors from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em I\+P\+I\+V} & On exit, the pivot indices that define the permutations.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S matrix of right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaff4ad087d2efc588d2ca4152c4edd398_gaff4ad087d2efc588d2ca4152c4edd398}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga1a8bb4c4851dd9c4221070eb655286df_ga1a8bb4c4851dd9c4221070eb655286df}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga5ec3217862ee4b820b9cd9d4b343bfae_ga5ec3217862ee4b820b9cd9d4b343bfae}{P\+L\+A\+S\+M\+A\+\_\+cgesv} 

\hyperlink{group__double_gae380e95b53e07b9b1261aec244191c0f_gae380e95b53e07b9b1261aec244191c0f}{P\+L\+A\+S\+M\+A\+\_\+dgesv} 

\hyperlink{group__float_ga39018420f926f77ef11c50c82f66da77_ga39018420f926f77ef11c50c82f66da77}{P\+L\+A\+S\+M\+A\+\_\+sgesv} 
\end{DoxySeeAlso}
\hypertarget{group__float_gab9dab6c3f22b6cf8dad0fa2f1b563988_gab9dab6c3f22b6cf8dad0fa2f1b563988}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+L, }
\item[{int $\ast$}]{I\+P\+I\+V, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_gab9dab6c3f22b6cf8dad0fa2f1b563988_gab9dab6c3f22b6cf8dad0fa2f1b563988}
P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\+N matrix and X and B are N-\/by-\/\+N\+R\+H\+S matrices. The tile L\+U decomposition with partial tile pivoting and row interchanges is used to factor A. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\+e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the N-\/by-\/\+N coefficient matrix A. On exit, the tile L and U factors from the factorization (not equivalent to L\+A\+P\+A\+C\+K).\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em desc\+L} & On exit, auxiliary factorization data, related to the tile L factor, necessary to solve the system of equations.\\
\hline
\mbox{\tt out}  & {\em I\+P\+I\+V} & On exit, the pivot indices that define the permutations (not equivalent to L\+A\+P\+A\+C\+K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S matrix of right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gae9d3d027fb34165de038eaa5d0bcebec_gae9d3d027fb34165de038eaa5d0bcebec}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga2d26ce9c7cee9f0eb59542bbc88c3ede_ga2d26ce9c7cee9f0eb59542bbc88c3ede}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gade54f0cdad2648b241e2701e0e07cbce_gade54f0cdad2648b241e2701e0e07cbce}{P\+L\+A\+S\+M\+A\+\_\+cgesv\+\_\+incpiv} 

\hyperlink{group__double_gaaf143240840f5315cf672d66dead1111_gaaf143240840f5315cf672d66dead1111}{P\+L\+A\+S\+M\+A\+\_\+dgesv\+\_\+incpiv} 

\hyperlink{group__float_gab9dab6c3f22b6cf8dad0fa2f1b563988_gab9dab6c3f22b6cf8dad0fa2f1b563988}{P\+L\+A\+S\+M\+A\+\_\+sgesv\+\_\+incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_gabaf1acf98c5bbd242f4e603c2bbfffb1_gabaf1acf98c5bbd242f4e603c2bbfffb1}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgesvd@{P\+L\+A\+S\+M\+A\+\_\+sgesvd}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgesvd@{P\+L\+A\+S\+M\+A\+\_\+sgesvd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgesvd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgesvd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobu, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobvt, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{S, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{U, }
\item[{int}]{L\+D\+U, }
\item[{float $\ast$}]{V\+T, }
\item[{int}]{L\+D\+V\+T}
\end{DoxyParamCaption}
)}\label{group__float_gabaf1acf98c5bbd242f4e603c2bbfffb1_gabaf1acf98c5bbd242f4e603c2bbfffb1}
P\+L\+A\+S\+M\+A\+\_\+sgesvd -\/ computes the singular value decomposition (S\+V\+D) of a complex M-\/by-\/\+N matrix A, optionally computing the left and/or right singular vectors. The S\+V\+D is written \begin{DoxyVerb} A = U * SIGMA * transpose(V)
\end{DoxyVerb}


where S\+I\+G\+M\+A is an M-\/by-\/\+N matrix which is zero except for its min(m,n) diagonal elements, U is an M-\/by-\/\+M orthogonal matrix, and V is an N-\/by-\/\+N orthogonal matrix. The diagonal elements of S\+I\+G\+M\+A are the singular values of A; they are real and non-\/negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns V$\ast$$\ast$\+T, not V.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobu} & Specifies options for computing all or part of the matrix U. Intended usage\+: = Plasma\+Vec = \textquotesingle{}A\textquotesingle{}(lapack)\+: all M columns of U are returned in array U; = Plasma\+No\+Vec = \textquotesingle{}N\textquotesingle{}\+: no columns of U (no left singular vectors) are computed. = Plasma\+S\+Vec = \textquotesingle{}S\textquotesingle{}\+: the first min(m,n) columns of U (the left singular vectors) are returned in the array U; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T = Plasma\+O\+Vec = \textquotesingle{}O\textquotesingle{}\+: the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T\\
\hline
\mbox{\tt in}  & {\em jobvt} & Specifies options for computing all or part of the matrix V$\ast$$\ast$\+T. Intended usage\+: = Plasma\+Vec = \textquotesingle{}A\textquotesingle{}(lapack)\+: all N rows of V$\ast$$\ast$\+T are returned in the array V\+T; = Plasma\+No\+Vec = \textquotesingle{}N\textquotesingle{}\+: no rows of V$\ast$$\ast$\+T (no right singular vectors) are computed. = Plasma\+S\+Vec = \textquotesingle{}S\textquotesingle{}\+: the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors) are returned in the array V\+T; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T = Plasma\+O\+Vec = \textquotesingle{}O\textquotesingle{}\+: the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors) are overwritten on the array A; N\+O\+T S\+U\+P\+P\+O\+R\+T\+T\+E\+D Y\+E\+T\\
\hline
\end{DoxyParams}
Note\+: jobu and jobvt cannot both be Plasma\+O\+Vec.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix A. On exit, if J\+O\+B\+U = \textquotesingle{}O\textquotesingle{}, A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\+O\+B\+V\+T = \textquotesingle{}O\textquotesingle{}, A is overwritten with the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors, stored rowwise); if J\+O\+B\+U .ne. \textquotesingle{}O\textquotesingle{} and J\+O\+B\+V\+T .ne. \textquotesingle{}O\textquotesingle{}, the contents of A are destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em S} & The real singular values of A, sorted so that S(i) $>$= S(i+1).\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+sgesvd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em U} & (L\+D\+U,M) if J\+O\+B\+U = \textquotesingle{}A\textquotesingle{} or (L\+D\+U,min(\+M,\+N)) if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{}. If J\+O\+B\+U = \textquotesingle{}A\textquotesingle{}, U contains the M-\/by-\/\+M unitary matrix U; if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{}, U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\+O\+B\+U = \textquotesingle{}N\textquotesingle{} or \textquotesingle{}O\textquotesingle{}, U is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+U} & The leading dimension of the array U. L\+D\+U $>$= 1; if J\+O\+B\+U = \textquotesingle{}S\textquotesingle{} or \textquotesingle{}A\textquotesingle{}, L\+D\+U $>$= M.\\
\hline
\mbox{\tt out}  & {\em V\+T} & If J\+O\+B\+V\+T = \textquotesingle{}A\textquotesingle{}, V\+T contains the N-\/by-\/\+N unitary matrix V$\ast$$\ast$\+T; if J\+O\+B\+V\+T = \textquotesingle{}S\textquotesingle{}, V\+T contains the first min(m,n) rows of V$\ast$$\ast$\+T (the right singular vectors, stored rowwise); if J\+O\+B\+V\+T = \textquotesingle{}N\textquotesingle{} or \textquotesingle{}O\textquotesingle{}, V\+T is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+V\+T} & The leading dimension of the array V\+T. L\+D\+V\+T $>$= 1; if J\+O\+B\+V\+T = \textquotesingle{}A\textquotesingle{}, L\+D\+V\+T $>$= N; if J\+O\+B\+V\+T = \textquotesingle{}S\textquotesingle{}, L\+D\+V\+T $>$= min(\+M,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gad636cb478efcce3495f47a9a2e9fbc76_gad636cb478efcce3495f47a9a2e9fbc76}{P\+L\+A\+S\+M\+A\+\_\+sgesvd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaf68d5ffa5f54c50e76e4ce08b1bbe413_gaf68d5ffa5f54c50e76e4ce08b1bbe413}{P\+L\+A\+S\+M\+A\+\_\+sgesvd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gaf3b4470de63deb5f9f8e52247d0ec951_gaf3b4470de63deb5f9f8e52247d0ec951}{P\+L\+A\+S\+M\+A\+\_\+cgesvd} 

\hyperlink{group__double_ga02d390fe38b9b983a604f2a8557abafa_ga02d390fe38b9b983a604f2a8557abafa}{P\+L\+A\+S\+M\+A\+\_\+dgesvd} 

\hyperlink{group__float_gabaf1acf98c5bbd242f4e603c2bbfffb1_gabaf1acf98c5bbd242f4e603c2bbfffb1}{P\+L\+A\+S\+M\+A\+\_\+sgesvd} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga51861b9bdc9c8058822c32807a78fca7_ga51861b9bdc9c8058822c32807a78fca7}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetmi@{P\+L\+A\+S\+M\+A\+\_\+sgetmi}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetmi@{P\+L\+A\+S\+M\+A\+\_\+sgetmi}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetmi}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetmi (
\begin{DoxyParamCaption}
\item[{int}]{m, }
\item[{int}]{n, }
\item[{float $\ast$}]{A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+in, }
\item[{int}]{imb, }
\item[{int}]{inb}
\end{DoxyParamCaption}
)}\label{group__float_ga51861b9bdc9c8058822c32807a78fca7_ga51861b9bdc9c8058822c32807a78fca7}
P\+L\+A\+S\+M\+A\+\_\+sgetmi Implementation of inplace transposition based on the G\+K\+K algorithm by Gustavson, Karlsson, Kagstrom. This algorithm shift some cycles to transpose the matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em m} & Number of rows of matrix A\\
\hline
\mbox{\tt in}  & {\em n} & Number of columns of matrix A\\
\hline
\mbox{\tt in,out}  & {\em A} & Matrix of size L$\ast$m$\ast$n.\\
\hline
\mbox{\tt in}  & {\em f\+\_\+in} & Original layout of the matrix A. Must be part of\+: Plasma\+C\+M\+: if A is stored in Column Major, Plasma\+R\+M\+: if A is stored in Row Major, Plasma\+C\+C\+R\+B\+: if A is stored in Column Column Rectangular Block layout, Plasma\+C\+R\+R\+B\+: if A is stored in Column Row Rectangular Block layout, Plasma\+R\+C\+R\+B\+: if A is stored in Row Column Rectangular Block layout, Plasma\+R\+R\+R\+B\+: if A is stored in Row Row Rectangular Block layout; where the first Column/\+Row stand for the order in which tiles are sorted, and the secon Column/\+Row stand for the layout inside each tile.\\
\hline
\mbox{\tt in}  & {\em imb} & Number of rows of the problem\\
\hline
\mbox{\tt in}  & {\em inb} & Number of columns in the problem\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float_gaa35042844f1c885bc26a5f47293e3d45_gaa35042844f1c885bc26a5f47293e3d45}{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaa35042844f1c885bc26a5f47293e3d45_gaa35042844f1c885bc26a5f47293e3d45}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async@{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async@{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async (
\begin{DoxyParamCaption}
\item[{int}]{m, }
\item[{int}]{n, }
\item[{float $\ast$}]{A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{f\+\_\+in, }
\item[{int}]{mb, }
\item[{int}]{nb, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+sequence} $\ast$}]{sequence, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+request} $\ast$}]{request}
\end{DoxyParamCaption}
)}\label{group__float_gaa35042844f1c885bc26a5f47293e3d45_gaa35042844f1c885bc26a5f47293e3d45}
P\+L\+A\+S\+M\+A\+\_\+sgetmi\+\_\+\+Async Implementation of inplace transposition based on the G\+K\+K algorithm by Gustavson, Karlsson, Kagstrom. This algorithm shift some cycles to transpose the matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em m} & Number of rows of matrix A\\
\hline
\mbox{\tt in}  & {\em n} & Number of columns of matrix A\\
\hline
\mbox{\tt in,out}  & {\em A} & Matrix of size L$\ast$m$\ast$n.\\
\hline
\mbox{\tt in}  & {\em f\+\_\+in} & Original format of the matrix A. Must be part of (Plasma\+C\+M, Plasma\+R\+M, Plasma\+C\+C\+R\+B, Plasma\+C\+R\+R\+B, Plasma\+R\+C\+R\+B, Plasma\+R\+R\+R\+B)\\
\hline
\mbox{\tt in}  & {\em mb} & Number of rows of the problem\\
\hline
\mbox{\tt in}  & {\em nb} & Number of columns in the problem\\
\hline
\mbox{\tt in}  & {\em sequence} & Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).\\
\hline
\mbox{\tt out}  & {\em request} & Identifies this function call (for exception handling purposes).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float_ga51861b9bdc9c8058822c32807a78fca7_ga51861b9bdc9c8058822c32807a78fca7}{P\+L\+A\+S\+M\+A\+\_\+sgetmi} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrf@{P\+L\+A\+S\+M\+A\+\_\+sgetrf}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrf@{P\+L\+A\+S\+M\+A\+\_\+sgetrf}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int $\ast$}]{I\+P\+I\+V}
\end{DoxyParamCaption}
)}\label{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}
P\+L\+A\+S\+M\+A\+\_\+sgetrf -\/ Computes an L\+U factorization of a general M-\/by-\/\+N matrix A using the tile L\+U algorithm with partial tile pivoting with row interchanges.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em I\+P\+I\+V} & The pivot indices that define the permutations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga1a6955304fcecceca1052439c28f3522_ga1a6955304fcecceca1052439c28f3522}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gae899a1ecfe2fcd225ac993fbd1e88eba_gae899a1ecfe2fcd225ac993fbd1e88eba}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga9a372dbe56f1ef00531a284e1bf3a694_ga9a372dbe56f1ef00531a284e1bf3a694}{P\+L\+A\+S\+M\+A\+\_\+cgetrf} 

\hyperlink{group__double_gaa626e37ec710bfb5c98fef7b00511ea8_gaa626e37ec710bfb5c98fef7b00511ea8}{P\+L\+A\+S\+M\+A\+\_\+dgetrf} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+L, }
\item[{int $\ast$}]{I\+P\+I\+V}
\end{DoxyParamCaption}
)}\label{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}
P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv -\/ Computes an L\+U factorization of a general M-\/by-\/\+N matrix A using the tile L\+U algorithm with partial tile pivoting with row interchanges.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em desc\+L} & On exit, auxiliary factorization data, related to the tile L factor, required by P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv to solve the system of equations.\\
\hline
\mbox{\tt out}  & {\em I\+P\+I\+V} & The pivot indices that define the permutations (not equivalent to L\+A\+P\+A\+C\+K).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga94fd97f1f6db26be8f5f230cd34a278f_ga94fd97f1f6db26be8f5f230cd34a278f}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga5efaa488eacff97a946efcbfe2948b28_ga5efaa488eacff97a946efcbfe2948b28}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gaaeca906ffb473a1bc1772671fb4f558f_gaaeca906ffb473a1bc1772671fb4f558f}{P\+L\+A\+S\+M\+A\+\_\+cgetrf\+\_\+incpiv} 

\hyperlink{group__double_gad1a9ffdf2bf95696d94eac58177c3964_gad1a9ffdf2bf95696d94eac58177c3964}{P\+L\+A\+S\+M\+A\+\_\+dgetrf\+\_\+incpiv} 

\hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv} 

\hyperlink{group__float_gae593ed2d7e164acc75c4e6efdca4d95a_gae593ed2d7e164acc75c4e6efdca4d95a}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga1c9ced92c5818ef3a6af88e6545ba1e6_ga1c9ced92c5818ef3a6af88e6545ba1e6}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_ga1c9ced92c5818ef3a6af88e6545ba1e6_ga1c9ced92c5818ef3a6af88e6545ba1e6}
P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv -\/ Computes an L\+U factorization of a general M-\/by-\/\+N matrix A using the tile L\+U algorithm without row pivoting. W\+A\+R\+N\+I\+N\+G\+: Don\textquotesingle{}t use this function if you are not sure your matrix is diagonal dominant.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gac69f83430a75ebaad0d19442761004b6_gac69f83430a75ebaad0d19442761004b6}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga2889753e80c6a0d719b19c77a04e4689_ga2889753e80c6a0d719b19c77a04e4689}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga8a4dcd6c85d88e7af17115cc07ecd72d_ga8a4dcd6c85d88e7af17115cc07ecd72d}{P\+L\+A\+S\+M\+A\+\_\+cgetrf\+\_\+nopiv} 

\hyperlink{group__double_ga8a7ad8ad13ca055f1cece944ffa8185a_ga8a7ad8ad13ca055f1cece944ffa8185a}{P\+L\+A\+S\+M\+A\+\_\+dgetrf\+\_\+nopiv} 

\hyperlink{group__float_ga1c9ced92c5818ef3a6af88e6545ba1e6_ga1c9ced92c5818ef3a6af88e6545ba1e6}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga4a519bbf13b7a335ca2dd079693f9edc_ga4a519bbf13b7a335ca2dd079693f9edc}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int $\ast$}]{I\+P\+I\+V}
\end{DoxyParamCaption}
)}\label{group__float_ga4a519bbf13b7a335ca2dd079693f9edc_ga4a519bbf13b7a335ca2dd079693f9edc}
P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv -\/ Computes an L\+U factorization of a general M-\/by-\/\+N matrix A using the tile L\+U algorithm with tournament pivoting based on L\+U decomposition at each round.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\+N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em I\+P\+I\+V} & The pivot indices that define the permutations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 

\hyperlink{group__float_ga1c9ced92c5818ef3a6af88e6545ba1e6_ga1c9ced92c5818ef3a6af88e6545ba1e6}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+nopiv} 

\hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv} 

\hyperlink{group__float__Tile_gae07b9e0af4e3d12491dfe0a2cc6eef31_gae07b9e0af4e3d12491dfe0a2cc6eef31}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga22dc7cb89a18ee635418e53fb71b4821_ga22dc7cb89a18ee635418e53fb71b4821}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga0e2626958aa6a838bdaebbb164fddb7e_ga0e2626958aa6a838bdaebbb164fddb7e}{P\+L\+A\+S\+M\+A\+\_\+cgetrf\+\_\+tntpiv} 

\hyperlink{group__double_gac5e965a28bb5189491690e9cdfcc2b61_gac5e965a28bb5189491690e9cdfcc2b61}{P\+L\+A\+S\+M\+A\+\_\+dgetrf\+\_\+tntpiv} 

\hyperlink{group__float_ga4a519bbf13b7a335ca2dd079693f9edc_ga4a519bbf13b7a335ca2dd079693f9edc}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+tntpiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_gadb78715cdd99791aa77c2640f1325f8e_gadb78715cdd99791aa77c2640f1325f8e}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetri@{P\+L\+A\+S\+M\+A\+\_\+sgetri}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetri@{P\+L\+A\+S\+M\+A\+\_\+sgetri}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetri}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetri (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int $\ast$}]{I\+P\+I\+V}
\end{DoxyParamCaption}
)}\label{group__float_gadb78715cdd99791aa77c2640f1325f8e_gadb78715cdd99791aa77c2640f1325f8e}
P\+L\+A\+S\+M\+A\+\_\+sgetri -\/ Computes the inverse of a matrix using the L\+U factorization computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf. This method inverts U and then computes inv(\+A) by solving the system inv(\+A)$\ast$\+L = inv(\+U) for inv(\+A).


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor L or U from the factorization A = P$\ast$\+L$\ast$\+U as computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf. On exit, if return value = 0, the inverse of the original matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices that define the permutations as returned by P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the (i,i) element of the factor U is exactly zero; The matrix is singular and its inverse could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga6c9b470cb25b778f3a2328e1a7217868_ga6c9b470cb25b778f3a2328e1a7217868}{P\+L\+A\+S\+M\+A\+\_\+sgetri\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaaa53ab212ba282b26473c329e9137f8c_gaaa53ab212ba282b26473c329e9137f8c}{P\+L\+A\+S\+M\+A\+\_\+sgetri\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gaecd124d0a04fc7a679385fd13018fa02_gaecd124d0a04fc7a679385fd13018fa02}{P\+L\+A\+S\+M\+A\+\_\+cgetri} 

\hyperlink{group__double_gaef9247e762016885c0b31dc28356bab7_gaef9247e762016885c0b31dc28356bab7}{P\+L\+A\+S\+M\+A\+\_\+dgetri} 

\hyperlink{group__float_gadb78715cdd99791aa77c2640f1325f8e_gadb78715cdd99791aa77c2640f1325f8e}{P\+L\+A\+S\+M\+A\+\_\+sgetri} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga655cb742ac1c78e5ce86070f4ce1271b_ga655cb742ac1c78e5ce86070f4ce1271b}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrs@{P\+L\+A\+S\+M\+A\+\_\+sgetrs}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrs@{P\+L\+A\+S\+M\+A\+\_\+sgetrs}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrs (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{const int $\ast$}]{I\+P\+I\+V, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga655cb742ac1c78e5ce86070f4ce1271b_ga655cb742ac1c78e5ce86070f4ce1271b}
P\+L\+A\+S\+M\+A\+\_\+sgetrs -\/ Solves a system of linear equations A $\ast$ X = B, with a general N-\/by-\/\+N matrix A using the tile L\+U factorization computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended to specify the the form of the system of equations\+: = Plasma\+No\+Trans\+: A $\ast$ X = B (No transpose) = Plasma\+Trans\+: A$\ast$$\ast$\+T $\ast$ X = B (Transpose) = Plasma\+Trans\+: A$\ast$$\ast$\+T $\ast$ X = B (Conjugate transpose)\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & The tile factors L and U from the factorization, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf. Remark\+: If out-\/of-\/place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices from P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S matrix of right hand side matrix B. On exit, the solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gadb6246bd33d383f96297ddafdbfc0599_gadb6246bd33d383f96297ddafdbfc0599}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga89f118911b8b996c80ab0ba9c2f7b369_ga89f118911b8b996c80ab0ba9c2f7b369}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga898ea98a3d182865980c7393dfca2c27_ga898ea98a3d182865980c7393dfca2c27}{P\+L\+A\+S\+M\+A\+\_\+cgetrs} 

\hyperlink{group__double_gaff3c22db4affbede58e22311320a2b85_gaff3c22db4affbede58e22311320a2b85}{P\+L\+A\+S\+M\+A\+\_\+dgetrs} 

\hyperlink{group__float_ga655cb742ac1c78e5ce86070f4ce1271b_ga655cb742ac1c78e5ce86070f4ce1271b}{P\+L\+A\+S\+M\+A\+\_\+sgetrs} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_gae593ed2d7e164acc75c4e6efdca4d95a_gae593ed2d7e164acc75c4e6efdca4d95a}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv@{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+L, }
\item[{const int $\ast$}]{I\+P\+I\+V, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_gae593ed2d7e164acc75c4e6efdca4d95a_gae593ed2d7e164acc75c4e6efdca4d95a}
P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv -\/ Solves a system of linear equations A $\ast$ X = B, with a general N-\/by-\/\+N matrix A using the tile L\+U factorization computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended to specify the the form of the system of equations\+: = Plasma\+No\+Trans\+: A $\ast$ X = B (No transpose) = Plasma\+Trans\+: A$\ast$$\ast$\+T $\ast$ X = B (Transpose) = Plasma\+Trans\+: A$\ast$$\ast$\+T $\ast$ X = B (Conjugate transpose) Currently only Plasma\+No\+Trans is supported.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em desc\+L} & Auxiliary factorization data, related to the tile L factor, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv.\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices from P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv (not equivalent to L\+A\+P\+A\+C\+K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S matrix of right hand side matrix B. On exit, the solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaa98543a9a1cd907186e2782b747b24e7_gaa98543a9a1cd907186e2782b747b24e7}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga7689f3c883479e874b034ef9bce467a8_ga7689f3c883479e874b034ef9bce467a8}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga0f056cec00c55830b06c4439d4892165_ga0f056cec00c55830b06c4439d4892165}{P\+L\+A\+S\+M\+A\+\_\+cgetrs\+\_\+incpiv} 

\hyperlink{group__double_ga39d27f0353921e5b63e0fdc9cca4b19c_ga39d27f0353921e5b63e0fdc9cca4b19c}{P\+L\+A\+S\+M\+A\+\_\+dgetrs\+\_\+incpiv} 

\hyperlink{group__float_gae593ed2d7e164acc75c4e6efdca4d95a_gae593ed2d7e164acc75c4e6efdca4d95a}{P\+L\+A\+S\+M\+A\+\_\+sgetrs\+\_\+incpiv} 

\hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga2ae5e8cc7cf6222bf521a6decd6c27a1_ga2ae5e8cc7cf6222bf521a6decd6c27a1}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slacpy@{P\+L\+A\+S\+M\+A\+\_\+slacpy}}
\index{P\+L\+A\+S\+M\+A\+\_\+slacpy@{P\+L\+A\+S\+M\+A\+\_\+slacpy}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slacpy}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slacpy (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga2ae5e8cc7cf6222bf521a6decd6c27a1_ga2ae5e8cc7cf6222bf521a6decd6c27a1}
P\+L\+A\+S\+M\+A\+\_\+slacpy copies all or part of a two-\/dimensional matrix A to another matrix B


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the part of the matrix A to be copied to B. = Plasma\+Upper\+Lower\+: All the matrix A = Plasma\+Upper\+: Upper triangular part = Plasma\+Lower\+: Lower triangular part\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\+N matrix A. If uplo = Plasma\+Upper, only the upper trapezium is accessed; if U\+P\+L\+O = Plasma\+Lower, only the lower trapezium is accessed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt out}  & {\em B} & The M-\/by-\/\+N matrix B. On exit, B = A in the locations specified by U\+P\+L\+O.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga193e5c454b84586721c37715e256e031_ga193e5c454b84586721c37715e256e031}{P\+L\+A\+S\+M\+A\+\_\+slacpy\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gacb8f83fe97e9c2528882d6047fb17bc0_gacb8f83fe97e9c2528882d6047fb17bc0}{P\+L\+A\+S\+M\+A\+\_\+slacpy\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga898cba57b9144416a37de9c72386c58a_ga898cba57b9144416a37de9c72386c58a}{P\+L\+A\+S\+M\+A\+\_\+clacpy} 

\hyperlink{group__double_gaa1c69f5b82fa24bd925055b4e0595dab_gaa1c69f5b82fa24bd925055b4e0595dab}{P\+L\+A\+S\+M\+A\+\_\+dlacpy} 

\hyperlink{group__float_ga2ae5e8cc7cf6222bf521a6decd6c27a1_ga2ae5e8cc7cf6222bf521a6decd6c27a1}{P\+L\+A\+S\+M\+A\+\_\+slacpy} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaf12ff85306bc548593674ce694d5e5be_gaf12ff85306bc548593674ce694d5e5be}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slange@{P\+L\+A\+S\+M\+A\+\_\+slange}}
\index{P\+L\+A\+S\+M\+A\+\_\+slange@{P\+L\+A\+S\+M\+A\+\_\+slange}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slange}]{\setlength{\rightskip}{0pt plus 5cm}float P\+L\+A\+S\+M\+A\+\_\+slange (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{norm, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaf12ff85306bc548593674ce694d5e5be_gaf12ff85306bc548593674ce694d5e5be}
P\+L\+A\+S\+M\+A\+\_\+slange returns the value

slange = ( max(abs(\+A(i,j))), N\+O\+R\+M = Plasma\+Max\+Norm ( ( norm1(\+A), N\+O\+R\+M = Plasma\+One\+Norm ( ( norm\+I(\+A), N\+O\+R\+M = Plasma\+Inf\+Norm ( ( norm\+F(\+A), N\+O\+R\+M = Plasma\+Frobenius\+Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\+I denotes the infinity norm of a matrix (maximum row sum) and norm\+F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(\+A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\+Max\+Norm\+: Max norm = Plasma\+One\+Norm\+: One norm = Plasma\+Inf\+Norm\+: Infinity norm = Plasma\+Frobenius\+Norm\+: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0. When M = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\+N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga61ffd2b03e42781889b76ea9809984dc_ga61ffd2b03e42781889b76ea9809984dc}{P\+L\+A\+S\+M\+A\+\_\+slange\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaba19b4320b156b021b3f7cca09e5f9bd_gaba19b4320b156b021b3f7cca09e5f9bd}{P\+L\+A\+S\+M\+A\+\_\+slange\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gaaab2b12f7ba721c391c670feb35d8def_gaaab2b12f7ba721c391c670feb35d8def}{P\+L\+A\+S\+M\+A\+\_\+clange} 

\hyperlink{group__double_ga51325eef4ca9e4ccd314358ec47535ec_ga51325eef4ca9e4ccd314358ec47535ec}{P\+L\+A\+S\+M\+A\+\_\+dlange} 

\hyperlink{group__float_gaf12ff85306bc548593674ce694d5e5be_gaf12ff85306bc548593674ce694d5e5be}{P\+L\+A\+S\+M\+A\+\_\+slange} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaad7d8cac5c5334f8cc144f36050bbdc3_gaad7d8cac5c5334f8cc144f36050bbdc3}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slansy@{P\+L\+A\+S\+M\+A\+\_\+slansy}}
\index{P\+L\+A\+S\+M\+A\+\_\+slansy@{P\+L\+A\+S\+M\+A\+\_\+slansy}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slansy}]{\setlength{\rightskip}{0pt plus 5cm}float P\+L\+A\+S\+M\+A\+\_\+slansy (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{norm, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaad7d8cac5c5334f8cc144f36050bbdc3_gaad7d8cac5c5334f8cc144f36050bbdc3}
P\+L\+A\+S\+M\+A\+\_\+slansy returns the value

slansy = ( max(abs(\+A(i,j))), N\+O\+R\+M = Plasma\+Max\+Norm ( ( norm1(\+A), N\+O\+R\+M = Plasma\+One\+Norm ( ( norm\+I(\+A), N\+O\+R\+M = Plasma\+Inf\+Norm ( ( norm\+F(\+A), N\+O\+R\+M = Plasma\+Frobenius\+Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\+I denotes the infinity norm of a matrix (maximum row sum) and norm\+F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(\+A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\+Max\+Norm\+: Max norm = Plasma\+One\+Norm\+: One norm = Plasma\+Inf\+Norm\+: Infinity norm = Plasma\+Frobenius\+Norm\+: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns/rows of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\+N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga322b3d40025bb05fcf66cf49ad0fb852_ga322b3d40025bb05fcf66cf49ad0fb852}{P\+L\+A\+S\+M\+A\+\_\+slansy\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga86b3d7267a86e5a2389a5aab0e1d96f2_ga86b3d7267a86e5a2389a5aab0e1d96f2}{P\+L\+A\+S\+M\+A\+\_\+slansy\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gafb115b9c58b142623cd960afcd17fa77_gafb115b9c58b142623cd960afcd17fa77}{P\+L\+A\+S\+M\+A\+\_\+clansy} 

\hyperlink{group__double_ga7d2422fb6092b7ad92fa0121d5c2d792_ga7d2422fb6092b7ad92fa0121d5c2d792}{P\+L\+A\+S\+M\+A\+\_\+dlansy} 

\hyperlink{group__float_gaad7d8cac5c5334f8cc144f36050bbdc3_gaad7d8cac5c5334f8cc144f36050bbdc3}{P\+L\+A\+S\+M\+A\+\_\+slansy} 
\end{DoxySeeAlso}
\hypertarget{group__float_gac89a3f7eb1600d358791d38d2e662cb1_gac89a3f7eb1600d358791d38d2e662cb1}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slantr@{P\+L\+A\+S\+M\+A\+\_\+slantr}}
\index{P\+L\+A\+S\+M\+A\+\_\+slantr@{P\+L\+A\+S\+M\+A\+\_\+slantr}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slantr}]{\setlength{\rightskip}{0pt plus 5cm}float P\+L\+A\+S\+M\+A\+\_\+slantr (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{norm, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{diag, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gac89a3f7eb1600d358791d38d2e662cb1_gac89a3f7eb1600d358791d38d2e662cb1}
P\+L\+A\+S\+M\+A\+\_\+slantr returns the value

slantr = ( max(abs(\+A(i,j))), N\+O\+R\+M = Plasma\+Max\+Norm ( ( norm1(\+A), N\+O\+R\+M = Plasma\+One\+Norm ( ( norm\+I(\+A), N\+O\+R\+M = Plasma\+Inf\+Norm ( ( norm\+F(\+A), N\+O\+R\+M = Plasma\+Frobenius\+Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\+I denotes the infinity norm of a matrix (maximum row sum) and norm\+F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(\+A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\+Max\+Norm\+: Max norm = Plasma\+One\+Norm\+: One norm = Plasma\+Inf\+Norm\+: Infinity norm = Plasma\+Frobenius\+Norm\+: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\+: = Plasma\+Non\+Unit\+: A is non unit; = Plasma\+Unit\+: A us unit.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0. When M = 0, the returned value is set to zero. If uplo == Plasma\+Upper, M $<$= N.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero. If uplo == Plasma\+Lower, N $<$= M.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\+N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga38d0034b144f319eff737318000185e7_ga38d0034b144f319eff737318000185e7}{P\+L\+A\+S\+M\+A\+\_\+slantr\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga7324fd090f464276de6c8e4aee11d4bb_ga7324fd090f464276de6c8e4aee11d4bb}{P\+L\+A\+S\+M\+A\+\_\+slantr\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gacec6cdd47e1d81482eecda3b20442572_gacec6cdd47e1d81482eecda3b20442572}{P\+L\+A\+S\+M\+A\+\_\+clantr} 

\hyperlink{group__double_gaaf76c1c67ebfa8c5c07b63d63c6b3522_gaaf76c1c67ebfa8c5c07b63d63c6b3522}{P\+L\+A\+S\+M\+A\+\_\+dlantr} 

\hyperlink{group__float_gac89a3f7eb1600d358791d38d2e662cb1_gac89a3f7eb1600d358791d38d2e662cb1}{P\+L\+A\+S\+M\+A\+\_\+slantr} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile@{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile}}
\index{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile@{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile (
\begin{DoxyParamCaption}
\item[{float $\ast$}]{Af77, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{A}
\end{DoxyParamCaption}
)}\label{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}
P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile -\/ Conversion from L\+A\+P\+A\+C\+K layout to tile layout. It automatically infers the layout translation mode base on the values of Af77 and A-\/$>$mat pointers. If (A-\/$>$mat == Af77 $\vert$$\vert$ A-\/$>$mat == N\+U\+L\+L $\vert$$\vert$ Af77 == N\+U\+L\+L), P\+L\+A\+S\+M\+A\+\_\+\+T\+R\+A\+N\+S\+L\+A\+T\+I\+O\+N\+\_\+\+M\+O\+D\+E is set to P\+L\+A\+S\+M\+A\+\_\+\+I\+N\+P\+L\+A\+C\+E to do inplace layout translation of the matrix. If (A-\/$>$mat != Af77 \&\& A-\/$>$mat != N\+U\+L\+L \&\& Af77 != N\+U\+L\+L), P\+L\+A\+S\+M\+A\+\_\+\+T\+R\+A\+N\+S\+L\+A\+T\+I\+O\+N\+\_\+\+M\+O\+D\+E is set to P\+L\+A\+S\+M\+A\+\_\+\+O\+U\+T\+O\+F\+P\+L\+A\+C\+E to do out of place layout translation of the matrix. Both A-\/$>$mat and Af77 have to be allocated to store the full matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em Af77} & L\+A\+P\+A\+C\+K matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the matrix Af77.\\
\hline
\mbox{\tt in,out}  & {\em A} & Descriptor of the P\+L\+A\+S\+M\+A matrix in tile layout.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile__Async_ga969824bfa635dd2db87ca01ee3a15d00_ga969824bfa635dd2db87ca01ee3a15d00}{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack} 

\hyperlink{group__PLASMA__Complex32__t_ga44c99c1388a7830a6efbc4fc1ab328f3_ga44c99c1388a7830a6efbc4fc1ab328f3}{P\+L\+A\+S\+M\+A\+\_\+c\+Lapack\+\_\+to\+\_\+\+Tile} 

\hyperlink{group__double_ga36e9254b8f24778e1aed6bcee1165450_ga36e9254b8f24778e1aed6bcee1165450}{P\+L\+A\+S\+M\+A\+\_\+d\+Lapack\+\_\+to\+\_\+\+Tile} 

\hyperlink{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga70bbb11d008076ce34d89399a31d5ca2_ga70bbb11d008076ce34d89399a31d5ca2}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slascal@{P\+L\+A\+S\+M\+A\+\_\+slascal}}
\index{P\+L\+A\+S\+M\+A\+\_\+slascal@{P\+L\+A\+S\+M\+A\+\_\+slascal}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slascal}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slascal (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_ga70bbb11d008076ce34d89399a31d5ca2_ga70bbb11d008076ce34d89399a31d5ca2}
P\+L\+A\+S\+M\+A\+\_\+slascal -\/ Scales a matrix by the scalar alpha as in Sca\+L\+A\+P\+A\+C\+K pslascal().

\[ A = \alpha A \],

alpha is a scalar, and A a general, upper or lower trapezoidal matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the shape of A\+: = Plasma\+Upper\+Lower\+: A is a general matrix. = Plasma\+Upper\+: A is an upper trapezoidal matrix. = Plasma\+Lower\+: A is a lower trapezoidal matrix.\\
\hline
\mbox{\tt in}  & {\em M} & M specifies the number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha\\
\hline
\mbox{\tt in,out}  & {\em A} & A is a L\+D\+A-\/by-\/\+N matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gade4d5b02320ac7c43db295331f9a59d5_gade4d5b02320ac7c43db295331f9a59d5}{P\+L\+A\+S\+M\+A\+\_\+slascal\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga6a4e47bc770be8ab47852749032b39d0_ga6a4e47bc770be8ab47852749032b39d0}{P\+L\+A\+S\+M\+A\+\_\+clascal} 

\hyperlink{group__double_ga856971154c38103f1f9b57a3cab19734_ga856971154c38103f1f9b57a3cab19734}{P\+L\+A\+S\+M\+A\+\_\+dlascal} 

\hyperlink{group__float_ga70bbb11d008076ce34d89399a31d5ca2_ga70bbb11d008076ce34d89399a31d5ca2}{P\+L\+A\+S\+M\+A\+\_\+slascal} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slaset@{P\+L\+A\+S\+M\+A\+\_\+slaset}}
\index{P\+L\+A\+S\+M\+A\+\_\+slaset@{P\+L\+A\+S\+M\+A\+\_\+slaset}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slaset}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slaset (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float}]{alpha, }
\item[{float}]{beta, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}
P\+L\+A\+S\+M\+A\+\_\+slaset sets all or part of a two-\/dimensional matrix A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the part of the matrix A to be set. = Plasma\+Upper\+Lower\+: All the matrix A = Plasma\+Upper\+: Upper triangular part is set. The lower triangle is unchanged. = Plasma\+Lower\+: Lower triangular part is set. The upper triangle is unchange.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & All the offdiagonal array elements are set to alpha.\\
\hline
\mbox{\tt in}  & {\em beta} & All the diagonal array elements are set to beta.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the m by n matrix A. On exit, A(i,j) = A\+L\+P\+H\+A, 1 $<$= i $<$= m, 1 $<$= j $<$= n, i.\+ne.\+j; A(i,i) = B\+E\+T\+A, 1 $<$= i $<$= min(m,n)\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga828b9b130d38b4b3084650f7ac806cde_ga828b9b130d38b4b3084650f7ac806cde}{P\+L\+A\+S\+M\+A\+\_\+slaset\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gac9ef7c897ceb63da77cd2491c202f6f8_gac9ef7c897ceb63da77cd2491c202f6f8}{P\+L\+A\+S\+M\+A\+\_\+slaset\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gabe5cbe444d3395d525dad261b92295f0_gabe5cbe444d3395d525dad261b92295f0}{P\+L\+A\+S\+M\+A\+\_\+claset} 

\hyperlink{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}{P\+L\+A\+S\+M\+A\+\_\+slaset} 

\hyperlink{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}{P\+L\+A\+S\+M\+A\+\_\+slaset} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaa20663314d5fd0c31c8a8a2fd6efc7e5_gaa20663314d5fd0c31c8a8a2fd6efc7e5}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slaswp@{P\+L\+A\+S\+M\+A\+\_\+slaswp}}
\index{P\+L\+A\+S\+M\+A\+\_\+slaswp@{P\+L\+A\+S\+M\+A\+\_\+slaswp}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slaswp}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slaswp (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int}]{K1, }
\item[{int}]{K2, }
\item[{const int $\ast$}]{I\+P\+I\+V, }
\item[{int}]{I\+N\+C\+X}
\end{DoxyParamCaption}
)}\label{group__float_gaa20663314d5fd0c31c8a8a2fd6efc7e5_gaa20663314d5fd0c31c8a8a2fd6efc7e5}
P\+L\+A\+S\+M\+A\+\_\+slaswp -\/ performs a series of row interchanges on the matrix A. One row interchange is initiated for each of rows K1 through K2 of A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em K1} & The first element of I\+P\+I\+V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em K2} & The last element of I\+P\+I\+V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices from P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\mbox{\tt in}  & {\em I\+N\+C\+X} & The increment between successive values of I\+P\+I\+V. If I\+P\+I\+V is negative, the pivots are applied in reverse order.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gad5b3f7d921625de64163aaffd05ca4ba_gad5b3f7d921625de64163aaffd05ca4ba}{P\+L\+A\+S\+M\+A\+\_\+slaswp\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga35e4c0888d047bfd6b299d0096fe189a_ga35e4c0888d047bfd6b299d0096fe189a}{P\+L\+A\+S\+M\+A\+\_\+slaswp\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga2eefac923b3f9c1aa0233709c38a264d_ga2eefac923b3f9c1aa0233709c38a264d}{P\+L\+A\+S\+M\+A\+\_\+claswp} 

\hyperlink{group__double_ga2f62c99800ab0165fa0fb2c58cb2869a_ga2f62c99800ab0165fa0fb2c58cb2869a}{P\+L\+A\+S\+M\+A\+\_\+dlaswp} 

\hyperlink{group__float_gaa20663314d5fd0c31c8a8a2fd6efc7e5_gaa20663314d5fd0c31c8a8a2fd6efc7e5}{P\+L\+A\+S\+M\+A\+\_\+slaswp} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga044b505b0a887de1be5636328ebe60ab_ga044b505b0a887de1be5636328ebe60ab}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slaswpc@{P\+L\+A\+S\+M\+A\+\_\+slaswpc}}
\index{P\+L\+A\+S\+M\+A\+\_\+slaswpc@{P\+L\+A\+S\+M\+A\+\_\+slaswpc}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slaswpc}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slaswpc (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{int}]{K1, }
\item[{int}]{K2, }
\item[{const int $\ast$}]{I\+P\+I\+V, }
\item[{int}]{I\+N\+C\+X}
\end{DoxyParamCaption}
)}\label{group__float_ga044b505b0a887de1be5636328ebe60ab_ga044b505b0a887de1be5636328ebe60ab}
P\+L\+A\+S\+M\+A\+\_\+slaswpc -\/ performs a series of row interchanges on the matrix A. One row interchange is initiated for each of rows K1 through K2 of A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em K1} & The first element of I\+P\+I\+V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em K2} & The last element of I\+P\+I\+V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices from P\+L\+A\+S\+M\+A\+\_\+sgetrf.\\
\hline
\mbox{\tt in}  & {\em I\+N\+C\+X} & The increment between successive values of I\+P\+I\+V. If I\+P\+I\+V is negative, the pivots are applied in reverse order.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga765f714264c08f2c497aae9d3a989e29_ga765f714264c08f2c497aae9d3a989e29}{P\+L\+A\+S\+M\+A\+\_\+slaswpc\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaa1af4fe7c58a13fa70c1315ecbd72e95_gaa1af4fe7c58a13fa70c1315ecbd72e95}{P\+L\+A\+S\+M\+A\+\_\+slaswpc\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gae22c29ff94608a4de968c347ec67f45b_gae22c29ff94608a4de968c347ec67f45b}{P\+L\+A\+S\+M\+A\+\_\+claswpc} 

\hyperlink{group__double_gaf05cd57bcd5a74823cc4f71d91a299bc_gaf05cd57bcd5a74823cc4f71d91a299bc}{P\+L\+A\+S\+M\+A\+\_\+dlaswpc} 

\hyperlink{group__float_ga044b505b0a887de1be5636328ebe60ab_ga044b505b0a887de1be5636328ebe60ab}{P\+L\+A\+S\+M\+A\+\_\+slaswpc} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\+L\+A\+S\+M\+A\+\_\+sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaafb49f230a9c4dbdc635144f46f680f6_gaafb49f230a9c4dbdc635144f46f680f6}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+slauum@{P\+L\+A\+S\+M\+A\+\_\+slauum}}
\index{P\+L\+A\+S\+M\+A\+\_\+slauum@{P\+L\+A\+S\+M\+A\+\_\+slauum}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+slauum}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+slauum (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaafb49f230a9c4dbdc635144f46f680f6_gaafb49f230a9c4dbdc635144f46f680f6}
P\+L\+A\+S\+M\+A\+\_\+slauum -\/ Computes the product U $\ast$ U\textquotesingle{} or L\textquotesingle{} $\ast$ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.

If U\+P\+L\+O = \textquotesingle{}U\textquotesingle{} or \textquotesingle{}u\textquotesingle{} then the upper triangle of the result is stored, overwriting the factor U in A. If U\+P\+L\+O = \textquotesingle{}L\textquotesingle{} or \textquotesingle{}l\textquotesingle{} then the lower triangle of the result is stored, overwriting the factor L in A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the triangular factor U or L. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor U or L. On exit, if U\+P\+L\+O = \textquotesingle{}U\textquotesingle{}, the upper triangle of A is overwritten with the upper triangle of the product U $\ast$ U\textquotesingle{}; if U\+P\+L\+O = \textquotesingle{}L\textquotesingle{}, the lower triangle of A is overwritten with the lower triangle of the product L\textquotesingle{} $\ast$ L.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga746291d04f29d541feed78901a0350ee_ga746291d04f29d541feed78901a0350ee}{P\+L\+A\+S\+M\+A\+\_\+slauum\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaaa01b3ab2e7be4bec4e0c61aabb4b708_gaaa01b3ab2e7be4bec4e0c61aabb4b708}{P\+L\+A\+S\+M\+A\+\_\+slauum\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga937589f5f8ae6b95a4e81589f5471d3e_ga937589f5f8ae6b95a4e81589f5471d3e}{P\+L\+A\+S\+M\+A\+\_\+clauum} 

\hyperlink{group__double_ga67ff8abfce111a501fb5cec37333756f_ga67ff8abfce111a501fb5cec37333756f}{P\+L\+A\+S\+M\+A\+\_\+dlauum} 

\hyperlink{group__float_gaafb49f230a9c4dbdc635144f46f680f6_gaafb49f230a9c4dbdc635144f46f680f6}{P\+L\+A\+S\+M\+A\+\_\+slauum} 

\hyperlink{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{P\+L\+A\+S\+M\+A\+\_\+spotri} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga2f8b6c06f4346761e024c9fa00427a61_ga2f8b6c06f4346761e024c9fa00427a61}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sorglq@{P\+L\+A\+S\+M\+A\+\_\+sorglq}}
\index{P\+L\+A\+S\+M\+A\+\_\+sorglq@{P\+L\+A\+S\+M\+A\+\_\+sorglq}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sorglq}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sorglq (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga2f8b6c06f4346761e024c9fa00427a61_ga2f8b6c06f4346761e024c9fa00427a61}
P\+L\+A\+S\+M\+A\+\_\+sorglq -\/ Generates an M-\/by-\/\+N matrix Q with orthonormal rows, which is defined as the first M rows of a product of the elementary reflectors returned by P\+L\+A\+S\+M\+A\+\_\+sgelqf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix Q. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix Q. N $>$= M.\\
\hline
\mbox{\tt in}  & {\em K} & The number of rows of elementary tile reflectors whose product defines the matrix Q. M $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the L\+Q factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, the M-\/by-\/\+N matrix Q.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & $<$0 if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gae62c41d7980dbddbd3b0554ac186f4eb_gae62c41d7980dbddbd3b0554ac186f4eb}{P\+L\+A\+S\+M\+A\+\_\+sorglq\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga7fb841270fbdaadef4cdc38d7a879145_ga7fb841270fbdaadef4cdc38d7a879145}{P\+L\+A\+S\+M\+A\+\_\+sorglq\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gad8f450a6bb48fac4dc912211fef0e912_gad8f450a6bb48fac4dc912211fef0e912}{P\+L\+A\+S\+M\+A\+\_\+cunglq} 

\hyperlink{group__double_gae71a8dbbe843b68aca052074db93409d_gae71a8dbbe843b68aca052074db93409d}{P\+L\+A\+S\+M\+A\+\_\+dorglq} 

\hyperlink{group__float_ga2f8b6c06f4346761e024c9fa00427a61_ga2f8b6c06f4346761e024c9fa00427a61}{P\+L\+A\+S\+M\+A\+\_\+sorglq} 

\hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\+L\+A\+S\+M\+A\+\_\+sgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga4b6a6aa9e5da7961424f3afb62a69562_ga4b6a6aa9e5da7961424f3afb62a69562}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sorgqr@{P\+L\+A\+S\+M\+A\+\_\+sorgqr}}
\index{P\+L\+A\+S\+M\+A\+\_\+sorgqr@{P\+L\+A\+S\+M\+A\+\_\+sorgqr}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sorgqr}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sorgqr (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga4b6a6aa9e5da7961424f3afb62a69562_ga4b6a6aa9e5da7961424f3afb62a69562}
P\+L\+A\+S\+M\+A\+\_\+sorgqr -\/ Generates an M-\/by-\/\+N matrix Q with orthonormal columns, which is defined as the first N columns of a product of the elementary reflectors returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix Q. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix Q. M $>$= N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & The number of columns of elementary tile reflectors whose product defines the matrix Q. N $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the Q\+R factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf, where the K first columns are the reflectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, the M-\/by-\/\+N matrix Q.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaec88819afb466ae7e88a1743915aebac_gaec88819afb466ae7e88a1743915aebac}{P\+L\+A\+S\+M\+A\+\_\+sorgqr\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaf15801641689a99513f4493164c19e0f_gaf15801641689a99513f4493164c19e0f}{P\+L\+A\+S\+M\+A\+\_\+sorgqr\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga6c696165c8c276260ba80eff16e4d291_ga6c696165c8c276260ba80eff16e4d291}{P\+L\+A\+S\+M\+A\+\_\+cungqr} 

\hyperlink{group__double_ga5137c6e07ebf2faddae220daa28999ba_ga5137c6e07ebf2faddae220daa28999ba}{P\+L\+A\+S\+M\+A\+\_\+dorgqr} 

\hyperlink{group__float_ga4b6a6aa9e5da7961424f3afb62a69562_ga4b6a6aa9e5da7961424f3afb62a69562}{P\+L\+A\+S\+M\+A\+\_\+sorgqr} 

\hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga4f42eb41e34bdf290b36fe5ce8e576b7_ga4f42eb41e34bdf290b36fe5ce8e576b7}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sormlq@{P\+L\+A\+S\+M\+A\+\_\+sormlq}}
\index{P\+L\+A\+S\+M\+A\+\_\+sormlq@{P\+L\+A\+S\+M\+A\+\_\+sormlq}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sormlq}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sormlq (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_ga4f42eb41e34bdf290b36fe5ce8e576b7_ga4f42eb41e34bdf290b36fe5ce8e576b7}
P\+L\+A\+S\+M\+A\+\_\+sormlq -\/ Overwrites the general complex M-\/by-\/\+N matrix C with \begin{DoxyVerb}            SIDE = 'L'     SIDE = 'R'
\end{DoxyVerb}
 T\+R\+A\+N\+S = \textquotesingle{}N\textquotesingle{}\+: Q $\ast$ C C $\ast$ Q T\+R\+A\+N\+S = \textquotesingle{}C\textquotesingle{}\+: Q$\ast$$\ast$\+T $\ast$ C C $\ast$ Q$\ast$$\ast$\+T

where Q is a complex unitary matrix defined as the product of k elementary reflectors \begin{DoxyVerb}  Q = H(1) H(2) . . . H(k)
\end{DoxyVerb}


as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf. Q is of order M if S\+I\+D\+E = Plasma\+Left and of order N if S\+I\+D\+E = Plasma\+Right.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Intended usage\+: = Plasma\+Left\+: apply Q or Q$\ast$$\ast$\+T from the left; = Plasma\+Right\+: apply Q or Q$\ast$$\ast$\+T from the right.\\
\hline
\mbox{\tt in}  & {\em trans} & Intended usage\+: = Plasma\+No\+Trans\+: no transpose, apply Q; = Plasma\+Trans\+: ugate transpose, apply Q$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & The number of rows of elementary tile reflectors whose product defines the matrix Q. If side == Plasma\+Left, M $>$= K $>$= 0. If side == Plasma\+Right, N $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the L\+Q factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+K).\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgelqf.\\
\hline
\mbox{\tt in,out}  & {\em C} & On entry, the M-\/by-\/\+N matrix C. On exit, C is overwritten by Q$\ast$\+C or Q$\ast$$\ast$\+T$\ast$\+C.\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga8033d8163163f2681562008e5f4a3ccb_ga8033d8163163f2681562008e5f4a3ccb}{P\+L\+A\+S\+M\+A\+\_\+sormlq\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga4fb93ad68adf32cbd022eeaa0b55ba7b_ga4fb93ad68adf32cbd022eeaa0b55ba7b}{P\+L\+A\+S\+M\+A\+\_\+sormlq\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gac9aca2d8444a6e5630fe4674505a2afd_gac9aca2d8444a6e5630fe4674505a2afd}{P\+L\+A\+S\+M\+A\+\_\+cunmlq} 

\hyperlink{group__double_ga7c70d5b53e69f9ab564126c78938002a_ga7c70d5b53e69f9ab564126c78938002a}{P\+L\+A\+S\+M\+A\+\_\+dormlq} 

\hyperlink{group__float_ga4f42eb41e34bdf290b36fe5ce8e576b7_ga4f42eb41e34bdf290b36fe5ce8e576b7}{P\+L\+A\+S\+M\+A\+\_\+sormlq} 

\hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\+L\+A\+S\+M\+A\+\_\+sgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga3d2c263d860db4a6d63fd13156262bd2_ga3d2c263d860db4a6d63fd13156262bd2}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sormqr@{P\+L\+A\+S\+M\+A\+\_\+sormqr}}
\index{P\+L\+A\+S\+M\+A\+\_\+sormqr@{P\+L\+A\+S\+M\+A\+\_\+sormqr}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sormqr}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sormqr (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_ga3d2c263d860db4a6d63fd13156262bd2_ga3d2c263d860db4a6d63fd13156262bd2}
P\+L\+A\+S\+M\+A\+\_\+sormqr -\/ Overwrites the general complex M-\/by-\/\+N matrix C with \begin{DoxyVerb}            SIDE = 'L'     SIDE = 'R'
\end{DoxyVerb}
 T\+R\+A\+N\+S = \textquotesingle{}N\textquotesingle{}\+: Q $\ast$ C C $\ast$ Q T\+R\+A\+N\+S = \textquotesingle{}C\textquotesingle{}\+: Q$\ast$$\ast$\+T $\ast$ C C $\ast$ Q$\ast$$\ast$\+T

where Q is a complex unitary matrix defined as the product of k elementary reflectors \begin{DoxyVerb}  Q = H(1) H(2) . . . H(k)
\end{DoxyVerb}


as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf. Q is of order M if S\+I\+D\+E = Plasma\+Left and of order N if S\+I\+D\+E = Plasma\+Right.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Intended usage\+: = Plasma\+Left\+: apply Q or Q$\ast$$\ast$\+T from the left; = Plasma\+Right\+: apply Q or Q$\ast$$\ast$\+T from the right.\\
\hline
\mbox{\tt in}  & {\em trans} & Intended usage\+: = Plasma\+No\+Trans\+: no transpose, apply Q; = Plasma\+Trans\+: ugate transpose, apply Q$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & The number of elementary reflectors whose product defines the matrix Q. If side == Plasma\+Left, M $>$= K $>$= 0. If side == Plasma\+Right, N $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the Q\+R factorization of the original matrix A as returned by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. If side == Plasma\+Left, L\+D\+A $>$= max(1,\+M). If side == Plasma\+Right, L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em desc\+T} & Auxiliary factorization data, computed by P\+L\+A\+S\+M\+A\+\_\+sgeqrf.\\
\hline
\mbox{\tt in,out}  & {\em C} & On entry, the M-\/by-\/\+N matrix C. On exit, C is overwritten by Q$\ast$\+C or Q$\ast$$\ast$\+T$\ast$\+C.\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga3fdeed46ef1d25052ce1535bfd40c07e_ga3fdeed46ef1d25052ce1535bfd40c07e}{P\+L\+A\+S\+M\+A\+\_\+sormqr\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga0d590a7126c4bdd845552f0515b9cd9d_ga0d590a7126c4bdd845552f0515b9cd9d}{P\+L\+A\+S\+M\+A\+\_\+sormqr\+\_\+\+Tile\+\_\+\+Async} 

P\+L\+A\+S\+M\+A\+\_\+cormqr 

\hyperlink{group__double_ga9623493d89eb656c0f5aa44c7772294c_ga9623493d89eb656c0f5aa44c7772294c}{P\+L\+A\+S\+M\+A\+\_\+dormqr} 

\hyperlink{group__float_ga3d2c263d860db4a6d63fd13156262bd2_ga3d2c263d860db4a6d63fd13156262bd2}{P\+L\+A\+S\+M\+A\+\_\+sormqr} 

\hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\+L\+A\+S\+M\+A\+\_\+sgeqrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+splgsy@{P\+L\+A\+S\+M\+A\+\_\+splgsy}}
\index{P\+L\+A\+S\+M\+A\+\_\+splgsy@{P\+L\+A\+S\+M\+A\+\_\+splgsy}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+splgsy}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+splgsy (
\begin{DoxyParamCaption}
\item[{float}]{bump, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}\label{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}
P\+L\+A\+S\+M\+A\+\_\+splgsy -\/ Generate a random hermitian matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em bump} & The value to add to the diagonal to be sure to have a positive definite matrix.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The random hermitian matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaf848b57db71b77ac83f655c925a9c1ce_gaf848b57db71b77ac83f655c925a9c1ce}{P\+L\+A\+S\+M\+A\+\_\+splgsy\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaeee90dc0db10bd50a634bfd24658a5c6_gaeee90dc0db10bd50a634bfd24658a5c6}{P\+L\+A\+S\+M\+A\+\_\+splgsy\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga3fc244eb71f8484ede01d0a8fb8b7243_ga3fc244eb71f8484ede01d0a8fb8b7243}{P\+L\+A\+S\+M\+A\+\_\+cplgsy} 

\hyperlink{group__double_ga267c9f85256181c2024279e1dc55e84b_ga267c9f85256181c2024279e1dc55e84b}{P\+L\+A\+S\+M\+A\+\_\+dplgsy} 

\hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\+L\+A\+S\+M\+A\+\_\+splgsy} 

\hyperlink{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}{P\+L\+A\+S\+M\+A\+\_\+splrnt} 

\hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\+L\+A\+S\+M\+A\+\_\+splgsy} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+splrnt@{P\+L\+A\+S\+M\+A\+\_\+splrnt}}
\index{P\+L\+A\+S\+M\+A\+\_\+splrnt@{P\+L\+A\+S\+M\+A\+\_\+splrnt}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+splrnt}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+splrnt (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}\label{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}
P\+L\+A\+S\+M\+A\+\_\+splrnt -\/ Generate a random matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of A.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The random matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga8acae46eec2aa940148afebdaf3662c4_ga8acae46eec2aa940148afebdaf3662c4}{P\+L\+A\+S\+M\+A\+\_\+splrnt\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga890ff04d43c21904fb6213d9b3b152fb_ga890ff04d43c21904fb6213d9b3b152fb}{P\+L\+A\+S\+M\+A\+\_\+splrnt\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gadc1ab86fbc4e1acd67411bcf7d18ccc1_gadc1ab86fbc4e1acd67411bcf7d18ccc1}{P\+L\+A\+S\+M\+A\+\_\+cplrnt} 

\hyperlink{group__double_gafca5b7ac3183e0a107df9f88ecde4cdf_gafca5b7ac3183e0a107df9f88ecde4cdf}{P\+L\+A\+S\+M\+A\+\_\+dplrnt} 

\hyperlink{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}{P\+L\+A\+S\+M\+A\+\_\+splrnt} 

\hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\+L\+A\+S\+M\+A\+\_\+splgsy} 

\hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\+L\+A\+S\+M\+A\+\_\+splgsy} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+spltmg@{P\+L\+A\+S\+M\+A\+\_\+spltmg}}
\index{P\+L\+A\+S\+M\+A\+\_\+spltmg@{P\+L\+A\+S\+M\+A\+\_\+spltmg}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+spltmg}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+spltmg (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{mtxtype, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}\label{group__float_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1}
P\+L\+A\+S\+M\+A\+\_\+spltmg -\/ Generate a test matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em mtxtype} & \begin{DoxyItemize}
\item Plasma\+Matrix\+Cauchy\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1019317}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1019317}\end{DoxyItemize}
Cauchy matrix\\
\hline
\end{DoxyParams}
Returns an n-\/by-\/n matrix C such that, C(i,j) = 1/(i + j).

\begin{DoxyItemize}
\item Plasma\+Matrix\+Chebvand\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999859}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999859}\end{DoxyItemize}
Vandermonde-\/like matrix for the Chebyshev polynomials

Produces the (primal) Chebyshev Vandermonde matrix based on the vector of points p, which define where the Chebyshev polynomial is calculated.

If seed != 0, C(i,j) = Ti – 1(p(j)) where Ti – 1 is the Chebyshev polynomial of degree i – 1, and p is a vector of N equally spaced points on the interval \mbox{[}0,1\mbox{]}.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Circul\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999880}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999880}\end{DoxyItemize}
Circulant matrix

A circulant matrix has the property that each row is obtained from the previous one by cyclically permuting the entries one step forward. It is a special Toeplitz matrix in which the diagonals \char`\"{}wrap around.\char`\"{}

The eigensystem of C (n-\/by-\/n) is known explicitly\+: If t is an nth root of unity, then the inner product of v and w = \mbox{[}1 t t2 ... t(n – 1)\mbox{]} is an eigenvalue of C and w(n\+:-\/1\+:1) is an eigenvector, where v is the first column of C.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Compan\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/compan.html}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/compan.\+html}\end{DoxyItemize}
Companion matrix

A = compan(u) returns the corresponding companion matrix whose first row is -\/u(2\+:n)/u(1), where u is a vector of polynomial coefficients. The eigenvalues of compan(u) are the roots of the polynomial.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Condex\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999898}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999898} gallery(\textquotesingle{}condex\textquotesingle{},n,4,100)\end{DoxyItemize}
Returns a \char`\"{}counter-\/example\char`\"{} matrix to a condition estimator. It has order n and scalar parameter theta (default 100).

L\+A\+P\+A\+C\+K (R\+C\+O\+N\+D)\+: It is the inverse of this matrix that is a counter-\/example.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Demmel\+: See \mbox{[}1\mbox{]} J. Demmel, Applied Numerical Linear Algebra, S\+I\+A\+M, Philadelphia, 1997\end{DoxyItemize}
Returns a matrix defined by\+: A = D $\ast$ ( I + 1e-\/7$\ast$ rand(n)), where D = diag(10$^\wedge$\{14$\ast$(0\+:n-\/1)/n\})

\begin{DoxyItemize}
\item Plasma\+Matrix\+Dorr\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999936}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999936}\end{DoxyItemize}
Diagonally dominant, ill-\/conditioned, tridiagonal matrix

Returns the n-\/by-\/n matrix, row diagonally dominant, tridiagonal matrix that is ill-\/conditioned for small nonnegative values of theta. The default value of theta is 0.\+01. The Dorr matrix itself is the same as gallery(\textquotesingle{}tridiag\textquotesingle{},c,d,e).

\begin{DoxyItemize}
\item Plasma\+Matrix\+Fiedler\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999960}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999960}\end{DoxyItemize}
Fiedler matrix of size n-\/by-\/n is defined throug a random vector c of size n, such that each element is equal to abs(n(i)-\/n(j)).

Matrix A has a dominant positive eigenvalue and all the other eigenvalues are negative.

Explicit formulas for inv(\+A) and det(\+A) are given in \mbox{[}Todd, J., Basic Numerical Mathematics, Vol. 2\+: Numerical Algebra, Birkhauser, Basel, and Academic Press, New York, 1977, p. 159\mbox{]} and attributed to Fiedler. These indicate that inv(\+A) is tridiagonal except for nonzero (1,n) and (n,1) elements.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Foster\+: See \mbox{[}1\mbox{]} L. V. Foster, Gaussian Elimination with Partial Pivoting Can Fail in Practice, S\+I\+A\+M J. Matrix Anal. Appl., 15 (1994), pp. 1354-\/1362.\end{DoxyItemize}
\mbox{[}2\mbox{]} L. V. Foster, The growth factor and efficiency of Gaussian elimination with rook pivoting, J. Comput. Appl. Math., 86 (1997), pp. 177-\/194

A pathological case for L\+U with gaussian elimination.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Hadamard\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/hadamard.html}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/hadamard.\+html}\end{DoxyItemize}
Initialize the tile A to create the Hadamard matrix of order g\+N.

Hadamard matrices are matrices of 1\textquotesingle{}s and -\/1\textquotesingle{}s whose columns are orthogonal,

H\textquotesingle{}$\ast$\+H = g\+N$\ast$\+I

where \mbox{[}g\+N g\+N\mbox{]}=size(\+H) and I = eye(g\+N,g\+N) ,.

They have applications in several different areas, including combinatorics, signal processing, and numerical analysis.

An n-\/by-\/n Hadamard matrix with n $>$ 2 exists only if rem(n,4) = 0. This function handles only the cases where n is a power of 2.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Hankel\+: See \href{http://en.wikipedia.org/wiki/Hankel_matrix}{\tt http\+://en.\+wikipedia.\+org/wiki/\+Hankel\+\_\+matrix}\end{DoxyItemize}
Hankel matrix

In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix with constant skew-\/diagonals (positive sloping diagonals), e.\+g.\+:

\[ \begin{bmatrix} a & b & c & d & e \\ b & c & d & e & f \\ c & d & e & f & g \\ d & e & f & g & h \\ e & f & g & h & i \\ \end{bmatrix} \].

A(i,j) = A(i-\/1,j+1)

\begin{DoxyItemize}
\item Plasma\+Matrix\+Hilb\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/hilb.html}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/hilb.\+html}\end{DoxyItemize}
Hilbert Matrix

The Hilbert matrix is a notable example of a poorly conditioned matrix. The elements of the Hilbert matrices are\+: H(i,j) = 1/(i $\ast$ + j – 1).

\begin{DoxyItemize}
\item Plasma\+Matrix\+House\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-999993}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/999993}\end{DoxyItemize}
Householder matrix

Generates a random column vector of size M, and returns the housholder matrix H = eye(n,n) -\/ beta$\ast$v$\ast$v\textquotesingle{} that satisfies the relationship

H$\ast$x = -\/sign(x(1))$\ast$norm(x)$\ast$e1

where e1 is the first column of eye(n,n). Note that if x is complex, then sign(x) exp(i$\ast$arg(x)) (which equals x./abs(x) when x is nonzero).

\begin{DoxyItemize}
\item Plasma\+Matrix\+Invhess\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000000}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000000}\end{DoxyItemize}
Inverse of an upper Hessenberg matrix

A = gallery(\textquotesingle{}invhess\textquotesingle{},x,y), where x is a length n vector and y is a length n-\/1 vector, returns the matrix whose lower triangle agrees with that of ones(n,1)$\ast$x\textquotesingle{} and whose strict upper triangle agrees with that of \mbox{[}1 y\mbox{]}$\ast$ones(1,n).

The matrix is nonsingular if x(1) $\sim$= 0 and x(i+1) $\sim$= y(i) for all i, and its inverse is an upper Hessenberg matrix. Argument y defaults to -\/x(1\+:n-\/1).

If x is a scalar, invhess(x) is the same as invhess(1\+:x).

Here\+: gallery(\textquotesingle{}invhess\textquotesingle{}, g\+M)

\begin{DoxyItemize}
\item Plasma\+Matrix\+Kms\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000026}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000026}\end{DoxyItemize}
Kac-\/\+Murdock-\/\+Szego Toeplitz matrix

Returns the n-\/by-\/n Kac-\/\+Murdock-\/\+Szego Toeplitz matrix such that A(i,j) = rho$^\wedge$(abs(i-\/j)), for real rho.

For complex rho, the same formula holds except that elements below the diagonal are ugated. rho defaults to 0.\+5.

The K\+M\+S matrix A has these properties\+:
\begin{DoxyItemize}
\item An L\+D\+L\textquotesingle{} factorization with L inv(gallery(\textquotesingle{}triw\textquotesingle{},n,-\/rho,1))\textquotesingle{}, and D(i,i) (1-\/abs(rho)$^\wedge$2)$\ast$eye(n), except D(1,1) = 1.
\item Positive definite if and only if 0 $<$ abs(rho) $<$ 1.
\item The inverse inv(\+A) is tridiagonal.\+Symmetric Hankel matrix
\end{DoxyItemize}

In this function, rho is set to 0.\+5 and cannot be changed.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Langou\+: Generates a pathological case for L\+U with gaussian elimination.\end{DoxyItemize}
Returns a random matrix on which, the columns from N/4 to N/2 are scaled down by eps. These matrices fails on L\+U with partial pivoting, but Hybrid L\+U-\/\+Q\+R algorithms manage to recover the scaled down columns.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Lehmer\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000049}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000049}\end{DoxyItemize}
Symmetric positive definite matrix

Returns the symmetric positive definite n-\/by-\/n matrix such that A(i,j) = i/j for j $>$= i.

The Lehmer matrix A has these properties\+:
\begin{DoxyItemize}
\item A is totally nonnegative.
\item The inverse inv(\+A) is tridiagonal and explicitly known.
\item The order n $<$= cond(\+A) $<$= 4$\ast$n$\ast$n.Matrix associated with the Riemann hypothesis
\end{DoxyItemize}

\begin{DoxyItemize}
\item Plasma\+Matrix\+Lotkin\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000062}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000062}\end{DoxyItemize}
Lotkin matrix

Returns the Hilbert matrix with its first row altered to all ones. The Lotkin matrix A is nonsymmetric, ill-\/conditioned, and has many negative eigenvalues of small magnitude. Its inverse has integer entries and is known explicitly.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Minij\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000066}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000066}\end{DoxyItemize}
Symmetric positive definite matrix

Returns the n-\/by-\/n symmetric positive definite matrix with A(i,j) = min(i,j).

The minij matrix has these properties\+:
\begin{DoxyItemize}
\item The inverse inv(\+A) is tridiagonal and equal to -\/1 times the second difference matrix, except its (n,n) element is 1.
\item Givens\textquotesingle{} matrix, 2$\ast$\+A-\/ones(size(\+A)), has tridiagonal inverse and eigenvalues 0.\+5$\ast$sec((2$\ast$r-\/1)$\ast$pi/(4$\ast$n))$^\wedge$2, where r=1\+:n.
\item (n+1)$\ast$ones(size(\+A))-\/\+A has elements that are max(i,j) and a tridiagonal inverse.
\end{DoxyItemize}

\begin{DoxyItemize}
\item Plasma\+Matrix\+Moler\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000074}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000074}\end{DoxyItemize}
Symmetric positive definite matrix

Returns the symmetric positive definite n-\/by-\/n matrix U\textquotesingle{}$\ast$\+U, where U = gallery(\textquotesingle{}triw\textquotesingle{},n,alpha).

For the default alpha = -\/1, A(i,j) = min(i,j)-\/2, and A(i,i) = i. One of the eigenvalues of A is small.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Orthog\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000083}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000083}\end{DoxyItemize}
Orthogonal and nearly orthogonal matrices

Returns the matrix Q of order n, such that\+: Q(i,j) = sqrt(2/(n+1)) $\ast$ sin(i$\ast$j$\ast$pi/(n+1))

Symmetric eigenvector matrix for second difference matrix.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Parter\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000116}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000116}\end{DoxyItemize}
Toeplitz matrix with singular values near pi. Returns the tile A, such that the elment of the matrix are 1/(i-\/j+0.5).

C is a Cauchy matrix and a Toeplitz matrix. Most of the singular values of C are very close to pi.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Random\+: Random matrix with values between -\/0.\+5 and 0.\+5.\end{DoxyItemize}
\begin{DoxyItemize}
\item Plasma\+Matrix\+Riemann\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000232}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000232}\end{DoxyItemize}
Matrix associated with the Riemann hypothesis

Returns an n-\/by-\/n matrix for which the Riemann hypothesis is true if and only if for every eps $>$ 0.

The Riemann matrix is defined by\+:

A = B(2\+:n+1,2\+:n+1)

where B(i,j) = i-\/1 if i divides j, and B(i,j) = -\/1 otherwise.

The Riemann matrix has these properties\+:
\begin{DoxyItemize}
\item Each eigenvalue e(i) satisfies abs(e(i)) $<$= m-\/1/m, where m = n+1.
\item i $<$= e(i) $<$= i+1 with at most m-\/sqrt(m) exceptions.
\item All integers in the interval (m/3, m/2\mbox{]} are eigenvalues.
\end{DoxyItemize}

\begin{DoxyItemize}
\item Plasma\+Matrix\+Ris\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000243}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000243}\end{DoxyItemize}
Symmetric Hankel matrix Returns a symmetric g\+N-\/by-\/g\+N Hankel matrix with elements. \begin{DoxyVerb}A(i,j) = 0.5/(n-i-j+1.5)
\end{DoxyVerb}


The eigenvalues of A cluster around π/2 and –π/2. This matrix was invented by F.\+N. Ris.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Toeppd\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/gallery.html#f84-1000272}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/gallery.\+html\#f84-\/1000272}\end{DoxyItemize}
A toeppd matrix is an n-\/by-\/n symmetric, positive semi-\/definite (S\+P\+D) Toeplitz matrix composed of the sum of m rank 2 (or, for certain theta, rank 1) S\+P\+D Toeplitz matrices. Specifically,

T = w(1)$\ast$\+T(theta(1)) + ... + w(m)$\ast$\+T(theta(m))

where T(theta(k)) has (i,j) element cos(2$\ast$pi$\ast$theta(k)$\ast$(i-\/j)).

In this matrix generation\+: w = rand(m,1), and theta = rand(m,1).

\begin{DoxyItemize}
\item Plasma\+Matrix\+Wilkinson\+: See \href{http://www.mathworks.fr/fr/help/matlab/ref/wilkinson.html}{\tt http\+://www.\+mathworks.\+fr/fr/help/matlab/ref/wilkinson.\+html}\end{DoxyItemize}
Wilkinson\textquotesingle{}s eigenvalue test matrix

Returns one of J. H. Wilkinson\textquotesingle{}s eigenvalue test matrices. It is a symmetric, tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues.

\begin{DoxyItemize}
\item Plasma\+Matrix\+Wright\+: See \mbox{[}3\mbox{]} S. J. Wright, A collection of problems for which Gaussian elimination with partial pivoting is unstable, S\+I\+A\+M J. S\+C\+I. S\+T\+A\+T\+I\+S\+T. C\+O\+M\+P\+U\+T., 14 (1993), pp. 231-\/238.\end{DoxyItemize}
A pathological case for L\+U with gaussian elimination.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of A.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga68fe8bd8a7f5edfc934d558ba34e3da4_ga68fe8bd8a7f5edfc934d558ba34e3da4}{P\+L\+A\+S\+M\+A\+\_\+spltmg\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gabbc2518f1b3e7493ad860eb743ccb452_gabbc2518f1b3e7493ad860eb743ccb452}{P\+L\+A\+S\+M\+A\+\_\+spltmg\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gae69ed47baf0586751c50c701b1bba434_gae69ed47baf0586751c50c701b1bba434}{P\+L\+A\+S\+M\+A\+\_\+cpltmg} 

\hyperlink{group__double_ga6cde89e43a8752b706704ed7ec7d3917_ga6cde89e43a8752b706704ed7ec7d3917}{P\+L\+A\+S\+M\+A\+\_\+dpltmg} 

\hyperlink{group__float_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1_gaf78afc5a8cd9c1f43eb9cfecd9c0f7a1}{P\+L\+A\+S\+M\+A\+\_\+spltmg} 
\end{DoxySeeAlso}
\hypertarget{group__float_gae4ca020dbb8fa3516e2e4c89a6b60b1a_gae4ca020dbb8fa3516e2e4c89a6b60b1a}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+spocon@{P\+L\+A\+S\+M\+A\+\_\+spocon}}
\index{P\+L\+A\+S\+M\+A\+\_\+spocon@{P\+L\+A\+S\+M\+A\+\_\+spocon}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+spocon}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+spocon (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{Anorm, }
\item[{float $\ast$}]{rcond}
\end{DoxyParamCaption}
)}\label{group__float_gae4ca020dbb8fa3516e2e4c89a6b60b1a_gae4ca020dbb8fa3516e2e4c89a6b60b1a}
P\+L\+A\+S\+M\+A\+\_\+spocon -\/ estimates the reciprocal of the condition number (in the 1-\/norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T computed by \hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\+L\+A\+S\+M\+A\+\_\+spotrf()}.

An estimate is obtained for norm(inv(\+A)), and the reciprocal of the condition number is computed as

\[ rcond = \frac{1}{\|\|A\-\| \times \-\|A^{-1}\|\|} \]


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\+N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em Anorm} & If norm = Plasma\+One\+Norm, the 1-\/norm of the original matrix A. If norm = Plasma\+Inf\+Norm, the infinity-\/norm of the original matrix A.\\
\hline
\mbox{\tt out}  & {\em rcond} & The reciprocal of the condition number of the matrix A, computed as stated above.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga77c4e9a5bcfacbb8cd5672f3ff30542e_ga77c4e9a5bcfacbb8cd5672f3ff30542e}{P\+L\+A\+S\+M\+A\+\_\+spocon\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga1d037b0a07761992e43c235ad307d042_ga1d037b0a07761992e43c235ad307d042}{P\+L\+A\+S\+M\+A\+\_\+spocon\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga49718ad20a5a6701a7f3f91dc64173ba_ga49718ad20a5a6701a7f3f91dc64173ba}{P\+L\+A\+S\+M\+A\+\_\+cpocon} 

\hyperlink{group__double_ga2e52f461973867ecb409cfaa3d4cac36_ga2e52f461973867ecb409cfaa3d4cac36}{P\+L\+A\+S\+M\+A\+\_\+dpocon} 

\hyperlink{group__float_gae4ca020dbb8fa3516e2e4c89a6b60b1a_gae4ca020dbb8fa3516e2e4c89a6b60b1a}{P\+L\+A\+S\+M\+A\+\_\+spocon} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga113c09b4a9f41fc4c19358a52477d685_ga113c09b4a9f41fc4c19358a52477d685}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+sposv@{P\+L\+A\+S\+M\+A\+\_\+sposv}}
\index{P\+L\+A\+S\+M\+A\+\_\+sposv@{P\+L\+A\+S\+M\+A\+\_\+sposv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+sposv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+sposv (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga113c09b4a9f41fc4c19358a52477d685_ga113c09b4a9f41fc4c19358a52477d685}
P\+L\+A\+S\+M\+A\+\_\+sposv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\+N symmetric positive definite (or Hermitian positive definite in the complex case) matrix and X and B are N-\/by-\/\+N\+R\+H\+S matrices. The Cholesky decomposition is used to factor A as

\[ A = \{_{L\times L^H, if uplo = PlasmaLower}^{U^H\times U, if uplo = PlasmaUpper} \]

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\+e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric positive definite (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If U\+P\+L\+O = \textquotesingle{}L\textquotesingle{}, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga161633108104c031c61b103b8645f029_ga161633108104c031c61b103b8645f029}{P\+L\+A\+S\+M\+A\+\_\+sposv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga566d68b010e8cfe877b1426ce1f26feb_ga566d68b010e8cfe877b1426ce1f26feb}{P\+L\+A\+S\+M\+A\+\_\+sposv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gacb9e52ca26891e283878a10c6b7f24b7_gacb9e52ca26891e283878a10c6b7f24b7}{P\+L\+A\+S\+M\+A\+\_\+cposv} 

\hyperlink{group__double_ga83015e9476d13f0c9f056eac9b54804f_ga83015e9476d13f0c9f056eac9b54804f}{P\+L\+A\+S\+M\+A\+\_\+dposv} 

\hyperlink{group__float_ga113c09b4a9f41fc4c19358a52477d685_ga113c09b4a9f41fc4c19358a52477d685}{P\+L\+A\+S\+M\+A\+\_\+sposv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+spotrf@{P\+L\+A\+S\+M\+A\+\_\+spotrf}}
\index{P\+L\+A\+S\+M\+A\+\_\+spotrf@{P\+L\+A\+S\+M\+A\+\_\+spotrf}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+spotrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+spotrf (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}
P\+L\+A\+S\+M\+A\+\_\+spotrf -\/ Computes the Cholesky factorization of a symmetric positive definite (or Hermitian positive definite in the complex case) matrix A. The factorization has the form

\[ A = \{_{L\times L^H, if uplo = PlasmaLower}^{U^H\times U, if uplo = PlasmaUpper} \]

where U is an upper triangular matrix and L is a lower triangular matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric positive definite (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If U\+P\+L\+O = \textquotesingle{}L\textquotesingle{}, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga0518a079c049cdcd32b8ae408e0d5e28_ga0518a079c049cdcd32b8ae408e0d5e28}{P\+L\+A\+S\+M\+A\+\_\+spotrf\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga9a217d8289a1d9bc19a5b6902e774343_ga9a217d8289a1d9bc19a5b6902e774343}{P\+L\+A\+S\+M\+A\+\_\+spotrf\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga9a02052646386252f5b41c09c8d18684_ga9a02052646386252f5b41c09c8d18684}{P\+L\+A\+S\+M\+A\+\_\+cpotrf} 

\hyperlink{group__double_ga08c3851e861086761123a375b8472df2_ga08c3851e861086761123a375b8472df2}{P\+L\+A\+S\+M\+A\+\_\+dpotrf} 

\hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\+L\+A\+S\+M\+A\+\_\+spotrf} 

\hyperlink{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}{P\+L\+A\+S\+M\+A\+\_\+spotrs} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+spotri@{P\+L\+A\+S\+M\+A\+\_\+spotri}}
\index{P\+L\+A\+S\+M\+A\+\_\+spotri@{P\+L\+A\+S\+M\+A\+\_\+spotri}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+spotri}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+spotri (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}
P\+L\+A\+S\+M\+A\+\_\+spotri -\/ Computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T computed by P\+L\+A\+S\+M\+A\+\_\+spotrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor U or L from the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T, as computed by P\+L\+A\+S\+M\+A\+\_\+spotrf. On exit, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga3f2b23232748f3fde3e58d06757af2ff_ga3f2b23232748f3fde3e58d06757af2ff}{P\+L\+A\+S\+M\+A\+\_\+spotri\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga8069a24dfebe70194fa0bd6e9bb8ed62_ga8069a24dfebe70194fa0bd6e9bb8ed62}{P\+L\+A\+S\+M\+A\+\_\+spotri\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga2bbe242c5e06f243640fb6287b4a85ab_ga2bbe242c5e06f243640fb6287b4a85ab}{P\+L\+A\+S\+M\+A\+\_\+cpotri} 

\hyperlink{group__double_ga01b70786730b5e4c314b4584fe3697c5_ga01b70786730b5e4c314b4584fe3697c5}{P\+L\+A\+S\+M\+A\+\_\+dpotri} 

\hyperlink{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{P\+L\+A\+S\+M\+A\+\_\+spotri} 

\hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\+L\+A\+S\+M\+A\+\_\+spotrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+spotrs@{P\+L\+A\+S\+M\+A\+\_\+spotrs}}
\index{P\+L\+A\+S\+M\+A\+\_\+spotrs@{P\+L\+A\+S\+M\+A\+\_\+spotrs}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+spotrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+spotrs (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}
P\+L\+A\+S\+M\+A\+\_\+spotrs -\/ Solves a system of linear equations A $\ast$ X = B with a symmetric positive definite (or Hermitian positive definite in the complex case) matrix A using the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T computed by P\+L\+A\+S\+M\+A\+\_\+spotrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & The triangular factor U or L from the Cholesky factorization A = U$\ast$$\ast$\+T$\ast$\+U or A = L$\ast$\+L$\ast$$\ast$\+T, computed by P\+L\+A\+S\+M\+A\+\_\+spotrf. Remark\+: If out-\/of-\/place layout translation is used, the matrix A can be considered as input, however if inplace layout translation is enabled, the content of A will be reordered for computation and restored before exiting the function.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaf5ba3c807c89d3363ea8cf648b11b40d_gaf5ba3c807c89d3363ea8cf648b11b40d}{P\+L\+A\+S\+M\+A\+\_\+spotrs\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga5a9d82d08cb6da30647e71a4e3e3fc70_ga5a9d82d08cb6da30647e71a4e3e3fc70}{P\+L\+A\+S\+M\+A\+\_\+spotrs\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gaf429b7116507625912226d3c91bdfecc_gaf429b7116507625912226d3c91bdfecc}{P\+L\+A\+S\+M\+A\+\_\+cpotrs} 

\hyperlink{group__double_ga2d3c0509f11f1e9a9cf06b95109e62f5_ga2d3c0509f11f1e9a9cf06b95109e62f5}{P\+L\+A\+S\+M\+A\+\_\+dpotrs} 

\hyperlink{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}{P\+L\+A\+S\+M\+A\+\_\+spotrs} 

\hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\+L\+A\+S\+M\+A\+\_\+spotrf} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssyev@{P\+L\+A\+S\+M\+A\+\_\+ssyev}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssyev@{P\+L\+A\+S\+M\+A\+\_\+ssyev}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssyev}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssyev (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{W, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}
P\+L\+A\+S\+M\+A\+\_\+ssyev -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-\/stage approach\+: First stage\+: reduction to band tridiagonal form; Second stage\+: reduction from band to tridiagonal form.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes eigenvalues only; = Plasma\+Vec\+: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssyev On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\+N\+F\+O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga4cea879175261b653369407d34b2d358_ga4cea879175261b653369407d34b2d358}{P\+L\+A\+S\+M\+A\+\_\+ssyev\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gac9cbb6cbbdf3fa90ce59fc6909c8a846_gac9cbb6cbbdf3fa90ce59fc6909c8a846}{P\+L\+A\+S\+M\+A\+\_\+ssyev\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga0d2fe45268be2c3d25593d80dd0c547f_ga0d2fe45268be2c3d25593d80dd0c547f}{P\+L\+A\+S\+M\+A\+\_\+cheev} 

\hyperlink{group__double_gac7ea19b1441c1325f45c0f6a9cfd8a8a_gac7ea19b1441c1325f45c0f6a9cfd8a8a}{P\+L\+A\+S\+M\+A\+\_\+dsyev} 

\hyperlink{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{P\+L\+A\+S\+M\+A\+\_\+ssyev} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga71305bb114c063946ddd9003bea058bf_ga71305bb114c063946ddd9003bea058bf}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssyevd@{P\+L\+A\+S\+M\+A\+\_\+ssyevd}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssyevd@{P\+L\+A\+S\+M\+A\+\_\+ssyevd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssyevd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssyevd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{W, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga71305bb114c063946ddd9003bea058bf_ga71305bb114c063946ddd9003bea058bf}
P\+L\+A\+S\+M\+A\+\_\+ssyevd -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-\/stage approach\+: First stage\+: reduction to band tridiagonal form; Second stage\+: reduction from band to tridiagonal form.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes eigenvalues only; = Plasma\+Vec\+: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssyevd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\+N\+F\+O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga2fc7699488f0b8d17c875b7864577ef8_ga2fc7699488f0b8d17c875b7864577ef8}{P\+L\+A\+S\+M\+A\+\_\+ssyevd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gace8db2bf803edf81b914362fe8ef9c9f_gace8db2bf803edf81b914362fe8ef9c9f}{P\+L\+A\+S\+M\+A\+\_\+ssyevd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga73b59abe87bcb46382a26a50c70345ad_ga73b59abe87bcb46382a26a50c70345ad}{P\+L\+A\+S\+M\+A\+\_\+cheevd} 

\hyperlink{group__double_gac7ea19b1441c1325f45c0f6a9cfd8a8a_gac7ea19b1441c1325f45c0f6a9cfd8a8a}{P\+L\+A\+S\+M\+A\+\_\+dsyev} 

\hyperlink{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{P\+L\+A\+S\+M\+A\+\_\+ssyev} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga850dfaa20a85559bd1ef0042e4218ecd_ga850dfaa20a85559bd1ef0042e4218ecd}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssyevr@{P\+L\+A\+S\+M\+A\+\_\+ssyevr}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssyevr@{P\+L\+A\+S\+M\+A\+\_\+ssyevr}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssyevr}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssyevr (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{range, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{vl, }
\item[{float}]{vu, }
\item[{int}]{il, }
\item[{int}]{iu, }
\item[{float}]{abstol, }
\item[{int $\ast$}]{nbcomputedeig, }
\item[{float $\ast$}]{W, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga850dfaa20a85559bd1ef0042e4218ecd_ga850dfaa20a85559bd1ef0042e4218ecd}
P\+L\+A\+S\+M\+A\+\_\+ssyevr -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-\/stage approach\+: First stage\+: reduction to band tridiagonal form; Second stage\+: reduction from band to tridiagonal form.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes eigenvalues only; = Plasma\+Vec\+: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em range} & = Plasma\+All\+Vec\+: all eigenvalues will be found. = Plasma\+Vec\+: all eigenvalues in the half-\/open interval (V\+L,V\+U\mbox{]} will be found. = Plasma\+Ivec\+: the I\+L-\/th through I\+U-\/th eigenvalues will be found. For range = Plasma\+Vec or Plasma\+Ivec and I\+U -\/ I\+L $<$ N -\/ 1, D\+S\+T\+E\+B\+Z and Z\+S\+T\+E\+I\+N are called.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em vl} & see vu.\\
\hline
\mbox{\tt in}  & {\em vu} & If R\+A\+N\+G\+E=Plasma\+Vec, the lower and upper bounds of the interval to be searched for eigenvalues. V\+L $<$ V\+U. Not referenced if R\+A\+N\+G\+E = Plasma\+All\+Vec or Plasma\+Ivec.\\
\hline
\mbox{\tt in}  & {\em il} & see iu.\\
\hline
\mbox{\tt in}  & {\em iu} & If R\+A\+N\+G\+E=Plasma\+Ivec, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 $<$= I\+L $<$= I\+U $<$= N, if N $>$ 0; I\+L = 1 and I\+U = 0 if N = 0. Not referenced if R\+A\+N\+G\+E = Plasma\+All\+Vec or Plasma\+Vec.\\
\hline
\mbox{\tt in}  & {\em abstol} & The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval \mbox{[}a,b\mbox{]} of width less than or equal to \begin{DoxyVerb}    ABSTOL + EPS *   max( |a|,|b| ) ,
\end{DoxyVerb}
\\
\hline
\end{DoxyParams}
where E\+P\+S is the machine precision. If A\+B\+S\+T\+O\+L is less than or equal to zero, then E\+P\+S$\ast$$\vert$\+T$\vert$ will be used in its place, where $\vert$\+T$\vert$ is the 1-\/norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.

See \char`\"{}\+Computing Small Singular Values of Bidiagonal Matrices
         with Guaranteed High Relative Accuracy,\char`\"{} by Demmel and Kahan, L\+A\+P\+A\+C\+K Working Note \#3.

If high relative accuracy is important, set A\+B\+S\+T\+O\+L to S\+L\+A\+M\+C\+H( \textquotesingle{}Safe minimum\textquotesingle{} ). Doing so will guarantee that eigenvalues are computed to high relative accuracy when possible in future releases. The current code does not make any guarantees about high relative accuracy, but furutre releases will. See J. Barlow and J. Demmel, \char`\"{}\+Computing Accurate Eigensystems of Scaled Diagonally
         Dominant Matrices\char`\"{}, L\+A\+P\+A\+C\+K Working Note \#7, for a discussion of which matrices define their eigenvalues to high relative accuracy. (hard set to use tryrac=1).


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em nbcomputedeig} & The total number of eigenvalues found. 0 $<$= M $<$= N. If R\+A\+N\+G\+E = Plasma\+All\+Vec, M = N, and if R\+A\+N\+G\+E = Plasma\+Ivec, M = I\+U-\/\+I\+L+1.\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssyevr On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\+N\+F\+O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga0515679d76f496ab88d79c3904e8b2f4_ga0515679d76f496ab88d79c3904e8b2f4}{P\+L\+A\+S\+M\+A\+\_\+ssyevr\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaed935568555dff5c9f8cf4f5eb18612d_gaed935568555dff5c9f8cf4f5eb18612d}{P\+L\+A\+S\+M\+A\+\_\+ssyevr\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga69b1739ca8db9edc416275eaff7cab65_ga69b1739ca8db9edc416275eaff7cab65}{P\+L\+A\+S\+M\+A\+\_\+cheevr} 

\hyperlink{group__double_gac40bc729f1349cf26c573be350c92de4_gac40bc729f1349cf26c573be350c92de4}{P\+L\+A\+S\+M\+A\+\_\+dsyevr} 

\hyperlink{group__float_ga850dfaa20a85559bd1ef0042e4218ecd_ga850dfaa20a85559bd1ef0042e4218ecd}{P\+L\+A\+S\+M\+A\+\_\+ssyevr} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga66b77c0de44f80760c4184756250e75e_ga66b77c0de44f80760c4184756250e75e}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssygst@{P\+L\+A\+S\+M\+A\+\_\+ssygst}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssygst@{P\+L\+A\+S\+M\+A\+\_\+ssygst}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssygst}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssygst (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{itype, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga66b77c0de44f80760c4184756250e75e_ga66b77c0de44f80760c4184756250e75e}
P\+L\+A\+S\+M\+A\+\_\+ssygst -\/ reduces a complex Hermitian-\/definite generalized eigenproblem to standard form. If Plasma\+Itype == 1, the problem is A$\ast$x = lambda$\ast$\+B$\ast$x, and A is overwritten by inv(\+U$\ast$$\ast$\+T)$\ast$\+A$\ast$inv(U) or inv(\+L)$\ast$\+A$\ast$inv(L$\ast$$\ast$\+T) If Plasma\+Itype == 2 or 3, the problem is A$\ast$\+B$\ast$x = lambda$\ast$x or B$\ast$\+A$\ast$x = lambda$\ast$x, and A is overwritten by U$\ast$\+A$\ast$\+U$\ast$$\ast$\+T or L$\ast$$\ast$\+T$\ast$\+A$\ast$\+L. B must have been previously factorized as U$\ast$$\ast$\+T$\ast$\+U or L$\ast$\+L$\ast$$\ast$\+T by P\+L\+A\+S\+M\+A\+\_\+\+S\+P\+O\+T\+R\+F.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\+: = 1\+: A$\ast$x=(lambda)$\ast$\+B$\ast$x = 2\+: A$\ast$\+Bx=(lambda)$\ast$x = 3\+: B$\ast$\+A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrices A and B. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value == 0, the transformed matrix, stored in the same format as A.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the triangular factor from the Cholesky factorization of B, as returned by P\+L\+A\+S\+M\+A\+\_\+\+S\+P\+O\+T\+R\+F.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga47edc276e115a0eb253b2a4bda9a3b9e_ga47edc276e115a0eb253b2a4bda9a3b9e}{P\+L\+A\+S\+M\+A\+\_\+ssygst\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga0ba80975dba7d12181f27baaae46c3eb_ga0ba80975dba7d12181f27baaae46c3eb}{P\+L\+A\+S\+M\+A\+\_\+ssygst\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gac4b81a8ac8396c84a27d8a0b719bc379_gac4b81a8ac8396c84a27d8a0b719bc379}{P\+L\+A\+S\+M\+A\+\_\+chegst} 

\hyperlink{group__double_ga7ab44c615960d36295086012efc45a7d_ga7ab44c615960d36295086012efc45a7d}{P\+L\+A\+S\+M\+A\+\_\+dsygst} 

\hyperlink{group__float_ga66b77c0de44f80760c4184756250e75e_ga66b77c0de44f80760c4184756250e75e}{P\+L\+A\+S\+M\+A\+\_\+ssygst} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaa5deb8e85d037eff767d9a9e5e99fad9_gaa5deb8e85d037eff767d9a9e5e99fad9}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssygv@{P\+L\+A\+S\+M\+A\+\_\+ssygv}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssygv@{P\+L\+A\+S\+M\+A\+\_\+ssygv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssygv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssygv (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{itype, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B, }
\item[{float $\ast$}]{W, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_gaa5deb8e85d037eff767d9a9e5e99fad9_gaa5deb8e85d037eff767d9a9e5e99fad9}
P\+L\+A\+S\+M\+A\+\_\+ssygv -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-\/definite eigenproblem of the form\+: A$\ast$x=(lambda)$\ast$\+B$\ast$x, A$\ast$\+Bx=(lambda)$\ast$x, or B$\ast$\+A$\ast$x=(lambda)$\ast$x. Here A and B are assumed to be Hermitian and B is also positive definite.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\+: = 1\+: A$\ast$x=(lambda)$\ast$\+B$\ast$x = 2\+: A$\ast$\+Bx=(lambda)$\ast$x = 3\+: B$\ast$\+A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes eigenvalues only; = Plasma\+Vec\+: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A and B are stored; = Plasma\+Lower\+: Lower triangle of A and B are stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if jobz = Plasma\+Vec, then if return value = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows\+: if I\+T\+Y\+P\+E = 1 or 2, Z$\ast$$\ast$\+T$\ast$\+B$\ast$\+Z = I; if I\+T\+Y\+P\+E = 3, Z$\ast$$\ast$\+T$\ast$inv(B)$\ast$\+Z = I. If jobz = Plasma\+No\+Vec, then on exit the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the symmetric (or Hermitian) positive definite matrix B. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of B contains the upper triangular part of the matrix B, and the strictly lower triangular part of B is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of B contains the lower triangular part of the matrix B, and the strictly upper triangular part of B is not referenced. On exit, if return value $<$= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U$\ast$$\ast$\+T$\ast$\+U or B = L$\ast$\+L$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssygv On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of Q.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $<$=\+N} & if I\+N\+F\+O = i, plasma\+\_\+ssygv failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero. \\
\hline
{\em $>$\+N} & if I\+N\+F\+O = N + i, for 1 $<$= i $<$= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaf4fce913d91be59999ba6a842ec1ad8d_gaf4fce913d91be59999ba6a842ec1ad8d}{P\+L\+A\+S\+M\+A\+\_\+ssygv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga40eabad9bbb66303320e6fe3dbcf8d06_ga40eabad9bbb66303320e6fe3dbcf8d06}{P\+L\+A\+S\+M\+A\+\_\+ssygv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga7d0aad7dba26173b3cc6f35a74f6eaf0_ga7d0aad7dba26173b3cc6f35a74f6eaf0}{P\+L\+A\+S\+M\+A\+\_\+chegv} 

\hyperlink{group__double_ga7efdf7cffbb28696c69310d1627a100d_ga7efdf7cffbb28696c69310d1627a100d}{P\+L\+A\+S\+M\+A\+\_\+dsygv} 

\hyperlink{group__float_gaa5deb8e85d037eff767d9a9e5e99fad9_gaa5deb8e85d037eff767d9a9e5e99fad9}{P\+L\+A\+S\+M\+A\+\_\+ssygv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga366bd2466847e2b9f29bd39a9d699fb9_ga366bd2466847e2b9f29bd39a9d699fb9}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssygvd@{P\+L\+A\+S\+M\+A\+\_\+ssygvd}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssygvd@{P\+L\+A\+S\+M\+A\+\_\+ssygvd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssygvd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssygvd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{itype, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B, }
\item[{float $\ast$}]{W, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_ga366bd2466847e2b9f29bd39a9d699fb9_ga366bd2466847e2b9f29bd39a9d699fb9}
P\+L\+A\+S\+M\+A\+\_\+ssygvd -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-\/definite eigenproblem of the form\+: A$\ast$x=(lambda)$\ast$\+B$\ast$x, A$\ast$\+Bx=(lambda)$\ast$x, or B$\ast$\+A$\ast$x=(lambda)$\ast$x. Here A and B are assumed to be Hermitian and B is also positive definite.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\+: = 1\+: A$\ast$x=(lambda)$\ast$\+B$\ast$x = 2\+: A$\ast$\+Bx=(lambda)$\ast$x = 3\+: B$\ast$\+A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes eigenvalues only; = Plasma\+Vec\+: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A and B are stored; = Plasma\+Lower\+: Lower triangle of A and B are stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if jobz = Plasma\+Vec, then if return value = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows\+: if I\+T\+Y\+P\+E = 1 or 2, Z$\ast$$\ast$\+T$\ast$\+B$\ast$\+Z = I; if I\+T\+Y\+P\+E = 3, Z$\ast$$\ast$\+T$\ast$inv(B)$\ast$\+Z = I. If jobz = Plasma\+No\+Vec, then on exit the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the symmetric (or Hermitian) positive definite matrix B. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of B contains the upper triangular part of the matrix B, and the strictly lower triangular part of B is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of B contains the lower triangular part of the matrix B, and the strictly upper triangular part of B is not referenced. On exit, if return value $<$= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U$\ast$$\ast$\+T$\ast$\+U or B = L$\ast$\+L$\ast$$\ast$\+T.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssygvd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of Q.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $<$=\+N} & if I\+N\+F\+O = i, plasma\+\_\+ssygvd failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero. \\
\hline
{\em $>$\+N} & if I\+N\+F\+O = N + i, for 1 $<$= i $<$= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaabdc43dc2d083a9b795bd359ebdb1a69_gaabdc43dc2d083a9b795bd359ebdb1a69}{P\+L\+A\+S\+M\+A\+\_\+ssygvd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga97d8d042fe9b588ddb504259c1960e44_ga97d8d042fe9b588ddb504259c1960e44}{P\+L\+A\+S\+M\+A\+\_\+ssygvd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga7c4d8cc52849439d387178748f08d45b_ga7c4d8cc52849439d387178748f08d45b}{P\+L\+A\+S\+M\+A\+\_\+chegvd} 

\hyperlink{group__double_ga10b8c70c33dfee0cbbe6acb17217f717_ga10b8c70c33dfee0cbbe6acb17217f717}{P\+L\+A\+S\+M\+A\+\_\+dsygvd} 

\hyperlink{group__float_ga366bd2466847e2b9f29bd39a9d699fb9_ga366bd2466847e2b9f29bd39a9d699fb9}{P\+L\+A\+S\+M\+A\+\_\+ssygvd} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaaffcd386f207f3e3a3073a803e27e3f1_gaaffcd386f207f3e3a3073a803e27e3f1}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssymm@{P\+L\+A\+S\+M\+A\+\_\+ssymm}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssymm@{P\+L\+A\+S\+M\+A\+\_\+ssymm}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssymm}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssymm (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B, }
\item[{float}]{beta, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_gaaffcd386f207f3e3a3073a803e27e3f1_gaaffcd386f207f3e3a3073a803e27e3f1}
P\+L\+A\+S\+M\+A\+\_\+ssymm -\/ Performs one of the matrix-\/matrix operations

\[ C = \alpha \times A \times B + \beta \times C \]

or

\[ C = \alpha \times B \times A + \beta \times C \]

where alpha and beta are scalars, A is an symmetric matrix and B and C are m by n matrices.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether the symmetric matrix A appears on the left or right in the operation as follows\+: = Plasma\+Left\+: \[ C = \alpha \times A \times B + \beta \times C \] = Plasma\+Right\+: \[ C = \alpha \times B \times A + \beta \times C \]\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows\+: = Plasma\+Lower\+: Only the lower triangular part of the symmetric matrix A is to be referenced. = Plasma\+Upper\+: Only the upper triangular part of the symmetric matrix A is to be referenced.\\
\hline
\mbox{\tt in}  & {\em M} & Specifies the number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & Specifies the number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & Specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is M when side = Plasma\+Left, and is N otherwise. Only the uplo triangular part is referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,ka).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\+D\+B-\/by-\/\+N matrix, where the leading M-\/by-\/\+N part of the array B must contain the matrix B.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+M).\\
\hline
\mbox{\tt in}  & {\em beta} & Specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\+D\+C-\/by-\/\+N matrix. On exit, the array is overwritten by the M by N updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaed8391eebdf7b458e7a62dbfb6caff93_gaed8391eebdf7b458e7a62dbfb6caff93}{P\+L\+A\+S\+M\+A\+\_\+ssymm\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_gac62cd0bd5b290a074c3af371972266a4_gac62cd0bd5b290a074c3af371972266a4}{P\+L\+A\+S\+M\+A\+\_\+csymm} 

\hyperlink{group__double_ga1ab6ee29131efe4804f5ff940eeb699a_ga1ab6ee29131efe4804f5ff940eeb699a}{P\+L\+A\+S\+M\+A\+\_\+dsymm} 

\hyperlink{group__float_gaaffcd386f207f3e3a3073a803e27e3f1_gaaffcd386f207f3e3a3073a803e27e3f1}{P\+L\+A\+S\+M\+A\+\_\+ssymm} 
\end{DoxySeeAlso}
\hypertarget{group__float_gafac964a38a7c62696c3b95d35108ad9b_gafac964a38a7c62696c3b95d35108ad9b}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssyr2k@{P\+L\+A\+S\+M\+A\+\_\+ssyr2k}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssyr2k@{P\+L\+A\+S\+M\+A\+\_\+ssyr2k}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssyr2k}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssyr2k (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B, }
\item[{float}]{beta, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_gafac964a38a7c62696c3b95d35108ad9b_gafac964a38a7c62696c3b95d35108ad9b}
P\+L\+A\+S\+M\+A\+\_\+ssyr2k -\/ Performs one of the symmetric rank 2k operations

\[ C = \alpha [ op( A ) \times g( op( B )' )] + \alpha [ op( B ) \times g( op( A )' )] + \beta C \], or \[ C = \alpha [ g( op( A )' ) \times op( B ) ] + \alpha [ g( op( B )' ) \times op( A ) ] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = g( X\textquotesingle{} )

where alpha and beta are real scalars, C is an n-\/by-\/n symmetric matrix and A and B are an n-\/by-\/k matrices the first case and k-\/by-\/n matrices in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of C is stored; = Plasma\+Lower\+: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or ugate transposed\+: = Plasma\+No\+Trans\+: \[ C = \alpha [ op( A ) \times g( op( B )' )] + \alpha [ op( B ) \times g( op( A )' )] + \beta C \] = Plasma\+Trans\+: \[ C = \alpha [ g( op( A )' ) \times op( B ) ] + \alpha [ g( op( B )' ) \times op( A ) ] + \beta C \]\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the A and B matrices with trans = Plasma\+No\+Trans. K specifies the number of rows of the A and B matrices with trans = Plasma\+Trans.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is K when trans = Plasma\+No\+Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A must be at least max( 1, N ), otherwise L\+D\+A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\+D\+B-\/by-\/kb matrix, where kb is K when trans = Plasma\+No\+Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B must be at least max( 1, N ), otherwise L\+D\+B must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\+D\+C-\/by-\/\+N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga1c0cbf7def70b0d7783d944051aef00e_ga1c0cbf7def70b0d7783d944051aef00e}{P\+L\+A\+S\+M\+A\+\_\+ssyr2k\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga287e372b9d1ba9615e45738e628ee2f2_ga287e372b9d1ba9615e45738e628ee2f2}{P\+L\+A\+S\+M\+A\+\_\+ssyr2k\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga5a48c1ff1b73920651249deb75b9d0b7_ga5a48c1ff1b73920651249deb75b9d0b7}{P\+L\+A\+S\+M\+A\+\_\+csyr2k} 

\hyperlink{group__double_gaf9fa0e62110092a132cd17d8f48561f0_gaf9fa0e62110092a132cd17d8f48561f0}{P\+L\+A\+S\+M\+A\+\_\+dsyr2k} 

\hyperlink{group__float_gafac964a38a7c62696c3b95d35108ad9b_gafac964a38a7c62696c3b95d35108ad9b}{P\+L\+A\+S\+M\+A\+\_\+ssyr2k} 
\end{DoxySeeAlso}
\hypertarget{group__float_gae83f0347570d23dc62dd8b298eb14ad6_gae83f0347570d23dc62dd8b298eb14ad6}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssyrk@{P\+L\+A\+S\+M\+A\+\_\+ssyrk}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssyrk@{P\+L\+A\+S\+M\+A\+\_\+ssyrk}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssyrk}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssyrk (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{beta, }
\item[{float $\ast$}]{C, }
\item[{int}]{L\+D\+C}
\end{DoxyParamCaption}
)}\label{group__float_gae83f0347570d23dc62dd8b298eb14ad6_gae83f0347570d23dc62dd8b298eb14ad6}
P\+L\+A\+S\+M\+A\+\_\+ssyrk -\/ Performs one of the hermitian rank k operations

\[ C = \alpha [ op( A ) \times g( op( A )' )] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = g( X\textquotesingle{} )

where alpha and beta are real scalars, C is an n-\/by-\/n hermitian matrix and A is an n-\/by-\/k matrix in the first case and a k-\/by-\/n matrix in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of C is stored; = Plasma\+Lower\+: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is not transposed; = Plasma\+Trans \+: A is transposed.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the matrix op( A ).\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is K when trans = Plasma\+No\+Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A must be at least max( 1, N ) if trans == Plasma\+No\+Trans, otherwise L\+D\+A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\+D\+C-\/by-\/\+N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+C} & The leading dimension of the array C. L\+D\+C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gacf870fa2eddaa1a0c47b0ac8ddecab46_gacf870fa2eddaa1a0c47b0ac8ddecab46}{P\+L\+A\+S\+M\+A\+\_\+ssyrk\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga46d83814efe8df57c26e5e48f5bb12b4_ga46d83814efe8df57c26e5e48f5bb12b4}{P\+L\+A\+S\+M\+A\+\_\+ssyrk\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_gad7bae1673afbf5b73da18c20f376cb89_gad7bae1673afbf5b73da18c20f376cb89}{P\+L\+A\+S\+M\+A\+\_\+csyrk} 

\hyperlink{group__double_gacfdac462cfb1b2d6696e353bec9fd079_gacfdac462cfb1b2d6696e353bec9fd079}{P\+L\+A\+S\+M\+A\+\_\+dsyrk} 

\hyperlink{group__float_gae83f0347570d23dc62dd8b298eb14ad6_gae83f0347570d23dc62dd8b298eb14ad6}{P\+L\+A\+S\+M\+A\+\_\+ssyrk} 
\end{DoxySeeAlso}
\hypertarget{group__float_gadfee26871dee9a24b201bc329fccd81b_gadfee26871dee9a24b201bc329fccd81b}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+ssytrd@{P\+L\+A\+S\+M\+A\+\_\+ssytrd}}
\index{P\+L\+A\+S\+M\+A\+\_\+ssytrd@{P\+L\+A\+S\+M\+A\+\_\+ssytrd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+ssytrd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+ssytrd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{jobz, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{D, }
\item[{float $\ast$}]{E, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+T, }
\item[{float $\ast$}]{Q, }
\item[{int}]{L\+D\+Q}
\end{DoxyParamCaption}
)}\label{group__float_gadfee26871dee9a24b201bc329fccd81b_gadfee26871dee9a24b201bc329fccd81b}
P\+L\+A\+S\+M\+A\+\_\+ssytrd -\/ reduces a complex Hermitian matrix A to real symmetric tridiagonal form S using a two-\/stage approach First stage\+: reduction to band tridiagonal form (unitary Q1); Second stage\+: reduction from band to tridiagonal form (unitary Q2). Let Q = Q1 $\ast$ Q2 be the global unitary transformation; Q$\ast$$\ast$\+T $\ast$ A $\ast$ Q = S.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\+: = Plasma\+No\+Vec\+: computes tridiagonal only; = Plasma\+Vec\+: computes tridiagonal and generate the orthogonal matrix Q.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\+Lower) or the upper triangle (if uplo = Plasma\+Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt out}  & {\em D} & On exit, the diagonal elements of the tridiagonal matrix\+: D(i) = A(i,i).\\
\hline
\mbox{\tt out}  & {\em E} & On exit, he off-\/diagonal elements of the tridiagonal matrix\+: E(i) = A(i,i+1) if uplo = Plasma\+Upper, E(i) = A(i+1,i) if uplo = Plasma\+Lower.\\
\hline
\mbox{\tt out}  & {\em desc\+T} & On entry, descriptor as return by P\+L\+A\+S\+M\+A\+\_\+\+Alloc\+\_\+\+Workspace\+\_\+ssytrd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\+Vec, then if return value = 0, Q contains the N-\/by-\/\+N unitary matrix Q. If jobz = Plasma\+No\+Vec, then it is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\+D\+Q} & The leading dimension of the array Q. L\+D\+Q $>$= N.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\+N\+F\+O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga48bcda071b83ef090b76b5e19aedc803_ga48bcda071b83ef090b76b5e19aedc803}{P\+L\+A\+S\+M\+A\+\_\+ssytrd\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gab6e8f0c040e24c6f71d24979685683d0_gab6e8f0c040e24c6f71d24979685683d0}{P\+L\+A\+S\+M\+A\+\_\+ssytrd\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga72efb6e6664acbda79f267c167eae41c_ga72efb6e6664acbda79f267c167eae41c}{P\+L\+A\+S\+M\+A\+\_\+chetrd} 

\hyperlink{group__double_gaebb037c30606f77404ffef513f255d5c_gaebb037c30606f77404ffef513f255d5c}{P\+L\+A\+S\+M\+A\+\_\+dsytrd} 

\hyperlink{group__float_gadfee26871dee9a24b201bc329fccd81b_gadfee26871dee9a24b201bc329fccd81b}{P\+L\+A\+S\+M\+A\+\_\+ssytrd} 
\end{DoxySeeAlso}
\hypertarget{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack@{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack}}
\index{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack@{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack (
\begin{DoxyParamCaption}
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{A, }
\item[{float $\ast$}]{Af77, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}
P\+L\+A\+S\+M\+A\+\_\+\+Tile\+\_\+to\+\_\+\+Lapack -\/ Conversion from tile layout to L\+A\+P\+A\+C\+K layout. It automatically infers the layout translation mode base on the values of Af77 and A-\/$>$mat pointers. If (A-\/$>$mat == Af77 $\vert$$\vert$ A-\/$>$mat == N\+U\+L\+L $\vert$$\vert$ Af77 == N\+U\+L\+L), P\+L\+A\+S\+M\+A\+\_\+\+T\+R\+A\+N\+S\+L\+A\+T\+I\+O\+N\+\_\+\+M\+O\+D\+E is set to P\+L\+A\+S\+M\+A\+\_\+\+I\+N\+P\+L\+A\+C\+E to do inplace layout translation of the matrix. If (A-\/$>$mat != Af77 \&\& A-\/$>$mat != N\+U\+L\+L \&\& Af77 != N\+U\+L\+L), P\+L\+A\+S\+M\+A\+\_\+\+T\+R\+A\+N\+S\+L\+A\+T\+I\+O\+N\+\_\+\+M\+O\+D\+E is set to P\+L\+A\+S\+M\+A\+\_\+\+O\+U\+T\+O\+F\+P\+L\+A\+C\+E to do out of place layout translation of the matrix. Both A-\/$>$mat and Af77 have to be allocated to store the full matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em A} & Descriptor of the P\+L\+A\+S\+M\+A matrix in tile layout.\\
\hline
\mbox{\tt in,out}  & {\em Af77} & L\+A\+P\+A\+C\+K matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the matrix Af77.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile__Async_gab7028085811f206f5206599f0ee8f478_gab7028085811f206f5206599f0ee8f478}{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack\+\_\+\+Async} 

\hyperlink{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}{P\+L\+A\+S\+M\+A\+\_\+s\+Lapack\+\_\+to\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga7dce142b920d792a0443efcc922c71fc_ga7dce142b920d792a0443efcc922c71fc}{P\+L\+A\+S\+M\+A\+\_\+c\+Tile\+\_\+to\+\_\+\+Lapack} 

\hyperlink{group__double_ga1a9152c4ac00de6cafe8a5a4ad6718df_ga1a9152c4ac00de6cafe8a5a4ad6718df}{P\+L\+A\+S\+M\+A\+\_\+d\+Tile\+\_\+to\+\_\+\+Lapack} 

\hyperlink{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}{P\+L\+A\+S\+M\+A\+\_\+s\+Tile\+\_\+to\+\_\+\+Lapack} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga5395fb5a2b6c3f123e3fc7e5fba0dc56_ga5395fb5a2b6c3f123e3fc7e5fba0dc56}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+stradd@{P\+L\+A\+S\+M\+A\+\_\+stradd}}
\index{P\+L\+A\+S\+M\+A\+\_\+stradd@{P\+L\+A\+S\+M\+A\+\_\+stradd}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+stradd}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+stradd (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float}]{beta, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga5395fb5a2b6c3f123e3fc7e5fba0dc56_ga5395fb5a2b6c3f123e3fc7e5fba0dc56}
P\+L\+A\+S\+M\+A\+\_\+stradd -\/ Performs a matrix addition similarly to the pstradd() function from the P\+B\+L\+A\+S library\+:

\[ C = \alpha op( A ) + \beta B \],

where op( X ) is one of

op( X ) = X or op( X ) = X\textquotesingle{} or op( X ) = g( X\textquotesingle{} )

alpha and beta are scalars, and A, and B are two trapezoidal matrices, with op( A ) and B two m by n matrices.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the shape of A and B matrices\+: = Plasma\+Upper\+Lower\+: A and B are general matrices. = Plasma\+Upper\+: op(\+A) and B are upper trapezoidal matrices. = Plasma\+Lower\+: op(\+A) and B are lower trapezoidal matrices.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em M} & M specifies the number of rows of the matrix op( A ) and of the matrix B. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the number of columns of the matrix op( A ) and of the matrix B. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\+D\+A-\/by-\/ka matrix, where ka is N when trans = Plasma\+No\+Trans, and is M otherwise.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+K), where K is M when trans = Plasma\+No\+Trans, and is N when otherwise.\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em B} & B is a L\+D\+B-\/by-\/\+N matrix.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaf9bfae96f9bb34fa3008c593a5b5e948_gaf9bfae96f9bb34fa3008c593a5b5e948}{P\+L\+A\+S\+M\+A\+\_\+stradd\+\_\+\+Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga87ddb07f67b802e8e1cd0fde868680d4_ga87ddb07f67b802e8e1cd0fde868680d4}{P\+L\+A\+S\+M\+A\+\_\+ctradd} 

\hyperlink{group__double_gaac3009e1ff5468b93a66e6fd21c2221a_gaac3009e1ff5468b93a66e6fd21c2221a}{P\+L\+A\+S\+M\+A\+\_\+dtradd} 

\hyperlink{group__float_ga5395fb5a2b6c3f123e3fc7e5fba0dc56_ga5395fb5a2b6c3f123e3fc7e5fba0dc56}{P\+L\+A\+S\+M\+A\+\_\+stradd} 
\end{DoxySeeAlso}
\hypertarget{group__float_gabbc2cf7c018815bd2c1ce8a6623b2813_gabbc2cf7c018815bd2c1ce8a6623b2813}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+strmm@{P\+L\+A\+S\+M\+A\+\_\+strmm}}
\index{P\+L\+A\+S\+M\+A\+\_\+strmm@{P\+L\+A\+S\+M\+A\+\_\+strmm}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+strmm}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+strmm (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans\+A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_gabbc2cf7c018815bd2c1ce8a6623b2813_gabbc2cf7c018815bd2c1ce8a6623b2813}
P\+L\+A\+S\+M\+A\+\_\+strmm -\/ Computes B = alpha$\ast$op( A )$\ast$\+B or B = alpha$\ast$\+B$\ast$op( A ).


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\+: = Plasma\+Left\+: alpha$\ast$op( A )$\ast$\+B = Plasma\+Right\+: alpha$\ast$\+B$\ast$op( A )\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\+A} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is transposed; = Plasma\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\+: = Plasma\+Non\+Unit\+: A is non unit; = Plasma\+Unit\+: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\+Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_gaa0df9bf7d0c90ae68302342d80000324_gaa0df9bf7d0c90ae68302342d80000324}{P\+L\+A\+S\+M\+A\+\_\+strmm\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga3a6fbd4ed9e9625697c188247e6bce86_ga3a6fbd4ed9e9625697c188247e6bce86}{P\+L\+A\+S\+M\+A\+\_\+strmm\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga17234cfdde42bd11866b3435a9a8295a_ga17234cfdde42bd11866b3435a9a8295a}{P\+L\+A\+S\+M\+A\+\_\+ctrmm} 

\hyperlink{group__double_ga16876a8b4e9148ba2c8f4d37dca9eef4_ga16876a8b4e9148ba2c8f4d37dca9eef4}{P\+L\+A\+S\+M\+A\+\_\+dtrmm} 

\hyperlink{group__float_gabbc2cf7c018815bd2c1ce8a6623b2813_gabbc2cf7c018815bd2c1ce8a6623b2813}{P\+L\+A\+S\+M\+A\+\_\+strmm} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga572e80d04d4e9701bf3dd73d1f96d54c_ga572e80d04d4e9701bf3dd73d1f96d54c}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+strsm@{P\+L\+A\+S\+M\+A\+\_\+strsm}}
\index{P\+L\+A\+S\+M\+A\+\_\+strsm@{P\+L\+A\+S\+M\+A\+\_\+strsm}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+strsm}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+strsm (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans\+A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga572e80d04d4e9701bf3dd73d1f96d54c_ga572e80d04d4e9701bf3dd73d1f96d54c}
P\+L\+A\+S\+M\+A\+\_\+strsm -\/ Computes triangular solve A$\ast$\+X = B or X$\ast$\+A = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\+: = Plasma\+Left\+: A$\ast$\+X = B = Plasma\+Right\+: X$\ast$\+A = B\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\+A} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is transposed; = Plasma\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\+: = Plasma\+Non\+Unit\+: A is non unit; = Plasma\+Unit\+: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\+Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga0425cfe286874d53b29fe338b9affc12_ga0425cfe286874d53b29fe338b9affc12}{P\+L\+A\+S\+M\+A\+\_\+strsm\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga0d73c1a4354ba065c6934e54aeeca7b0_ga0d73c1a4354ba065c6934e54aeeca7b0}{P\+L\+A\+S\+M\+A\+\_\+strsm\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga59907687253f7978f60e1d56d6fe941c_ga59907687253f7978f60e1d56d6fe941c}{P\+L\+A\+S\+M\+A\+\_\+ctrsm} 

\hyperlink{group__double_ga7dab3739b47f3f77f68cb6166638f507_ga7dab3739b47f3f77f68cb6166638f507}{P\+L\+A\+S\+M\+A\+\_\+dtrsm} 

\hyperlink{group__float_ga572e80d04d4e9701bf3dd73d1f96d54c_ga572e80d04d4e9701bf3dd73d1f96d54c}{P\+L\+A\+S\+M\+A\+\_\+strsm} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga245da4f8540c426fde27a50eff39b64a_ga245da4f8540c426fde27a50eff39b64a}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+strsmpl@{P\+L\+A\+S\+M\+A\+\_\+strsmpl}}
\index{P\+L\+A\+S\+M\+A\+\_\+strsmpl@{P\+L\+A\+S\+M\+A\+\_\+strsmpl}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+strsmpl}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+strsmpl (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{{\bf P\+L\+A\+S\+M\+A\+\_\+desc} $\ast$}]{desc\+L, }
\item[{const int $\ast$}]{I\+P\+I\+V, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga245da4f8540c426fde27a50eff39b64a_ga245da4f8540c426fde27a50eff39b64a}
P\+L\+A\+S\+M\+A\+\_\+strsmpl -\/ Performs the forward substitution step of solving a system of linear equations after the tile L\+U factorization of the matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factor L from the factorization, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in}  & {\em desc\+L} & Auxiliary factorization data, related to the tile L factor, computed by P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv.\\
\hline
\mbox{\tt in}  & {\em I\+P\+I\+V} & The pivot indices from P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv (not equivalent to L\+A\+P\+A\+C\+K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga776ea81e7a0a701390b918ae3ffe53b0_ga776ea81e7a0a701390b918ae3ffe53b0}{P\+L\+A\+S\+M\+A\+\_\+strsmpl\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga45863a6ca53dd797a98db579bb58583f_ga45863a6ca53dd797a98db579bb58583f}{P\+L\+A\+S\+M\+A\+\_\+strsmpl\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga6f1a79fbd5420d08a1c0668c5f475f4f_ga6f1a79fbd5420d08a1c0668c5f475f4f}{P\+L\+A\+S\+M\+A\+\_\+ctrsmpl} 

\hyperlink{group__double_ga1ee42a61d4bf0294ed216add96e6ff37_ga1ee42a61d4bf0294ed216add96e6ff37}{P\+L\+A\+S\+M\+A\+\_\+dtrsmpl} 

\hyperlink{group__float_ga245da4f8540c426fde27a50eff39b64a_ga245da4f8540c426fde27a50eff39b64a}{P\+L\+A\+S\+M\+A\+\_\+strsmpl} 

\hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\+L\+A\+S\+M\+A\+\_\+sgetrf\+\_\+incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__float_ga7713151eac0c0ff54c5a6aac1957b5e0_ga7713151eac0c0ff54c5a6aac1957b5e0}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+strsmrv@{P\+L\+A\+S\+M\+A\+\_\+strsmrv}}
\index{P\+L\+A\+S\+M\+A\+\_\+strsmrv@{P\+L\+A\+S\+M\+A\+\_\+strsmrv}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+strsmrv}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+strsmrv (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{side, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{trans\+A, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\+R\+H\+S, }
\item[{float}]{alpha, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A, }
\item[{float $\ast$}]{B, }
\item[{int}]{L\+D\+B}
\end{DoxyParamCaption}
)}\label{group__float_ga7713151eac0c0ff54c5a6aac1957b5e0_ga7713151eac0c0ff54c5a6aac1957b5e0}
P\+L\+A\+S\+M\+A\+\_\+strsmrv -\/ Computes triangular solve A$\ast$\+X = B or X$\ast$\+A = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\+: = Plasma\+Left\+: A$\ast$\+X = B = Plasma\+Right\+: X$\ast$\+A = B\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\+: = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\+A} & Specifies whether the matrix A is transposed, not transposed or ugate transposed\+: = Plasma\+No\+Trans\+: A is transposed; = Plasma\+Trans\+: A is not transposed; = Plasma\+Trans\+: A is ugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\+: = Plasma\+Non\+Unit\+: A is non unit; = Plasma\+Unit\+: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\+R\+H\+S} & The number of right hand sides, i.\+e., the number of columns of the matrix B. N\+R\+H\+S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\+Upper, the leading N-\/by-\/\+N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\+Lower, the leading N-\/by-\/\+N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\+Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\+N\+R\+H\+S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\+N\+R\+H\+S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\+D\+B} & The leading dimension of the array B. L\+D\+B $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga197a6b89cd535edaa07c9deb1d583f2d_ga197a6b89cd535edaa07c9deb1d583f2d}{P\+L\+A\+S\+M\+A\+\_\+strsmrv\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_ga7fb1003bbfd4febbb772726766eaae29_ga7fb1003bbfd4febbb772726766eaae29}{P\+L\+A\+S\+M\+A\+\_\+strsmrv\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga4932d66d31f7970a6cab8381d373eb12_ga4932d66d31f7970a6cab8381d373eb12}{P\+L\+A\+S\+M\+A\+\_\+ctrsmrv} 

\hyperlink{group__double_ga01879443f745172ea8165d4882136d36_ga01879443f745172ea8165d4882136d36}{P\+L\+A\+S\+M\+A\+\_\+dtrsmrv} 

\hyperlink{group__float_ga7713151eac0c0ff54c5a6aac1957b5e0_ga7713151eac0c0ff54c5a6aac1957b5e0}{P\+L\+A\+S\+M\+A\+\_\+strsmrv} 
\end{DoxySeeAlso}
\hypertarget{group__float_gaaf0df7b8ff03a270a25da71b9f133abb_gaaf0df7b8ff03a270a25da71b9f133abb}{}\index{Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}!P\+L\+A\+S\+M\+A\+\_\+strtri@{P\+L\+A\+S\+M\+A\+\_\+strtri}}
\index{P\+L\+A\+S\+M\+A\+\_\+strtri@{P\+L\+A\+S\+M\+A\+\_\+strtri}!Simple Interface -\/ Single Real@{Simple Interface -\/ Single Real}}
\subsubsection[{P\+L\+A\+S\+M\+A\+\_\+strtri}]{\setlength{\rightskip}{0pt plus 5cm}int P\+L\+A\+S\+M\+A\+\_\+strtri (
\begin{DoxyParamCaption}
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{uplo, }
\item[{P\+L\+A\+S\+M\+A\+\_\+enum}]{diag, }
\item[{int}]{N, }
\item[{float $\ast$}]{A, }
\item[{int}]{L\+D\+A}
\end{DoxyParamCaption}
)}\label{group__float_gaaf0df7b8ff03a270a25da71b9f133abb_gaaf0df7b8ff03a270a25da71b9f133abb}
P\+L\+A\+S\+M\+A\+\_\+strtri -\/ Computes the inverse of a complex upper or lower triangular matrix A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\+Upper\+: Upper triangle of A is stored; = Plasma\+Lower\+: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em diag} & = Plasma\+Non\+Unit\+: A is non-\/unit triangular; = Plasma\+Unit\+: A is unit triangular.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular matrix A. If U\+P\+L\+O = \textquotesingle{}U\textquotesingle{}, the leading N-\/by-\/\+N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If U\+P\+L\+O = \textquotesingle{}L\textquotesingle{}, the leading N-\/by-\/\+N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If D\+I\+A\+G = \textquotesingle{}U\textquotesingle{}, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.\\
\hline
\mbox{\tt in}  & {\em L\+D\+A} & The leading dimension of the array A. L\+D\+A $>$= max(1,\+N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\+L\+A\+S\+M\+A\+\_\+\+S\+U\+C\+C\+E\+S\+S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See also}
\hyperlink{group__float__Tile_ga8a53f6df17ef16abe97a991c737e82dc_ga8a53f6df17ef16abe97a991c737e82dc}{P\+L\+A\+S\+M\+A\+\_\+strtri\+\_\+\+Tile} 

\hyperlink{group__float__Tile__Async_gaba8ab52eb1dd9bbca882c32faa829efe_gaba8ab52eb1dd9bbca882c32faa829efe}{P\+L\+A\+S\+M\+A\+\_\+strtri\+\_\+\+Tile\+\_\+\+Async} 

\hyperlink{group__PLASMA__Complex32__t_ga25e718997c7c1fd6f599d7b3a04fddad_ga25e718997c7c1fd6f599d7b3a04fddad}{P\+L\+A\+S\+M\+A\+\_\+ctrtri} 

\hyperlink{group__double_ga3968f78f69610b681ab7d6c411f92796_ga3968f78f69610b681ab7d6c411f92796}{P\+L\+A\+S\+M\+A\+\_\+dtrtri} 

\hyperlink{group__float_gaaf0df7b8ff03a270a25da71b9f133abb_gaaf0df7b8ff03a270a25da71b9f133abb}{P\+L\+A\+S\+M\+A\+\_\+strtri} 

\hyperlink{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{P\+L\+A\+S\+M\+A\+\_\+spotri} 
\end{DoxySeeAlso}
