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LAPACK LU-based substitution functions (getrs) | |
void | blaze::getrs (char trans, int n, int nrhs, const float *A, int lda, const int *ipiv, float *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a general single precision linear system of equations ( ![]() | |
void | blaze::getrs (char trans, int n, int nrhs, const double *A, int lda, const int *ipiv, double *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a general double precision linear system of equations ( ![]() | |
void | blaze::getrs (char trans, int n, int nrhs, const complex< float > *A, int lda, const int *ipiv, complex< float > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a general single precision complex linear system of equations ( ![]() | |
void | blaze::getrs (char trans, int n, int nrhs, const complex< double > *A, int lda, const int *ipiv, complex< double > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a general double precision complex linear system of equations ( ![]() | |
template<typename MT , bool SO, typename VT , bool TF> | |
void | blaze::getrs (const DenseMatrix< MT, SO > &A, DenseVector< VT, TF > &b, char trans, const int *ipiv) |
LAPACK kernel for the substitution step of solving a general linear system of equations ( ![]() | |
template<typename MT1 , bool SO1, typename MT2 , bool SO2> | |
void | blaze::getrs (const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &B, char trans, const int *ipiv) |
LAPACK kernel for the substitution step of solving a general linear system of equations ( ![]() | |
LAPACK LDLH-based substitution functions (hetrs) | |
void | blaze::hetrs (char uplo, int n, int nrhs, const complex< float > *A, int lda, const int *ipiv, complex< float > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision complex linear system of equations ( ![]() | |
void | blaze::hetrs (char uplo, int n, int nrhs, const complex< double > *A, int lda, const int *ipiv, complex< double > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision complex linear system of equations ( ![]() | |
template<typename MT , bool SO, typename VT , bool TF> | |
void | blaze::hetrs (const DenseMatrix< MT, SO > &A, DenseVector< VT, TF > &b, char uplo, const int *ipiv) |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ![]() | |
template<typename MT1 , bool SO1, typename MT2 , bool SO2> | |
void | blaze::hetrs (const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &B, char uplo, const int *ipiv) |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ![]() | |
LAPACK LLH-based substitution functions (potrs) | |
void | blaze::potrs (char uplo, int n, int nrhs, const float *A, int lda, float *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a positive definite single precision linear system of equations ( ![]() | |
void | blaze::potrs (char uplo, int n, int nrhs, const double *A, int lda, double *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a positive definite double precision linear system of equations ( ![]() | |
void | blaze::potrs (char uplo, int n, int nrhs, const complex< float > *A, int lda, complex< float > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a positive definite single precision complex linear system of equations ( ![]() | |
void | blaze::potrs (char uplo, int n, int nrhs, const complex< double > *A, int lda, complex< double > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a positive definite double precision complex linear system of equations ( ![]() | |
template<typename MT , bool SO, typename VT , bool TF> | |
void | blaze::potrs (const DenseMatrix< MT, SO > &A, DenseVector< VT, TF > &b, char uplo) |
LAPACK kernel for the substitution step of solving a positive definite linear system of equations ( ![]() | |
template<typename MT1 , bool SO1, typename MT2 , bool SO2> | |
void | blaze::potrs (const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &B, char uplo) |
LAPACK kernel for the substitution step of solving a positive definite linear system of equations ( ![]() | |
LAPACK LDLT-based substitution functions (sytrs) | |
void | blaze::sytrs (char uplo, int n, int nrhs, const float *A, int lda, const int *ipiv, float *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision linear system of equations ( ![]() | |
void | blaze::sytrs (char uplo, int n, int nrhs, const double *A, int lda, const int *ipiv, double *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision linear system of equations ( ![]() | |
void | blaze::sytrs (char uplo, int n, int nrhs, const complex< float > *A, int lda, const int *ipiv, complex< float > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision complex linear system of equations ( ![]() | |
void | blaze::sytrs (char uplo, int n, int nrhs, const complex< double > *A, int lda, const int *ipiv, complex< double > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision complex linear system of equations ( ![]() | |
template<typename MT , bool SO, typename VT , bool TF> | |
void | blaze::sytrs (const DenseMatrix< MT, SO > &A, DenseVector< VT, TF > &b, char uplo, const int *ipiv) |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ![]() | |
template<typename MT1 , bool SO1, typename MT2 , bool SO2> | |
void | blaze::sytrs (const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &B, char uplo, const int *ipiv) |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ![]() | |
LAPACK triangular substitution functions (trtrs) | |
void | blaze::trtrs (char uplo, char trans, char diag, int n, int nrhs, const float *A, int lda, float *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a triangular single precision linear system of equations ( ![]() | |
void | blaze::trtrs (char uplo, char trans, char diag, int n, int nrhs, const double *A, int lda, double *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a triangular double precision linear system of equations ( ![]() | |
void | blaze::trtrs (char uplo, char trans, char diag, int n, int nrhs, const complex< float > *A, int lda, complex< float > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a triangular single precision complex linear system of equations ( ![]() | |
void | blaze::trtrs (char uplo, char trans, char diag, int n, int nrhs, const complex< double > *A, int lda, complex< double > *B, int ldb, int *info) |
LAPACK kernel for the substitution step of solving a triangular double precision complex linear system of equations ( ![]() | |
template<typename MT , bool SO, typename VT , bool TF> | |
void | blaze::trtrs (const DenseMatrix< MT, SO > &A, DenseVector< VT, TF > &b, char uplo, char trans, char diag) |
LAPACK kernel for the substitution step of solving a triangular linear system of equations ( ![]() | |
template<typename MT1 , bool SO1, typename MT2 , bool SO2> | |
void | blaze::trtrs (const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &B, char uplo, char trans, char diag) |
LAPACK kernel for the substitution step of solving a triangular linear system of equations ( ![]() | |
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inline |
LAPACK kernel for the substitution step of solving a general single precision linear system of equations ( ).
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK sgetrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix that has already been factorized by the sgetrf() function and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the sgetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a general double precision linear system of equations ( ).
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK dgetrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix that has already been factorized by the dgetrf() function and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the dgetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a general single precision complex linear system of equations ( ).
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision complex column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK cgetrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix that has already been factorized by the cgetrf() function and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the cgetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a general double precision complex linear system of equations ( ).
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision complex column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK zgetrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix that has already been factorized by the zgetrf() function and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the zgetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a general linear system of equations ( ).
A | The system matrix. |
b | The right-hand side vector. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid trans argument provided. |
This function uses the LAPACK getrs() functions to perform the substitution step to compute the solution to the general system of linear equations:
In this context the general system matrix A is a n-by-n matrix that has already been factorized by the getrf() functions and x and b are n-dimensional vectors. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the vector b contains the solution of the linear system of equations. The function fails if ...
In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the getrs() functions (i.e. sgetrs(), dgetrs(), cgetrs(), and zgetrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a general linear system of equations ( ).
A | The system matrix. |
B | The matrix of right-hand sides. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid trans argument provided. |
std::invalid_argument | Matrix sizes do not match. |
This function uses the LAPACK getrs() functions to perform the substitution step to compute the solution to the general system of linear equations:
In this context the general system matrix A is a n-by-n matrix that has already been factorized by the getrf() functions and X and B are either row-major m-by-n matrices or column-major n-by-m matrices. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the matrix B contains the solutions of the linear system of equations. The function fails if ...
In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the getrs() functions (i.e. sgetrs(), dgetrs(), cgetrs(), and zgetrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the single precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK chetrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the chetrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the chetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the double precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK zhetrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the zhetrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the zhetrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ).
A | The system matrix. |
b | The right-hand side vector. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
This function uses the LAPACK hetrs() functions to perform the substitution step to compute the solution to the system of symmetric indefinite linear equations:
In this context the symmetric indefinite system matrix A is a n-by-n matrix that has already been factorized by the hetrf() functions and x and b are n-dimensional vectors. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the vector b contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the hetrs() functions (i.e. chetrs() and zhetrs()) see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ).
A | The system matrix. |
B | The matrix of right-hand sides. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
std::invalid_argument | Matrix sizes do not match. |
This function uses the LAPACK hetrs() functions to perform the substitution step to compute the solution to a system of symmetric indefinite linear equations:
In this context the symmetric indefinite system matrix A is a n-by-n matrix that has already been factorized by the hetrf() functions and X and B are either row-major m-by-n matrices or column-major n-by-m matrices. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the matrix B contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the hetrs() functions (i.e. chetrs() and zhetrs()) see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite single precision linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
B | Pointer to the first element of the single precision column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK spotrs() function to perform the substitution step to compute the solution to the positive definite system of linear equations , where A is a n-by-n matrix that has already been factorized by the spotrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the spotrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite double precision linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
B | Pointer to the first element of the double precision column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK dpotrs() function to perform the substitution step to compute the solution to the positive definite system of linear equations , where A is a n-by-n matrix that has already been factorized by the dpotrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the dpotrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite single precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
B | Pointer to the first element of the single precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK cpotrs() function to perform the substitution step to compute the solution to the positive definite system of linear equations , where A is a n-by-n matrix that has already been factorized by the cpotrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the cpotrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite double precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
B | Pointer to the first element of the double precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK zpotrs() function to perform the substitution step to compute the solution to the positive definite system of linear equations , where A is a n-by-n matrix that has already been factorized by the zpotrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the zpotrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite linear system of equations ( ).
A | The system matrix. |
b | The right-hand side vector. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
This function uses the LAPACK potrs() functions to perform the substitution step to compute the solution to the system of positive definite linear equations:
In this context the positive definite system matrix A is a n-by-n matrix that has already been factorized by the potrf() functions and x and b are n-dimensional vectors. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the vector b contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the potrs() functions (i.e. spotrs(), dpotrs(), cpotrs(), and zpotrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a positive definite linear system of equations ( ).
A | The system matrix. |
B | The matrix of right-hand sides. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
std::invalid_argument | Matrix sizes do not match. |
This function uses the LAPACK potrs() functions to perform the substitution step to compute the solution to a system of positive definite linear equations:
In this context the positive definite system matrix A is a n-by-n matrix that has already been factorized by the potrf() functions and X and B are either row-major m-by-n matrices or column-major n-by-m matrices. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the matrix B contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the potrs() functions (i.e. spotrs(), dpotrs(), cpotrs(), and zpotrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
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inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the single precision column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK ssytrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the ssytrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the ssytrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the double precision column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK dsytrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the dsytrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the dsytrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite single precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the single precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK csytrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the csytrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the csytrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite double precision complex linear system of equations ( ).
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision complex column-major square matrix. |
lda | The total number of elements between two columns of matrix A ![]() |
ipiv | Auxiliary array of size n for the pivot indices. |
B | Pointer to the first element of the double precision complex column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK zsytrs() function to perform the substitution step to compute the solution to the symmetric indefinite system of linear equations , where A is a n-by-n matrix that has already been factorized by the zsytrf() function and X and B are column-major n-by-nrhs matrices.
The info argument provides feedback on the success of the function call:
For more information on the zsytrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ).
A | The system matrix. |
b | The right-hand side vector. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
This function uses the LAPACK sytrs() functions to perform the substitution step to compute the solution to the system of symmetric indefinite linear equations:
In this context the symmetric indefinite system matrix A is a n-by-n matrix that has already been factorized by the sytrf() functions and x and b are n-dimensional vectors. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the vector b contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the sytrs() functions (i.e. ssytrs(), dsytrs(), csytrs(), and zsytrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a symmetric indefinite linear system of equations ( ).
A | The system matrix. |
B | The matrix of right-hand sides. |
uplo | 'L' to use the lower part of the matrix, 'U' to use the upper part. |
ipiv | Auxiliary array of size n for the pivot indices. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
std::invalid_argument | Matrix sizes do not match. |
This function uses the LAPACK sytrs() functions to perform the substitution step to compute the solution to a system of symmetric indefinite linear equations:
In this context the symmetric indefinite system matrix A is a n-by-n matrix that has already been factorized by the sytrf() functions and X and B are either row-major m-by-n matrices or column-major n-by-m matrices. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the matrix B contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the sytrs() functions (i.e. ssytrs(), dsytrs(), csytrs(), and zsytrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular single precision linear system of equations ( ).
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK strtrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the strtrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular double precision linear system of equations ( ).
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK dtrtrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the dtrtrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular single precision complex linear system of equations ( ).
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the single precision complex column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK ctrtrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the ctrtrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular double precision complex linear system of equations ( ).
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
n | The number of rows/columns of the column-major matrix ![]() |
nrhs | The number of right-hand side vectors ![]() |
A | Pointer to the first element of the double precision complex column-major square matrix. |
lda | The total number of elements between two columns of the matrix ![]() |
B | Pointer to the first element of the column-major matrix. |
ldb | The total number of elements between two columns of matrix B ![]() |
info | Return code of the function call. |
This function uses the LAPACK ztrtrs() function to perform the substitution step to compute the solution to the general system of linear equations ,
, or
, where A is a n-by-n matrix and X and B are column-major n-by-nrhs matrices. The trans argument specifies the form of the linear system of equations:
The info argument provides feedback on the success of the function call:
For more information on the ztrtrs() function, see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular linear system of equations ( ).
A | The system matrix. |
b | The right-hand side vector. |
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
std::invalid_argument | Invalid trans argument provided. |
std::invalid_argument | Invalid diag argument provided. |
This function uses the LAPACK trtrs() functions to perform the substitution step to compute the solution to the triangular system of linear equations:
In this context the triangular system matrix A is a n-by-n matrix and x and b are n-dimensional vectors. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the vector b contains the solution of the linear system of equations. The function fails if ...
'L'
nor 'U'
;'N'
nor 'T'
nor 'C'
;'U'
nor 'N'
.In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the trtrs() functions (i.e. strtrs(), dtrtrs(), ctrtrs(), and ztrtrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/
|
inline |
LAPACK kernel for the substitution step of solving a triangular linear system of equations ( ).
A | The system matrix. |
B | The matrix of right-hand sides. |
uplo | 'L' in case of a lower matrix, 'U' in case of an upper matrix. |
trans | 'N' for ![]() 'T' for ![]() C for ![]() |
diag | 'U' in case of a unitriangular matrix, 'N' otherwise. |
std::invalid_argument | Invalid non-square matrix provided. |
std::invalid_argument | Invalid uplo argument provided. |
std::invalid_argument | Invalid trans argument provided. |
std::invalid_argument | Invalid diag argument provided. |
std::invalid_argument | Matrix sizes do not match. |
This function uses the LAPACK getrs() functions to perform the substitution step to compute the solution to the triangular system of linear equations:
In this context the triangular system matrix A is a n-by-n matrix and X and B are either row-major m-by-n matrices or column-major n-by-m matrices. Note that the function only works for general, non-adapted matrices with float
, double
, complex<float>
, or complex<double>
element type. The attempt to call the function with adaptors or matrices of any other element type results in a compile time error!
If the function exits successfully, the matrix B contains the solutions of the linear system of equations. The function fails if ...
'L'
nor 'U'
;'N'
nor 'T'
nor 'C'
;'U'
nor 'N'
;In all failure cases a std::invalid_argument exception is thrown.
Examples:
For more information on the trtrs() functions (i.e. strtrs(), dtrtrs(), ctrtrs(), and ztrtrs()), see the LAPACK online documentation browser:
http://www.netlib.org/lapack/explore-html/