LAPACK++
2022.05.00
LAPACK C++ API
|
Functions | |
double | lapack::langb (lapack::Norm norm, int64_t n, int64_t kl, int64_t ku, double const *AB, int64_t ldab) |
float | lapack::langb (lapack::Norm norm, int64_t n, int64_t kl, int64_t ku, float const *AB, int64_t ldab) |
double | lapack::langb (lapack::Norm norm, int64_t n, int64_t kl, int64_t ku, std::complex< double > const *AB, int64_t ldab) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n band matrix A, with kl sub-diagonals and ku super-diagonals. More... | |
float | lapack::langb (lapack::Norm norm, int64_t n, int64_t kl, int64_t ku, std::complex< float > const *AB, int64_t ldab) |
double | lapack::lange (lapack::Norm norm, int64_t m, int64_t n, double const *A, int64_t lda) |
float | lapack::lange (lapack::Norm norm, int64_t m, int64_t n, float const *A, int64_t lda) |
double | lapack::lange (lapack::Norm norm, int64_t m, int64_t n, std::complex< double > const *A, int64_t lda) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex matrix A. More... | |
float | lapack::lange (lapack::Norm norm, int64_t m, int64_t n, std::complex< float > const *A, int64_t lda) |
double | lapack::langt (lapack::Norm norm, int64_t n, double const *DL, double const *D, double const *DU) |
float | lapack::langt (lapack::Norm norm, int64_t n, float const *DL, float const *D, float const *DU) |
double | lapack::langt (lapack::Norm norm, int64_t n, std::complex< double > const *DL, std::complex< double > const *D, std::complex< double > const *DU) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a tridiagonal matrix A. More... | |
float | lapack::langt (lapack::Norm norm, int64_t n, std::complex< float > const *DL, std::complex< float > const *D, std::complex< float > const *DU) |
double | lapack::lanhb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, double const *AB, int64_t ldab) |
float | lapack::lanhb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, float const *AB, int64_t ldab) |
double | lapack::lanhb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, std::complex< double > const *AB, int64_t ldab) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n hermitian band matrix A, with kd super-diagonals. More... | |
float | lapack::lanhb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, std::complex< float > const *AB, int64_t ldab) |
double | lapack::lanhe (lapack::Norm norm, lapack::Uplo uplo, int64_t n, double const *A, int64_t lda) |
float | lapack::lanhe (lapack::Norm norm, lapack::Uplo uplo, int64_t n, float const *A, int64_t lda) |
double | lapack::lanhe (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< double > const *A, int64_t lda) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex hermitian matrix A. More... | |
float | lapack::lanhe (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< float > const *A, int64_t lda) |
double | lapack::lanhp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, double const *AP) |
float | lapack::lanhp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, float const *AP) |
double | lapack::lanhp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< double > const *AP) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form. More... | |
float | lapack::lanhp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< float > const *AP) |
double | lapack::lanhs (lapack::Norm norm, int64_t n, double const *A, int64_t lda) |
float | lapack::lanhs (lapack::Norm norm, int64_t n, float const *A, int64_t lda) |
double | lapack::lanhs (lapack::Norm norm, int64_t n, std::complex< double > const *A, int64_t lda) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a Hessenberg matrix A. More... | |
float | lapack::lanhs (lapack::Norm norm, int64_t n, std::complex< float > const *A, int64_t lda) |
double | lapack::lanht (lapack::Norm norm, int64_t n, double const *D, std::complex< double > const *E) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a Hermitian tridiagonal matrix A. More... | |
double | lapack::lanht (lapack::Norm norm, int64_t n, double const *D, double const *E) |
float | lapack::lanht (lapack::Norm norm, int64_t n, float const *D, float const *E) |
float | lapack::lanht (lapack::Norm norm, int64_t n, float const *D, std::complex< float > const *E) |
double | lapack::lansb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, double const *AB, int64_t ldab) |
float | lapack::lansb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, float const *AB, int64_t ldab) |
double | lapack::lansb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, std::complex< double > const *AB, int64_t ldab) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n symmetric band matrix A, with kd super-diagonals. More... | |
float | lapack::lansb (lapack::Norm norm, lapack::Uplo uplo, int64_t n, int64_t kd, std::complex< float > const *AB, int64_t ldab) |
double | lapack::lansp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, double const *AP) |
float | lapack::lansp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, float const *AP) |
double | lapack::lansp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< double > const *AP) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form. More... | |
float | lapack::lansp (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< float > const *AP) |
double | lapack::lanst (lapack::Norm norm, int64_t n, double const *D, double const *E) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a symmetric tridiagonal matrix A. More... | |
float | lapack::lanst (lapack::Norm norm, int64_t n, float const *D, float const *E) |
double | lapack::lansy (lapack::Norm norm, lapack::Uplo uplo, int64_t n, double const *A, int64_t lda) |
float | lapack::lansy (lapack::Norm norm, lapack::Uplo uplo, int64_t n, float const *A, int64_t lda) |
double | lapack::lansy (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< double > const *A, int64_t lda) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex symmetric matrix A. More... | |
float | lapack::lansy (lapack::Norm norm, lapack::Uplo uplo, int64_t n, std::complex< float > const *A, int64_t lda) |
double | lapack::lantb (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, int64_t k, double const *AB, int64_t ldab) |
float | lapack::lantb (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, int64_t k, float const *AB, int64_t ldab) |
double | lapack::lantb (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, int64_t k, std::complex< double > const *AB, int64_t ldab) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n triangular band matrix A, with (k + 1) diagonals. More... | |
float | lapack::lantb (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, int64_t k, std::complex< float > const *AB, int64_t ldab) |
double | lapack::lantp (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, double const *AP) |
float | lapack::lantp (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, float const *AP) |
double | lapack::lantp (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, std::complex< double > const *AP) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form. More... | |
float | lapack::lantp (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t n, std::complex< float > const *AP) |
double | lapack::lantr (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t m, int64_t n, double const *A, int64_t lda) |
float | lapack::lantr (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t m, int64_t n, float const *A, int64_t lda) |
double | lapack::lantr (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t m, int64_t n, std::complex< double > const *A, int64_t lda) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. More... | |
float | lapack::lantr (lapack::Norm norm, lapack::Uplo uplo, lapack::Diag diag, int64_t m, int64_t n, std::complex< float > const *A, int64_t lda) |
double lapack::langb | ( | lapack::Norm | norm, |
int64_t | n, | ||
int64_t | kl, | ||
int64_t | ku, | ||
std::complex< double > const * | AB, | ||
int64_t | ldab | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n band matrix A, with kl sub-diagonals and ku super-diagonals.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | kl | The number of sub-diagonals of the matrix A. kl >= 0. |
[in] | ku | The number of super-diagonals of the matrix A. ku >= 0. |
[in] | AB | The n-by-n band matrix AB, stored in an ldab-by-n array. The band matrix A, stored in rows 1 to kl+ku+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku) <= i <= min(n,j+kl). |
[in] | ldab | The leading dimension of the array AB. ldab >= kl+ku+1. |
double lapack::lange | ( | lapack::Norm | norm, |
int64_t | m, | ||
int64_t | n, | ||
std::complex< double > const * | A, | ||
int64_t | lda | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | m | The number of rows of the matrix A. m >= 0. When m = 0, returns zero. |
[in] | n | The number of columns of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | A | The m-by-n matrix A, stored in an lda-by-n array. |
[in] | lda | The leading dimension of the array A. lda >= max(m,1). |
double lapack::langt | ( | lapack::Norm | norm, |
int64_t | n, | ||
std::complex< double > const * | DL, | ||
std::complex< double > const * | D, | ||
std::complex< double > const * | DU | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a tridiagonal matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | DL | The vector DL of length n-1. The (n-1) sub-diagonal elements of A. |
[in] | D | The vector D of length n. The diagonal elements of A. |
[in] | DU | The vector DU of length n-1. The (n-1) super-diagonal elements of A. |
double lapack::lanhb | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
int64_t | kd, | ||
std::complex< double > const * | AB, | ||
int64_t | ldab | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n hermitian band matrix A, with kd super-diagonals.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, this is an alias for lapack::lansb
. For complex symmetric matrices, see lapack::lansb
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the band matrix A is supplied.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | kd | The number of super-diagonals or sub-diagonals of the band matrix A. kd >= 0. |
[in] | AB | The kd+1-by-n matrix AB, stored in an ldab-by-n array. The upper or lower triangle of the hermitian band matrix A, stored in the first kd+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:
|
[in] | ldab | The leading dimension of the array AB. ldab >= kd+1. |
double lapack::lanhe | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
std::complex< double > const * | A, | ||
int64_t | lda | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex hermitian matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, this is an alias for lapack::lansy
. For complex symmetric matrices, see lapack::lansy
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the hermitian matrix A is to be referenced.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | A | The n-by-n matrix A, stored in an lda-by-n array. The hermitian matrix A.
|
[in] | lda | The leading dimension of the array A. lda >= max(n,1). |
double lapack::lanhp | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
std::complex< double > const * | AP | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, this is an alias for lapack::lansp
. For complex symmetric matrices, see lapack::lansp
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the hermitian matrix A is supplied.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | AP | The vector AP of length n*(n+1)/2. The upper or lower triangle of the hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
|
double lapack::lanhs | ( | lapack::Norm | norm, |
int64_t | n, | ||
std::complex< double > const * | A, | ||
int64_t | lda | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a Hessenberg matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | A | The n-by-n matrix A, stored in an lda-by-n array. The n-by-n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced. |
[in] | lda | The leading dimension of the array A. lda >= max(n,1). |
double lapack::lanht | ( | lapack::Norm | norm, |
int64_t | n, | ||
double const * | D, | ||
std::complex< double > const * | E | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a Hermitian tridiagonal matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, this is an alias for lapack::lanst
. For complex symmetric matrices, see lapack::lanst
.
[in] | norm | The value to be returned:
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | D | The vector D of length n. The diagonal elements of A. |
[in] | E | The vector E of length n-1. The (n-1) sub-diagonal or super-diagonal elements of A. |
double lapack::lansb | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
int64_t | kd, | ||
std::complex< double > const * | AB, | ||
int64_t | ldab | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n symmetric band matrix A, with kd super-diagonals.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, lapack::lanhb
is an alias for this. For complex Hermitian matrices, see lapack::lanhb
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the band matrix A is supplied.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | kd | The number of super-diagonals or sub-diagonals of the band matrix A. kd >= 0. |
[in] | AB | The kd+1-by-n matrix AB, stored in an ldab-by-n array. The upper or lower triangle of the symmetric band matrix A, stored in the first kd+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:
|
[in] | ldab | The leading dimension of the array AB. ldab >= kd+1. |
double lapack::lansp | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
std::complex< double > const * | AP | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, lapack::lanhp
is an alias for this. For complex Hermitian matrices, see lapack::lanhp
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the symmetric matrix A is supplied.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | AP | The vector AP of length n*(n+1)/2. The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
|
double lapack::lanst | ( | lapack::Norm | norm, |
int64_t | n, | ||
double const * | D, | ||
double const * | E | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a symmetric tridiagonal matrix A.
Overloaded versions are available for float
, double
. For real matrices, lapack::lanht
is an alias for this. For complex matrices, see lapack::lanht
.
[in] | norm | The value to be returned:
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | D | The vector D of length n. The diagonal elements of A. |
[in] | E | The vector E of length n-1. The (n-1) sub-diagonal or super-diagonal elements of A. |
double lapack::lansy | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
int64_t | n, | ||
std::complex< double > const * | A, | ||
int64_t | lda | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a complex symmetric matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
. For real matrices, lapack::lanhe
is an alias for this. For complex Hermitian matrices, see lapack::lanhe
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | A | The n-by-n matrix A, stored in an lda-by-n array. The symmetric matrix A.
|
[in] | lda | The leading dimension of the array A. lda >= max(n,1). |
double lapack::lantb | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
lapack::Diag | diag, | ||
int64_t | n, | ||
int64_t | k, | ||
std::complex< double > const * | AB, | ||
int64_t | ldab | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of an n-by-n triangular band matrix A, with (k + 1) diagonals.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the matrix A is upper or lower triangular.
|
[in] | diag | Whether or not the matrix A is unit triangular.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | k |
|
[in] | AB | The n-by-n band matrix AB, stored in an ldab-by-n array. The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:
|
[in] | ldab | The leading dimension of the array AB. ldab >= k+1. |
double lapack::lantp | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
lapack::Diag | diag, | ||
int64_t | n, | ||
std::complex< double > const * | AP | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the matrix A is upper or lower triangular.
|
[in] | diag | Whether or not the matrix A is unit triangular.
|
[in] | n | The order of the matrix A. n >= 0. When n = 0, returns zero. |
[in] | AP | The n-by-n matrix AP, packed in an (n*(n+1)/2) array. The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
|
double lapack::lantr | ( | lapack::Norm | norm, |
lapack::Uplo | uplo, | ||
lapack::Diag | diag, | ||
int64_t | m, | ||
int64_t | n, | ||
std::complex< double > const * | A, | ||
int64_t | lda | ||
) |
Returns the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | norm | The value to be returned:
|
[in] | uplo | Whether the matrix A is upper or lower trapezoidal.
|
[in] | diag | Whether or not the matrix A has unit diagonal.
|
[in] | m | The number of rows of the matrix A. m >= 0. When m = 0, returns zero.
|
[in] | n | The number of columns of the matrix A. When n = 0, returns zero. |
[in] | A | The m-by-n matrix A, stored in an lda-by-n array. The trapezoidal matrix A (A is triangular if m = n).
|
[in] | lda | The leading dimension of the array A. lda >= max(m,1). |