lapack.lapack

Members

Aliases

lapackint

alias lapackint = ptrdiff_t

lapackint

alias lapackint = int

Functions

chbev_

void chbev_(char jobz, char uplo, lapackint n, lapackint* kd, _cfloat* ab, lapackint ldab, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix.

chbevd_

void chbevd_(char jobz, char uplo, lapackint n, lapackint* kd, _cfloat* ab, lapackint ldab, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

chbevx_

void chbevx_(char jobz, char range, char uplo, lapackint n, lapackint* kd, _cfloat* ab, lapackint ldab, _cfloat* q, lapackint ldq, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a Hermitian band matrix.

chbgst_

void chbgst_(char vect, char uplo, lapackint n, lapackint* ka, lapackint* kb, _cfloat* ab, lapackint ldab, _cfloat* bb, lapackint ldbb, _cfloat* x, lapackint ldx, _cfloat* work, float* rwork, lapackint info)

Reduces a complex Hermitian-definite banded generalized eigenproblem A x = lambda B x to standard form, where B has been factorized by CPBSTF (Crawford's algorithm).

chbgv_

void chbgv_(char jobz, char uplo, lapackint n, lapackint* ka, lapackint* kb, _cfloat* ab, lapackint ldab, _cfloat* bb, lapackint ldbb, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint info)

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian and banded, and B is also positive definite.

chbgvd_

void chbgvd_(char jobz, char uplo, lapackint n, lapackint* ka, lapackint* kb, _cfloat* ab, lapackint ldab, _cfloat* bb, lapackint ldbb, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.

chbgvx_

void chbgvx_(char jobz, char range, char uplo, lapackint n, lapackint* ka, lapackint* kb, _cfloat* ab, lapackint ldab, _cfloat* bb, lapackint ldbb, _cfloat* q, lapackint ldq, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian and banded, and B is also positive definite.

chbtrd_

void chbtrd_(char vect, char uplo, lapackint n, lapackint* kd, _cfloat* ab, lapackint ldab, float* d, float* e, _cfloat* q, lapackint ldq, _cfloat* work, lapackint info)

Reduces a Hermitian band matrix to real symmetric tridiagonal form by a unitary similarity transformation.

checon_

void checon_(char uplo, lapackint n, _cfloat* a, lapackint lda, lapackint* ipiv, float* anorm, float rcond, _cfloat* work, lapackint info)

Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF.

cheev_

void cheev_(char jobz, char uplo, lapackint n, _cfloat* a, lapackint lda, float* w, _cfloat* work, lapackint lwork, float* rwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix.

cheevd_

void cheevd_(char jobz, char uplo, lapackint n, _cfloat* a, lapackint lda, float* w, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

cheevr_

void cheevr_(char jobz, char range, char uplo, lapackint n, _cfloat* a, lapackint lda, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, lapackint* isuppz, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes selected eigenvalues, and optionally, eigenvectors of a complex Hermitian matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDL^T representations (also known as Relatively Robust Representations).

cheevx_

void cheevx_(char jobz, char range, char uplo, lapackint n, _cfloat* a, lapackint lda, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a Hermitian matrix.

chegst_

void chegst_(lapackint* itype, char uplo, lapackint n, _cfloat* a, lapackint lda, _cfloat* b, lapackint ldb, lapackint info)

Reduces a Hermitian-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where B has been factorized by CPOTRF.

chegv_

void chegv_(lapackint* itype, char jobz, char uplo, lapackint n, _cfloat* a, lapackint lda, _cfloat* b, lapackint ldb, float* w, _cfloat* work, lapackint lwork, float* rwork, lapackint info)

Computes all eigenvalues and the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.

chegvd_

void chegvd_(lapackint* itype, char jobz, char uplo, lapackint n, _cfloat* a, lapackint lda, _cfloat* b, lapackint ldb, float* w, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. If eigenvectors are desired, it uses a divide and conquer algorithm.

chegvx_

void chegvx_(lapackint* itype, char jobz, char range, char uplo, lapackint n, _cfloat* a, lapackint lda, _cfloat* b, lapackint ldb, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.

cherfs_

void cherfs_(char uplo, lapackint n, lapackint nrhs, _cfloat* a, lapackint lda, _cfloat* af, lapackint ldaf, lapackint* ipiv, _cfloat* b, lapackint ldb, _cfloat* x, lapackint ldx, float* ferr, float* berr, _cfloat* work, float* rwork, lapackint info)

Improves the computed solution to a complex Hermitian indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution.

chesv_

void chesv_(char uplo, lapackint n, lapackint nrhs, _cfloat* a, lapackint lda, lapackint* ipiv, _cfloat* b, lapackint ldb, _cfloat* work, lapackint lwork, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B.

chesvx_

void chesvx_(char fact, char uplo, lapackint n, lapackint nrhs, _cfloat* a, lapackint lda, _cfloat* af, lapackint ldaf, lapackint* ipiv, _cfloat* b, lapackint ldb, _cfloat* x, lapackint ldx, float rcond, float* ferr, float* berr, _cfloat* work, lapackint lwork, float* rwork, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.

chetrd_

void chetrd_(char uplo, lapackint n, _cfloat* a, lapackint lda, float* d, float* e, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Reduces a Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation.

chetrf_

void chetrf_(char uplo, lapackint n, _cfloat* a, lapackint lda, lapackint* ipiv, _cfloat* work, lapackint lwork, lapackint info)

Computes the factorization of a complex Hermitian-indefinite matrix, using the diagonal pivoting method.

chetri_

void chetri_(char uplo, lapackint n, _cfloat* a, lapackint lda, lapackint* ipiv, _cfloat* work, lapackint info)

Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF.

chetrs_

void chetrs_(char uplo, lapackint n, lapackint nrhs, _cfloat* a, lapackint lda, lapackint* ipiv, _cfloat* b, lapackint ldb, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B, using the factorization computed by CHPTRF.

chpcon_

void chpcon_(char uplo, lapackint n, _cfloat* ap, lapackint* ipiv, float* anorm, float rcond, _cfloat* work, lapackint info)

Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF.

chpev_

void chpev_(char jobz, char uplo, lapackint n, _cfloat* ap, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint info)

Computes selected eigenvalues, and optionally, eigenvectors of a complex Hermitian matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDL^T representations (also known as Relatively Robust Representations). Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.

chpevd_

void chpevd_(char jobz, char uplo, lapackint n, _cfloat* ap, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.

chpevx_

void chpevx_(char jobz, char range, char uplo, lapackint n, _cfloat* ap, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a Hermitian matrix in packed storage.

chpgst_

void chpgst_(lapackint* itype, char uplo, lapackint n, _cfloat* ap, _cfloat* bp, lapackint info)

Reduces a Hermitian-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where A and B are held in packed storage, and B has been factorized by CPPTRF.

chpgv_

void chpgv_(lapackint* itype, char jobz, char uplo, lapackint n, _cfloat* ap, _cfloat* bp, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint info)

Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage.

chpgvd_

void chpgvd_(lapackint* itype, char jobz, char uplo, lapackint n, _cfloat* ap, _cfloat* bp, float* w, _cfloat* z, lapackint ldz, _cfloat* work, lapackint lwork, float* rwork, lapackint* lrwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.

chpgvx_

void chpgvx_(lapackint* itype, char jobz, char range, char uplo, lapackint n, _cfloat* ap, _cfloat* bp, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, _cfloat* z, lapackint ldz, _cfloat* work, float* rwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage.

chprfs_

void chprfs_(char uplo, lapackint n, lapackint nrhs, _cfloat* ap, _cfloat* afp, lapackint* ipiv, _cfloat* b, lapackint ldb, _cfloat* x, lapackint ldx, float* ferr, float* berr, _cfloat* work, float* rwork, lapackint info)

Improves the computed solution to a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.

chpsv_

void chpsv_(char uplo, lapackint n, lapackint nrhs, _cfloat* ap, lapackint* ipiv, _cfloat* b, lapackint ldb, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage.

chpsvx_

void chpsvx_(char fact, char uplo, lapackint n, lapackint nrhs, _cfloat* ap, _cfloat* afp, lapackint* ipiv, _cfloat* b, lapackint ldb, _cfloat* x, lapackint ldx, float rcond, float* ferr, float* berr, _cfloat* work, float* rwork, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.

chptrd_

void chptrd_(char uplo, lapackint n, _cfloat* ap, float* d, float* e, _cfloat* tau, lapackint info)

Reduces a Hermitian matrix in packed storage to real symmetric tridiagonal form by a unitary similarity transformation.

chptrf_

void chptrf_(char uplo, lapackint n, _cfloat* ap, lapackint* ipiv, lapackint info)

Computes the factorization of a complex Hermitian-indefinite matrix in packed storage, using the diagonal pivoting method.

chptri_

void chptri_(char uplo, lapackint n, _cfloat* ap, lapackint* ipiv, _cfloat* work, lapackint info)

Computes the inverse of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF.

chptrs_

void chptrs_(char uplo, lapackint n, lapackint nrhs, _cfloat* ap, lapackint* ipiv, _cfloat* b, lapackint ldb, lapackint info)

Solves a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by CHPTRF.

cungbr_

void cungbr_(char vect, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates the unitary transformation matrices from a reduction to bidiagonal form determined by CGEBRD.

cunghr_

void cunghr_(lapackint n, lapackint ilo, lapackint ihi, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates the unitary transformation matrix from a reduction to Hessenberg form determined by CGEHRD.

cunglq_

void cunglq_(lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates all or part of the unitary matrix Q from an LQ factorization determined by CGELQF.

cungql_

void cungql_(lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates all or part of the unitary matrix Q from a QL factorization determined by CGEQLF.

cungqr_

void cungqr_(lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates all or part of the unitary matrix Q from a QR factorization determined by CGEQRF.

cungrq_

void cungrq_(lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates all or part of the unitary matrix Q from an RQ factorization determined by CGERQF.

cungtr_

void cungtr_(char uplo, lapackint n, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* work, lapackint lwork, lapackint info)

Generates the unitary transformation matrix from a reduction to tridiagonal form determined by CHETRD.

cunmbr_

void cunmbr_(char vect, char side, char trans, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by one of the unitary transformation matrices from a reduction to bidiagonal form determined by CGEBRD.

cunmhr_

void cunmhr_(char side, char trans, lapackint m, lapackint n, lapackint ilo, lapackint ihi, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary transformation matrix from a reduction to Hessenberg form determined by CGEHRD.

cunmlq_

void cunmlq_(char side, char trans, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary matrix from an LQ factorization determined by CGELQF.

cunmql_

void cunmql_(char side, char trans, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary matrix from a QL factorization determined by CGEQLF.

cunmqr_

void cunmqr_(char side, char trans, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary matrix from a QR factorization determined by CGEQRF.

cunmr3_

void cunmr3_(char side, char trans, lapackint m, lapackint n, lapackint k, lapackint* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint info)

Multiples a general matrix by the unitary matrix from an RZ factorization determined by CTZRZF.

cunmrq_

void cunmrq_(char side, char trans, lapackint m, lapackint n, lapackint k, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary matrix from an RQ factorization determined by CGERQF.

cunmrz_

void cunmrz_(char side, char trans, lapackint m, lapackint n, lapackint k, lapackint* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiples a general matrix by the unitary matrix from an RZ factorization determined by CTZRZF.

cunmtr_

void cunmtr_(char side, char uplo, char trans, lapackint m, lapackint n, _cfloat* a, lapackint lda, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by CHETRD.

cupgtr_

void cupgtr_(char uplo, lapackint n, _cfloat* ap, _cfloat* tau, _cfloat* q, lapackint ldq, _cfloat* work, lapackint info)

Generates the unitary transformation matrix from a reduction to tridiagonal form determined by CHPTRD.

cupmtr_

void cupmtr_(char side, char uplo, char trans, lapackint m, lapackint n, _cfloat* ap, _cfloat* tau, _cfloat* c, lapackint ldc, _cfloat* work, lapackint info)

Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by CHPTRD.

dsecnd_

double dsecnd_()

ilaenv2stage_

lapackint ilaenv2stage_(lapackint ispec, const(char)* name, const(char)* opts, lapackint n1, lapackint n2, lapackint n3, lapackint n4)

ilaenv_

lapackint ilaenv_(lapackint ispec, const(char)* name, const(char)* opts, lapackint n1, lapackint n2, lapackint n3, lapackint n4)

ilaenvset_

void ilaenvset_(lapackint ispec, const(char)* name, const(char)* opts, lapackint n1, lapackint n2, lapackint n3, lapackint n4, lapackint nvalue, lapackint info)

sbdsdc_

void sbdsdc_(char uplo, char compq, lapackint n, float* d, float* e, float* u, lapackint ldu, float* vt, lapackint ldvt, float* q, lapackint* iq, float* work, lapackint* iwork, lapackint info)

Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using a divide and conquer method.

sbdsqr_

void sbdsqr_(char uplo, lapackint n, lapackint ncvt, lapackint nru, lapackint ncc, float* d, float* e, float* vt, lapackint ldvt, float* u, lapackint ldu, float* c, lapackint ldc, float* work, lapackint info)

Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using the bidiagonal QR algorithm.

sdisna_

void sdisna_(char job, lapackint m, lapackint n, float* d, float* sep, lapackint info)

Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix.

second_

lapack_float_ret_t second_()

sgbbrd_

void sgbbrd_(char vect, lapackint m, lapackint n, lapackint ncc, lapackint kl, lapackint ku, float* ab, lapackint ldab, float* d, float* e, float* q, lapackint ldq, float* pt, lapackint ldpt, float* c, lapackint ldc, float* work, lapackint info)

Reduces a general band matrix to real upper bidiagonal form by an orthogonal transformation.

sgbcon_

void sgbcon_(char norm, lapackint n, lapackint kl, lapackint ku, float* ab, lapackint ldab, lapackint* ipiv, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a general band matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF.

sgbequ_

void sgbequ_(lapackint m, lapackint n, lapackint kl, lapackint ku, float* ab, lapackint ldab, float* r, float* c, float* rowcnd, float* colcnd, float* amax, lapackint info)

Computes row and column scalings to equilibrate a general band matrix and reduce its condition number.

sgbrfs_

void sgbrfs_(char trans, lapackint n, lapackint kl, lapackint ku, lapackint nrhs, float* ab, lapackint ldab, float* afb, lapackint ldafb, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a general banded system of linear equations AX=B, A**T X=B or A**H X=B, and provides forward and backward error bounds for the solution.

sgbsv_

void sgbsv_(lapackint n, lapackint kl, lapackint ku, lapackint nrhs, float* ab, lapackint ldab, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a general banded system of linear equations AX=B.

sgbsvx_

void sgbsvx_(char fact, char trans, lapackint n, lapackint kl, lapackint ku, lapackint nrhs, float* ab, lapackint ldab, float* afb, lapackint ldafb, lapackint* ipiv, char equed, float* r, float* c, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a general banded system of linear equations AX=B, A**T X=B or A**H X=B, and provides an estimate of the condition number and error bounds on the solution.

sgbtrf_

void sgbtrf_(lapackint m, lapackint n, lapackint kl, lapackint ku, float* ab, lapackint ldab, lapackint* ipiv, lapackint info)

Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges.

sgbtrs_

void sgbtrs_(char trans, lapackint n, lapackint kl, lapackint ku, lapackint nrhs, float* ab, lapackint ldab, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a general banded system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGBTRF.

sgebak_

void sgebak_(char job, char side, lapackint n, lapackint ilo, lapackint ihi, float* scale, lapackint m, float* v, lapackint ldv, lapackint info)

Transforms eigenvectors of a balanced matrix to those of the original matrix supplied to SGEBAL.

sgebal_

void sgebal_(char job, lapackint n, float* a, lapackint lda, lapackint ilo, lapackint ihi, float* scale, lapackint info)

Balances a general matrix in order to improve the accuracy of computed eigenvalues.

sgebrd_

void sgebrd_(lapackint m, lapackint n, float* a, lapackint lda, float* d, float* e, float* tauq, float* taup, float* work, lapackint lwork, lapackint info)

Reduces a general rectangular matrix to real bidiagonal form by an orthogonal transformation.

sgecon_

void sgecon_(char norm, lapackint n, float* a, lapackint lda, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a general matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF.

sgeequ_

void sgeequ_(lapackint m, lapackint n, float* a, lapackint lda, float* r, float* c, float* rowcnd, float* colcnd, float* amax, lapackint info)

Computes row and column scalings to equilibrate a general rectangular matrix and reduce its condition number.

sgees_

void sgees_(char jobvs, char sort, FCB_SGEES_SELECT select, lapackint n, float* a, lapackint lda, lapackint* sdim, float* wr, float* wi, float* vs, lapackint ldvs, float* work, lapackint lwork, lapackint* bwork, lapackint info)

Computes the eigenvalues and Schur factorization of a general matrix, and orders the factorization so that selected eigenvalues are at the top left of the Schur form.

sgeesx_

void sgeesx_(char jobvs, char sort, FCB_SGEESX_SELECT select, char sense, lapackint n, float* a, lapackint lda, lapackint* sdim, float* wr, float* wi, float* vs, lapackint ldvs, float rconde, float rcondv, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint* bwork, lapackint info)

Computes the eigenvalues and Schur factorization of a general matrix, orders the factorization so that selected eigenvalues are at the top left of the Schur form, and computes reciprocal condition numbers for the average of the selected eigenvalues, and for the associated right invariant subspace.

sgeev_

void sgeev_(char jobvl, char jobvr, lapackint n, float* a, lapackint lda, float* wr, float* wi, float* vl, lapackint ldvl, float* vr, lapackint ldvr, float* work, lapackint lwork, lapackint info)

Computes the eigenvalues and left and right eigenvectors of a general matrix.

sgeevx_

void sgeevx_(char balanc, char jobvl, char jobvr, char sense, lapackint n, float* a, lapackint lda, float* wr, float* wi, float* vl, lapackint ldvl, float* vr, lapackint ldvr, lapackint ilo, lapackint ihi, float* scale, float abnrm, float rconde, float rcondv, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Computes the eigenvalues and left and right eigenvectors of a general matrix, with preliminary balancing of the matrix, and computes reciprocal condition numbers for the eigenvalues and right eigenvectors.

sgegs_

void sgegs_(char jobvsl, char jobvsr, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* vsl, lapackint ldvsl, float* vsr, lapackint ldvsr, float* work, lapackint lwork, lapackint info)

Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for a pair of nonsymmetric matrices

sgegv_

void sgegv_(char jobvl, char jobvr, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* vl, lapackint ldvl, float* vr, lapackint ldvr, float* work, lapackint lwork, lapackint info)

Computes the generalized eigenvalues, and left and/or right generalized eigenvectors for a pair of nonsymmetric matrices

sgehrd_

void sgehrd_(lapackint n, lapackint ilo, lapackint ihi, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Reduces a general matrix to upper Hessenberg form by an orthogonal similarity transformation.

sgelqf_

void sgelqf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Computes an LQ factorization of a general rectangular matrix.

sgels_

void sgels_(char trans, lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, float* work, lapackint lwork, lapackint info)

Computes the least squares solution to an over-determined system of linear equations, A X=B or A**H X=B, or the minimum norm solution of an under-determined system, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A.

sgelsd_

void sgelsd_(lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, float* s, float rcond, lapackint rank, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Computes the least squares solution to an over-determined system of linear equations, A X=B or A**H X=B, or the minimum norm solution of an under-determined system, using a divide and conquer method, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A.

sgelss_

void sgelss_(lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, float* s, float rcond, lapackint rank, float* work, lapackint lwork, lapackint info)

Computes the minimum norm least squares solution to an over- or under-determined system of linear equations A X=B, using the singular value decomposition of A.

sgelsx_

void sgelsx_(lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, lapackint* jpvt, float rcond, lapackint rank, float* work, lapackint info)

Computes the minimum norm least squares solution to an over- or under-determined system of linear equations A X=B, using a complete orthogonal factorization of A.

sgelsy_

void sgelsy_(lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, lapackint* jpvt, float rcond, lapackint rank, float* work, lapackint lwork, lapackint info)

Computes the minimum norm least squares solution to an over- or under-determined system of linear equations A X=B, using a complete orthogonal factorization of A.

sgeqlf_

void sgeqlf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Computes a QL factorization of a general rectangular matrix.

sgeqp3_

void sgeqp3_(lapackint m, lapackint n, float* a, lapackint lda, lapackint* jpvt, float* tau, float* work, lapackint lwork, lapackint info)

Computes a QR factorization with column pivoting of a general rectangular matrix using Level 3 BLAS.

sgeqpf_

void sgeqpf_(lapackint m, lapackint n, float* a, lapackint lda, lapackint* jpvt, float* tau, float* work, lapackint info)

Computes a QR factorization with column pivoting of a general rectangular matrix.

sgeqrf_

void sgeqrf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Computes a QR factorization of a general rectangular matrix.

sgeqrs_

void sgeqrs_(lapackint m, lapackint n, lapackint nrhs, float* a, lapackint lda, float* tau, float* b, lapackint ldb, float* work, lapackint lwork, lapackint info)

Solve the least squares problem using the QR factorization computed by GEQRF

sgerfs_

void sgerfs_(char trans, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a general system of linear equations AX=B, A**T X=B or A**H X=B, and provides forward and backward error bounds for the solution.

sgerqf_

void sgerqf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Computes an RQ factorization of a general rectangular matrix.

sgesdd_

void sgesdd_(char jobz, lapackint m, lapackint n, float* a, lapackint lda, float* s, float* u, lapackint ldu, float* vt, lapackint ldvt, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Computes the singular value decomposition (SVD) of a general rectangular matrix using divide-and-conquer.

sgesv_

void sgesv_(lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a general system of linear equations AX=B.

sgesvd_

void sgesvd_(char jobu, char jobvt, lapackint m, lapackint n, float* a, lapackint lda, float* s, float* u, lapackint ldu, float* vt, lapackint ldvt, float* work, lapackint lwork, lapackint info)

Computes the singular value decomposition (SVD) of a general rectangular matrix.

sgesvx_

void sgesvx_(char fact, char trans, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, lapackint* ipiv, char equed, float* r, float* c, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a general system of linear equations AX=B, A**T X=B or A**H X=B, and provides an estimate of the condition number and error bounds on the solution.

sgetrf_

void sgetrf_(lapackint m, lapackint n, float* a, lapackint lda, lapackint* ipiv, lapackint info)

Computes an LU factorization of a general matrix, using partial pivoting with row interchanges.

sgetri_

void sgetri_(lapackint n, float* a, lapackint lda, lapackint* ipiv, float* work, lapackint lwork, lapackint info)

Computes the inverse of a general matrix, using the LU factorization computed by SGETRF.

sgetrs_

void sgetrs_(char trans, lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a general system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGETRF.

sggbak_

void sggbak_(char job, char side, lapackint n, lapackint ilo, lapackint ihi, float* lscale, float* rscale, lapackint m, float* v, lapackint ldv, lapackint info)

Forms the right or left eigenvectors of the generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL.

sggbal_

void sggbal_(char job, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, lapackint ilo, lapackint ihi, float* lscale, float* rscale, float* work, lapackint info)

Balances a pair of general real matrices for the generalized eigenvalue problem A x = lambda B x.

sgges_

void sgges_(char jobvsl, char jobvsr, char sort, FCB_SGGES_SELCTG selctg, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, lapackint* sdim, float* alphar, float* alphai, float* betav, float* vsl, lapackint ldvsl, float* vsr, lapackint ldvsr, float* work, lapackint lwork, lapackint* bwork, lapackint info)

Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for a pair of nonsymmetric matrices

sggesx_

void sggesx_(char jobvsl, char jobvsr, char sort, FCB_SGGESX_SELCTG selctg, char sense, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, lapackint* sdim, float* alphar, float* alphai, float* betav, float* vsl, lapackint ldvsl, float* vsr, lapackint ldvsr, float rconde, float rcondv, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint* bwork, lapackint info)

Computes the generalized eigenvalues, the real Schur form, and, optionally, the left and/or right matrices of Schur vectors.

sggev_

void sggev_(char jobvl, char jobvr, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* vl, lapackint ldvl, float* vr, lapackint ldvr, float* work, lapackint lwork, lapackint info)

Computes the generalized eigenvalues, and left and/or right generalized eigenvectors for a pair of nonsymmetric matrices

sggevx_

void sggevx_(char balanc, char jobvl, char jobvr, char sense, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* vl, lapackint ldvl, float* vr, lapackint ldvr, lapackint ilo, lapackint ihi, float* lscale, float* rscale, float abnrm, float bbnrm, float rconde, float rcondv, float* work, lapackint lwork, lapackint* iwork, lapackint* bwork, lapackint info)

Computes the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

sggglm_

void sggglm_(lapackint n, lapackint m, lapackint p, float* a, lapackint lda, float* b, lapackint ldb, float* d, float* x, float* y, float* work, lapackint lwork, lapackint info)

Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization

sgghrd_

void sgghrd_(char compq, char compz, lapackint n, lapackint ilo, lapackint ihi, float* a, lapackint lda, float* b, lapackint ldb, float* q, lapackint ldq, float* z, lapackint ldz, lapackint info)

Reduces a pair of real matrices to generalized upper Hessenberg form using orthogonal transformations

sgglse_

void sgglse_(lapackint m, lapackint n, lapackint p, float* a, lapackint lda, float* b, lapackint ldb, float* c, float* d, float* x, float* work, lapackint lwork, lapackint info)

Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization

sggqrf_

void sggqrf_(lapackint n, lapackint m, lapackint p, float* a, lapackint lda, float* taua, float* b, lapackint ldb, float* taub, float* work, lapackint lwork, lapackint info)

Computes a generalized QR factorization of a pair of matrices.

sggrqf_

void sggrqf_(lapackint m, lapackint p, lapackint n, float* a, lapackint lda, float* taua, float* b, lapackint ldb, float* taub, float* work, lapackint lwork, lapackint info)

Computes a generalized RQ factorization of a pair of matrices.

sggsvd_

void sggsvd_(char jobu, char jobv, char jobq, lapackint m, lapackint n, lapackint p, lapackint k, lapackint l, float* a, lapackint lda, float* b, lapackint ldb, float* alphav, float* betav, float* u, lapackint ldu, float* v, lapackint ldv, float* q, lapackint ldq, float* work, lapackint* iwork, lapackint info)

Computes the Generalized Singular Value Decomposition

sggsvp_

void sggsvp_(char jobu, char jobv, char jobq, lapackint m, lapackint p, lapackint n, float* a, float* b, lapackint ldb, float* tola, float* tolb, lapackint k, lapackint ldu, float* v, lapackint ldv, float* q, lapackint ldq, lapackint* iwork, float* tau, float* work, lapackint info)

Computes orthogonal matrices as a preprocessing step for computing the generalized singular value decomposition

sgtcon_

void sgtcon_(char norm, lapackint n, float* dl, float* d, float* du, float* du2, lapackint* ipiv, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a general tridiagonal matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGTTRF.

sgtrfs_

void sgtrfs_(char trans, lapackint n, lapackint nrhs, float* dl, float* d, float* du, float* dlf, float* df, float* duf, float* du2, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a general tridiagonal system of linear equations AX=B, A**T X=B or A**H X=B, and provides forward and backward error bounds for the solution.

sgtsv_

void sgtsv_(lapackint n, lapackint nrhs, float* dl, float* d, float* du, float* b, lapackint ldb, lapackint info)

Solves a general tridiagonal system of linear equations AX=B.

sgtsvx_

void sgtsvx_(char fact, char trans, lapackint n, lapackint nrhs, float* dl, float* d, float* du, float* dlf, float* df, float* duf, float* du2, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a general tridiagonal system of linear equations AX=B, A**T X=B or A**H X=B, and provides an estimate of the condition number and error bounds on the solution.

sgttrf_

void sgttrf_(lapackint n, float* dl, float* d, float* du, float* du2, lapackint* ipiv, lapackint info)

Computes an LU factorization of a general tridiagonal matrix, using partial pivoting with row interchanges.

sgttrs_

void sgttrs_(char trans, lapackint n, lapackint nrhs, float* dl, float* d, float* du, float* du2, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a general tridiagonal system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGTTRF.

shgeqz_

void shgeqz_(char job, char compq, char compz, lapackint n, lapackint ilo, lapackint ihi, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* q, lapackint ldq, float* z, lapackint ldz, float* work, lapackint lwork, lapackint info)

Implements a single-/double-shift version of the QZ method for finding the generalized eigenvalues of the equation det(A - w(i) B) = 0

shsein_

void shsein_(char side, char eigsrc, char initv, lapackint select, lapackint n, float* h, lapackint ldh, float* wr, float* wi, float* vl, lapackint ldvl, float* vr, lapackint ldvr, lapackint mm, lapackint m, float* work, lapackint ifaill, lapackint ifailr, lapackint info)

Computes specified right and/or left eigenvectors of an upper Hessenberg matrix by inverse iteration.

shseqr_

void shseqr_(char job, char compz, lapackint n, lapackint ilo, lapackint ihi, float* h, lapackint ldh, float* wr, float* wi, float* z, lapackint ldz, float* work, lapackint lwork, lapackint info)

Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the multishift QR algorithm.

slamch_

float slamch_(char* cmach)

sopgtr_

void sopgtr_(char uplo, lapackint n, float* ap, float* tau, float* q, lapackint ldq, float* work, lapackint info)

Generates the orthogonal transformation matrix from a reduction to tridiagonal form determined by SSPTRD.

sopmtr_

void sopmtr_(char side, char uplo, char trans, lapackint m, lapackint n, float* ap, float* tau, float* c, lapackint ldc, float* work, lapackint info)

Multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form determined by SSPTRD.

sorgbr_

void sorgbr_(char vect, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates the orthogonal transformation matrices from a reduction to bidiagonal form determined by SGEBRD.

sorghr_

void sorghr_(lapackint n, lapackint ilo, lapackint ihi, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates the orthogonal transformation matrix from a reduction to Hessenberg form determined by SGEHRD.

sorglq_

void sorglq_(lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates all or part of the orthogonal matrix Q from an LQ factorization determined by SGELQF.

sorgql_

void sorgql_(lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates all or part of the orthogonal matrix Q from a QL factorization determined by SGEQLF.

sorgqr_

void sorgqr_(lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates all or part of the orthogonal matrix Q from a QR factorization determined by SGEQRF.

sorgrq_

void sorgrq_(lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates all or part of the orthogonal matrix Q from an RQ factorization determined by SGERQF.

sorgtr_

void sorgtr_(char uplo, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Generates the orthogonal transformation matrix from a reduction to tridiagonal form determined by SSYTRD.

sormbr_

void sormbr_(char vect, char side, char trans, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by one of the orthogonal transformation matrices from a reduction to bidiagonal form determined by SGEBRD.

sormhr_

void sormhr_(char side, char trans, lapackint m, lapackint n, lapackint ilo, lapackint ihi, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal transformation matrix from a reduction to Hessenberg form determined by SGEHRD.

sormlq_

void sormlq_(char side, char trans, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal matrix from an LQ factorization determined by SGELQF.

sormql_

void sormql_(char side, char trans, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal matrix from a QL factorization determined by SGEQLF.

sormqr_

void sormqr_(char side, char trans, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal matrix from a QR factorization determined by SGEQRF.

sormr3_

void sormr3_(char side, char trans, lapackint m, lapackint n, lapackint k, lapackint* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint info)

Multiples a general matrix by the orthogonal matrix from an RZ factorization determined by STZRZF.

sormrq_

void sormrq_(char side, char trans, lapackint m, lapackint n, lapackint k, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal matrix from an RQ factorization determined by SGERQF.

sormrz_

void sormrz_(char side, char trans, lapackint m, lapackint n, lapackint k, lapackint* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiples a general matrix by the orthogonal matrix from an RZ factorization determined by STZRZF.

sormtr_

void sormtr_(char side, char uplo, char trans, lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* c, lapackint ldc, float* work, lapackint lwork, lapackint info)

Multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form determined by SSYTRD.

spbcon_

void spbcon_(char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a symmetric positive definite band matrix, using the Cholesky factorization computed by SPBTRF.

spbequ_

void spbequ_(char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* s, float* scond, float* amax, lapackint info)

Computes row and column scalings to equilibrate a symmetric positive definite band matrix and reduce its condition number.

spbrfs_

void spbrfs_(char uplo, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* afb, lapackint ldafb, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a symmetric positive definite banded system of linear equations AX=B, and provides forward and backward error bounds for the solution.

spbstf_

void spbstf_(char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, lapackint info)

Computes a split Cholesky factorization of a real symmetric positive definite band matrix.

spbsv_

void spbsv_(char uplo, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite banded system of linear equations AX=B.

spbsvx_

void spbsvx_(char fact, char uplo, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* afb, lapackint ldafb, char equed, float* s, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a symmetric positive definite banded system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.

spbtrf_

void spbtrf_(char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, lapackint info)

Computes the Cholesky factorization of a symmetric positive definite band matrix.

spbtrs_

void spbtrs_(char uplo, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite banded system of linear equations AX=B, using the Cholesky factorization computed by SPBTRF.

spocon_

void spocon_(char uplo, lapackint n, float* a, lapackint lda, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a symmetric positive definite matrix, using the Cholesky factorization computed by SPOTRF.

spoequ_

void spoequ_(lapackint n, float* a, lapackint lda, float* s, float* scond, float* amax, lapackint info)

Computes row and column scalings to equilibrate a symmetric positive definite matrix and reduce its condition number.

sporfs_

void sporfs_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a symmetric positive definite system of linear equations AX=B, and provides forward and backward error bounds for the solution.

sposv_

void sposv_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B.

sposvx_

void sposvx_(char fact, char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, char equed, float* s, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.

spotrf_

void spotrf_(char uplo, lapackint n, float* a, lapackint lda, lapackint info)

Computes the Cholesky factorization of a symmetric positive definite matrix.

spotri_

void spotri_(char uplo, lapackint n, float* a, lapackint lda, lapackint info)

Computes the inverse of a symmetric positive definite matrix, using the Cholesky factorization computed by SPOTRF.

spotrs_

void spotrs_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B, using the Cholesky factorization computed by SPOTRF.

sppcon_

void sppcon_(char uplo, lapackint n, float* ap, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a symmetric positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF.

sppequ_

void sppequ_(char uplo, lapackint n, float* ap, float* s, float* scond, float* amax, lapackint info)

Computes row and column scalings to equilibrate a symmetric positive definite matrix in packed storage and reduce its condition number.

spprfs_

void spprfs_(char uplo, lapackint n, lapackint nrhs, float* ap, float* afp, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a symmetric positive definite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.

sppsv_

void sppsv_(char uplo, lapackint n, lapackint nrhs, float* ap, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B, where A is held in packed storage.

sppsvx_

void sppsvx_(char fact, char uplo, lapackint n, lapackint nrhs, float* ap, float* afp, char equed, float* s, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.

spptrf_

void spptrf_(char uplo, lapackint n, float* ap, lapackint info)

Computes the Cholesky factorization of a symmetric positive definite matrix in packed storage.

spptri_

void spptri_(char uplo, lapackint n, float* ap, lapackint info)

Computes the inverse of a symmetric positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF.

spptrs_

void spptrs_(char uplo, lapackint n, lapackint nrhs, float* ap, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite system of linear equations AX=B, where A is held in packed storage, using the Cholesky factorization computed by SPPTRF.

sptcon_

void sptcon_(lapackint n, float* d, float* e, float* anorm, float rcond, float* work, lapackint info)

Computes the reciprocal of the condition number of a symmetric positive definite tridiagonal matrix, using the LDL**H factorization computed by SPTTRF.

spteqr_

void spteqr_(char compz, lapackint n, float* d, float* e, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues and eigenvectors of a real symmetric positive definite tridiagonal matrix, by computing the SVD of its bidiagonal Cholesky factor.

sptrfs_

void sptrfs_(lapackint n, lapackint nrhs, float* d, float* e, float* df, float* ef, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint info)

Improves the computed solution to a symmetric positive definite tridiagonal system of linear equations AX=B, and provides forward and backward error bounds for the solution.

sptsv_

void sptsv_(lapackint n, lapackint nrhs, float* d, float* e, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite tridiagonal system of linear equations AX=B.

sptsvx_

void sptsvx_(char fact, lapackint n, lapackint nrhs, float* d, float* e, float* df, float* ef, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint info)

Solves a symmetric positive definite tridiagonal system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.

spttrf_

void spttrf_(lapackint n, float* d, float* e, lapackint info)

Computes the LDL**H factorization of a symmetric positive definite tridiagonal matrix.

spttrs_

void spttrs_(lapackint n, lapackint nrhs, float* d, float* e, float* b, lapackint ldb, lapackint info)

Solves a symmetric positive definite tridiagonal system of linear equations, using the LDL**H factorization computed by SPTTRF.

ssbev_

void ssbev_(char jobz, char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* w, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric band matrix.

ssbevd_

void ssbevd_(char jobz, char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

ssbevx_

void ssbevx_(char jobz, char range, char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* q, lapackint ldq, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a symmetric band matrix.

ssbgst_

void ssbgst_(char vect, char uplo, lapackint n, lapackint* ka, lapackint* kb, float* ab, lapackint ldab, float* bb, lapackint ldbb, float* x, lapackint ldx, float* work, lapackint info)

Reduces a real symmetric-definite banded generalized eigenproblem A x = lambda B x to standard form, where B has been factorized by SPBSTF (Crawford's algorithm).

ssbgv_

void ssbgv_(char jobz, char uplo, lapackint n, lapackint* ka, lapackint* kb, float* ab, lapackint ldab, float* bb, lapackint ldbb, float* w, float* z, lapackint ldz, float* work, lapackint info)

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be symmetric and banded, and B is also positive definite.

ssbgvd_

void ssbgvd_(char jobz, char uplo, lapackint n, lapackint* ka, lapackint* kb, float* ab, lapackint ldab, float* bb, lapackint ldbb, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be symmetric and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.

ssbgvx_

void ssbgvx_(char jobz, char range, char uplo, lapackint n, lapackint* ka, lapackint* kb, float* ab, lapackint ldab, float* bb, lapackint ldbb, float* q, lapackint ldq, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be symmetric and banded, and B is also positive definite.

ssbtrd_

void ssbtrd_(char vect, char uplo, lapackint n, lapackint* kd, float* ab, lapackint ldab, float* d, float* e, float* q, lapackint ldq, float* work, lapackint info)

Reduces a symmetric band matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.

sspcon_

void sspcon_(char uplo, lapackint n, float* ap, lapackint* ipiv, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a real symmetric indefinite matrix in packed storage, using the factorization computed by SSPTRF.

sspev_

void sspev_(char jobz, char uplo, lapackint n, float* ap, float* w, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix in packed storage.

sspevd_

void sspevd_(char jobz, char uplo, lapackint n, float* ap, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.

sspevx_

void sspevx_(char jobz, char range, char uplo, lapackint n, float* ap, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage.

sspgst_

void sspgst_(lapackint* itype, char uplo, lapackint n, float* ap, float* bp, lapackint info)

Reduces a symmetric-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where A and B are held in packed storage, and B has been factorized by SPPTRF.

sspgv_

void sspgv_(lapackint* itype, char jobz, char uplo, lapackint n, float* ap, float* bp, float* w, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues and eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage.

sspgvd_

void sspgvd_(lapackint* itype, char jobz, char uplo, lapackint n, float* ap, float* bp, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.

sspgvx_

void sspgvx_(lapackint* itype, char jobz, char range, char uplo, lapackint n, float* ap, float* bp, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed storage.

ssprfs_

void ssprfs_(char uplo, lapackint n, lapackint nrhs, float* ap, float* afp, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a real symmetric indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.

sspsv_

void sspsv_(char uplo, lapackint n, lapackint nrhs, float* ap, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, where A is held in packed storage.

sspsvx_

void sspsvx_(char fact, char uplo, lapackint n, lapackint nrhs, float* ap, float* afp, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.

ssptrd_

void ssptrd_(char uplo, lapackint n, float* ap, float* d, float* e, float* tau, lapackint info)

Reduces a symmetric matrix in packed storage to real symmetric tridiagonal form by an orthogonal similarity transformation.

ssptrf_

void ssptrf_(char uplo, lapackint n, float* ap, lapackint* ipiv, lapackint info)

Computes the factorization of a real symmetric-indefinite matrix in packed storage, using the diagonal pivoting method.

ssptri_

void ssptri_(char uplo, lapackint n, float* ap, lapackint* ipiv, float* work, lapackint info)

Computes the inverse of a real symmetric indefinite matrix in packed storage, using the factorization computed by SSPTRF.

ssptrs_

void ssptrs_(char uplo, lapackint n, lapackint nrhs, float* ap, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by SSPTRF.

sstebz_

void sstebz_(char range, char order, lapackint n, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, float* d, float* e, lapackint m, lapackint nsplit, float* w, lapackint* iblock, lapackint* isplit, float* work, lapackint* iwork, lapackint info)

Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection.

sstedc_

void sstedc_(char compz, lapackint n, float* d, float* e, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer algorithm.

sstegr_

void sstegr_(char jobz, char range, lapackint n, float* d, float* e, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, lapackint* isuppz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes selected eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix. The eigenvalues are computed by the dqds algorithm, while eigenvectors are computed from various "good" LDL^T representations (also known as Relatively Robust Representations.)

sstein_

void sstein_(lapackint n, float* d, float* e, lapackint m, float* w, lapackint* iblock, lapackint* isplit, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvectors of a real symmetric tridiagonal matrix by inverse iteration.

ssteqr_

void ssteqr_(char compz, lapackint n, float* d, float* e, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm.

ssterf_

void ssterf_(lapackint n, float* d, float* e, lapackint info)

Computes all eigenvalues of a real symmetric tridiagonal matrix, using a root-free variant of the QL or QR algorithm.

sstev_

void sstev_(char jobz, lapackint n, float* d, float* e, float* z, lapackint ldz, float* work, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix.

sstevd_

void sstevd_(char jobz, lapackint n, float* d, float* e, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

sstevr_

void sstevr_(char jobz, char range, lapackint n, float* d, float* e, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, lapackint* isuppz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes selected eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDL^T representations (also known as Relatively Robust Representations).

sstevx_

void sstevx_(char jobz, char range, lapackint n, float* d, float* e, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix.

ssycon_

void ssycon_(char uplo, lapackint n, float* a, lapackint lda, lapackint* ipiv, float* anorm, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a real symmetric indefinite matrix, using the factorization computed by SSYTRF.

ssyev_

void ssyev_(char jobz, char uplo, lapackint n, float* a, lapackint lda, float* w, float* work, lapackint lwork, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix.

ssyevd_

void ssyevd_(char jobz, char uplo, lapackint n, float* a, lapackint lda, float* w, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

ssyevr_

void ssyevr_(char jobz, char range, char uplo, lapackint n, float* a, lapackint lda, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, lapackint* isuppz, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes selected eigenvalues, and optionally, eigenvectors of a real symmetric matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDL^T representations (also known as Relatively Robust Representations).

ssyevx_

void ssyevx_(char jobz, char range, char uplo, lapackint n, float* a, lapackint lda, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues and eigenvectors of a symmetric matrix.

ssygst_

void ssygst_(lapackint* itype, char uplo, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, lapackint info)

Reduces a symmetric-definite generalized eigenproblem Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard form, where B has been factorized by SPOTRF.

ssygv_

void ssygv_(lapackint* itype, char jobz, char uplo, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* w, float* work, lapackint lwork, lapackint info)

Computes all eigenvalues and the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.

ssygvd_

void ssygvd_(lapackint* itype, char jobz, char uplo, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* w, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Computes all eigenvalues and the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x. If eigenvectors are desired, it uses a divide and conquer algorithm.

ssygvx_

void ssygvx_(lapackint* itype, char jobz, char range, char uplo, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* vl, float* vu, lapackint* il, lapackint* iu, float abstol, lapackint m, float* w, float* z, lapackint ldz, float* work, lapackint lwork, lapackint* iwork, lapackint* ifail, lapackint info)

Computes selected eigenvalues, and optionally, the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.

ssyrfs_

void ssyrfs_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Improves the computed solution to a real symmetric indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution.

ssysv_

void ssysv_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, float* work, lapackint lwork, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B.

ssysv_rk_

void ssysv_rk_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* e, lapackint* ipiv, float* b, lapackint ldb, float* work, lapackint lwork, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B. Rook method (LDL decomposition)

ssysv_rook_

void ssysv_rook_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, float* work, lapackint lwork, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B. Rook method (LDL decomposition)

ssysvx_

void ssysvx_(char fact, char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, float* af, lapackint ldaf, lapackint* ipiv, float* b, lapackint ldb, float* x, lapackint ldx, float rcond, float* ferr, float* berr, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.

ssytrd_

void ssytrd_(char uplo, lapackint n, float* a, lapackint lda, float* d, float* e, float* tau, float* work, lapackint lwork, lapackint info)

Reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.

ssytrf_

void ssytrf_(char uplo, lapackint n, float* a, lapackint lda, lapackint* ipiv, float* work, lapackint lwork, lapackint info)

Computes the factorization of a real symmetric-indefinite matrix, using the diagonal pivoting method.

ssytrf_rk_

void ssytrf_rk_(char uplo, lapackint n, float* a, lapackint lda, float* e, lapackint* ipiv, float* work, lapackint lwork, lapackint info)

Computes the factorization of a real symmetric-indefinite matrix, using the diagonal pivoting method.

ssytri_

void ssytri_(char uplo, lapackint n, float* a, lapackint lda, lapackint* ipiv, float* work, lapackint info)

Computes the inverse of a real symmetric indefinite matrix, using the factorization computed by SSYTRF.

ssytrs2_

void ssytrs2_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, float* work, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, using the factorization computed by SYTRF.

ssytrs_

void ssytrs_(char uplo, lapackint n, lapackint nrhs, float* a, lapackint lda, lapackint* ipiv, float* b, lapackint ldb, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, using the factorization computed by SSPTRF.

ssytrs_3_

void ssytrs_3_(char uplo, lapackint n, lapackint nrhs, const(float)* a, lapackint lda, const(float)* e, const(lapackint)* ipiv, float* b, lapackint ldb, lapackint info)

Solves a real symmetric indefinite system of linear equations AX=B, using the factorization computed by SSPTRF_RK.

stbcon_

void stbcon_(char norm, char uplo, char diag, lapackint n, lapackint* kd, float* ab, lapackint ldab, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a triangular band matrix, in either the 1-norm or the infinity-norm.

stbrfs_

void stbrfs_(char uplo, char trans, char diag, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Provides forward and backward error bounds for the solution of a triangular banded system of linear equations AX=B, A**T X=B or A**H X=B.

stbtrs_

void stbtrs_(char uplo, char trans, char diag, lapackint n, lapackint* kd, lapackint nrhs, float* ab, lapackint ldab, float* b, lapackint ldb, lapackint info)

Solves a triangular banded system of linear equations AX=B, A**T X=B or A**H X=B.

stgevc_

void stgevc_(char side, char howmny, lapackint select, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* vl, lapackint ldvl, float* vr, lapackint ldvr, lapackint mm, lapackint m, float* work, lapackint info)

Computes some or all of the right and/or left generalized eigenvectors of a pair of upper triangular matrices.

stgexc_

void stgexc_(lapackint wantq, lapackint wantz, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* q, lapackint ldq, float* z, lapackint ldz, lapackint ifst, lapackint ilst, float* work, lapackint lwork, lapackint info)

Reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation so that the diagonal block of (A,B) with row index IFST is moved to row ILST.

stgsen_

void stgsen_(lapackint ijob, lapackint wantq, lapackint wantz, lapackint select, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* alphar, float* alphai, float* betav, float* q, lapackint ldq, float* z, lapackint ldz, lapackint m, float pl, float pr, float* dif, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Reorders the generalized real Schur decomposition of a real matrix pair (A, B) so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and the upper triangular B.

stgsja_

void stgsja_(char jobu, char jobv, char jobq, lapackint m, lapackint p, lapackint n, lapackint k, lapackint l, float* a, lapackint lda, float* b, lapackint ldb, float* tola, float* tolb, float* alphav, float* betav, float* u, lapackint ldu, float* v, lapackint ldv, float* q, lapackint ldq, float* work, lapackint ncycle, lapackint info)

Computes the generalized singular value decomposition of two real upper triangular (or trapezoidal) matrices as output by SGGSVP.

stgsna_

void stgsna_(char job, char howmny, lapackint select, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* vl, lapackint ldvl, float* vr, lapackint ldvr, float* s, float* dif, lapackint mm, lapackint m, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form, as returned by SGGES.

stgsyl_

void stgsyl_(char trans, lapackint* ijob, lapackint m, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* c, lapackint ldc, float* d, lapackint ldd, float* e, lapackint lde, float* f, lapackint ldf, float* scale, float* dif, float* work, lapackint lwork, lapackint* iwork, lapackint info)

Solves the generalized Sylvester equation.

stpcon_

void stpcon_(char norm, char uplo, char diag, lapackint n, float* ap, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a triangular matrix in packed storage, in either the 1-norm or the infinity-norm.

stprfs_

void stprfs_(char uplo, char trans, char diag, lapackint n, lapackint nrhs, float* ap, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Provides forward and backward error bounds for the solution of a triangular system of linear equations AX=B, A**T X=B or A**H X=B, where A is held in packed storage.

stptri_

void stptri_(char uplo, char diag, lapackint n, float* ap, lapackint info)

Computes the inverse of a triangular matrix in packed storage.

stptrs_

void stptrs_(char uplo, char trans, char diag, lapackint n, lapackint nrhs, float* ap, float* b, lapackint ldb, lapackint info)

Solves a triangular system of linear equations AX=B, A**T X=B or A**H X=B, where A is held in packed storage.

strcon_

void strcon_(char norm, char uplo, char diag, lapackint n, float* a, lapackint lda, float rcond, float* work, lapackint* iwork, lapackint info)

Estimates the reciprocal of the condition number of a triangular matrix, in either the 1-norm or the infinity-norm.

strevc_

void strevc_(char side, char howmny, lapackint select, lapackint n, float* t, lapackint ldt, float* vl, lapackint ldvl, float* vr, lapackint ldvr, lapackint mm, lapackint m, float* work, lapackint info)

Computes some or all of the right and/or left eigenvectors of an upper quasi-triangular matrix.

strexc_

void strexc_(char compq, lapackint n, float* t, lapackint ldt, float* q, lapackint ldq, lapackint* ifst, lapackint* ilst, float* work, lapackint info)

Reorders the Schur factorization of a matrix by an orthogonal similarity transformation.

strrfs_

void strrfs_(char uplo, char trans, char diag, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, float* x, lapackint ldx, float* ferr, float* berr, float* work, lapackint* iwork, lapackint info)

Provides forward and backward error bounds for the solution of a triangular system of linear equations A X=B, A**T X=B or A**H X=B.

strsen_

void strsen_(char job, char compq, lapackint select, lapackint n, float* t, lapackint ldt, float* q, lapackint ldq, float* wr, float* wi, lapackint m, float s, float sep, float* work, lapackint lwork, lapackint* iwork, lapackint* liwork, lapackint info)

Reorders the Schur factorization of a matrix in order to find an orthonormal basis of a right invariant subspace corresponding to selected eigenvalues, and returns reciprocal condition numbers (sensitivities) of the average of the cluster of eigenvalues and of the invariant subspace.

strsna_

void strsna_(char job, char howmny, lapackint select, lapackint n, float* t, lapackint ldt, float* vl, lapackint ldvl, float* vr, lapackint ldvr, float* s, float* sep, lapackint mm, lapackint m, float* work, lapackint ldwork, lapackint* iwork, lapackint info)

Estimates the reciprocal condition numbers (sensitivities) of selected eigenvalues and eigenvectors of an upper quasi-triangular matrix.

strsyl_

void strsyl_(char trana, char tranb, lapackint* isgn, lapackint m, lapackint n, float* a, lapackint lda, float* b, lapackint ldb, float* c, lapackint ldc, float* scale, lapackint info)

Solves the Sylvester matrix equation A X +/- X B=C where A and B are upper quasi-triangular, and may be transposed.

strtri_

void strtri_(char uplo, char diag, lapackint n, float* a, lapackint lda, lapackint info)

Computes the inverse of a triangular matrix.

strtrs_

void strtrs_(char uplo, char trans, char diag, lapackint n, lapackint nrhs, float* a, lapackint lda, float* b, lapackint ldb, lapackint info)

Solves a triangular system of linear equations AX=B, A**T X=B or A**H X=B.

stzrqf_

void stzrqf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, lapackint info)

Computes an RQ factorization of an upper trapezoidal matrix.

stzrzf_

void stzrzf_(lapackint m, lapackint n, float* a, lapackint lda, float* tau, float* work, lapackint lwork, lapackint info)

Computes an RZ factorization of an upper trapezoidal matrix (blocked version of STZRQF).