hetrs_aa(3) Library Functions Manual hetrs_aa(3) NAME hetrs_aa - {he,sy}trs_aa: triangular solve using factor SYNOPSIS Functions subroutine chetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) CHETRS_AA subroutine csytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) CSYTRS_AA subroutine dsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) DSYTRS_AA subroutine ssytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) SSYTRS_AA subroutine zhetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) ZHETRS_AA subroutine zsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) ZSYTRS_AA Detailed Description Function Documentation subroutine chetrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info) CHETRS_AA Purpose: !> !> CHETRS_AA solves a system of linear equations A*X = B with a complex !> hermitian matrix A using the factorization A = U**H*T*U or !> A = L*T*L**H computed by CHETRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**H*T*U; !> = 'L': Lower triangular, form is A = L*T*L**H. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> Details of factors computed by CHETRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by CHETRF_AA. !> B !> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the minimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 135 of file chetrs_aa.f. subroutine csytrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info) CSYTRS_AA Purpose: !> !> CSYTRS_AA solves a system of linear equations A*X = B with a complex !> symmetric matrix A using the factorization A = U**T*T*U or !> A = L*T*L**T computed by CSYTRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**T*T*U; !> = 'L': Lower triangular, form is A = L*T*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> Details of factors computed by CSYTRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by CSYTRF_AA. !> B !> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= max(1,3*N-2). !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 129 of file csytrs_aa.f. subroutine dsytrs_aa (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info) DSYTRS_AA Purpose: !> !> DSYTRS_AA solves a system of linear equations A*X = B with a real !> symmetric matrix A using the factorization A = U**T*T*U or !> A = L*T*L**T computed by DSYTRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**T*T*U; !> = 'L': Lower triangular, form is A = L*T*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is DOUBLE PRECISION array, dimension (LDA,N) !> Details of factors computed by DSYTRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by DSYTRF_AA. !> B !> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the minimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 135 of file dsytrs_aa.f. subroutine ssytrs_aa (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info) SSYTRS_AA Purpose: !> !> SSYTRS_AA solves a system of linear equations A*X = B with a real !> symmetric matrix A using the factorization A = U**T*T*U or !> A = L*T*L**T computed by SSYTRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**T*T*U; !> = 'L': Lower triangular, form is A = L*T*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is REAL array, dimension (LDA,N) !> Details of factors computed by SSYTRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by SSYTRF_AA. !> B !> B is REAL array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is REAL array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the minimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 135 of file ssytrs_aa.f. subroutine zhetrs_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info) ZHETRS_AA Purpose: !> !> ZHETRS_AA solves a system of linear equations A*X = B with a complex !> hermitian matrix A using the factorization A = U**H*T*U or !> A = L*T*L**H computed by ZHETRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**H*T*U; !> = 'L': Lower triangular, form is A = L*T*L**H. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> Details of factors computed by ZHETRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by ZHETRF_AA. !> B !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the minimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 136 of file zhetrs_aa.f. subroutine zsytrs_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info) ZSYTRS_AA Purpose: !> !> ZSYTRS_AA solves a system of linear equations A*X = B with a complex !> symmetric matrix A using the factorization A = U**T*T*U or !> A = L*T*L**T computed by ZSYTRF_AA. !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U**T*T*U; !> = 'L': Lower triangular, form is A = L*T*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> NRHS !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> Details of factors computed by ZSYTRF_AA. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by ZSYTRF_AA. !> B !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= max(1,3*N-2). !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 129 of file zsytrs_aa.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 hetrs_aa(3)