--- name: "hetrs_aa" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/hetrs_aa" --- # hetrs\_aa(3) {he,sy}trs\_aa: triangular solve using factor ## 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.