--- name: "hetrs_rook" 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_rook" --- # hetrs\_rook(3) {he,sy}trs\_rook: triangular solve using factor ## NAME hetrs\_rook - {he,sy}trs\_rook: triangular solve using factor ## SYNOPSIS ### Functions subroutine **chetrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **CHETRS\_ROOK** computes the solution to a system of linear equations A \* X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) subroutine **csytrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **CSYTRS\_ROOK** subroutine **dsytrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **DSYTRS\_ROOK** subroutine **ssytrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **SSYTRS\_ROOK** subroutine **zhetrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **ZHETRS\_ROOK** computes the solution to a system of linear equations A \* X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) subroutine **zsytrs\_rook** (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)\ **ZSYTRS\_ROOK** ## Detailed Description ## Function Documentation ### subroutine chetrs\_rook (character uplo, integer n, integer nrhs, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( ldb, \* ) b, integer ldb, integer info) **CHETRS\_ROOK** computes the solution to a system of linear equations A \* X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) **Purpose:** ``` !> !> CHETRS_ROOK solves a system of linear equations A*X = B with a complex !> Hermitian matrix A using the factorization A = U*D*U**H or !> A = L*D*L**H computed by CHETRF_ROOK. !> ``` **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*D*U**H; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CHETRF_ROOK. !> ``` *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 and the block structure of D !> as determined by CHETRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **chetrs\_rook.f**. ### subroutine csytrs\_rook (character uplo, integer n, integer nrhs, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( ldb, \* ) b, integer ldb, integer info) **CSYTRS\_ROOK** **Purpose:** ``` !> !> CSYTRS_ROOK solves a system of linear equations A*X = B with !> a complex symmetric matrix A using the factorization A = U*D*U**T or !> A = L*D*L**T computed by CSYTRF_ROOK. !> ``` **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*D*U**T; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CSYTRF_ROOK. !> ``` *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 and the block structure of D !> as determined by CSYTRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **csytrs\_rook.f**. ### subroutine dsytrs\_rook (character uplo, integer n, integer nrhs, double precision, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision, dimension( ldb, \* ) b, integer ldb, integer info) **DSYTRS\_ROOK** **Purpose:** ``` !> !> DSYTRS_ROOK solves a system of linear equations A*X = B with !> a real symmetric matrix A using the factorization A = U*D*U**T or !> A = L*D*L**T computed by DSYTRF_ROOK. !> ``` **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*D*U**T; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by DSYTRF_ROOK. !> ``` *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 and the block structure of D !> as determined by DSYTRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **dsytrs\_rook.f**. ### subroutine ssytrs\_rook (character uplo, integer n, integer nrhs, real, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real, dimension( ldb, \* ) b, integer ldb, integer info) **SSYTRS\_ROOK** **Purpose:** ``` !> !> SSYTRS_ROOK solves a system of linear equations A*X = B with !> a real symmetric matrix A using the factorization A = U*D*U**T or !> A = L*D*L**T computed by SSYTRF_ROOK. !> ``` **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*D*U**T; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by SSYTRF_ROOK. !> ``` *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 and the block structure of D !> as determined by SSYTRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **ssytrs\_rook.f**. ### subroutine zhetrs\_rook (character uplo, integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( ldb, \* ) b, integer ldb, integer info) **ZHETRS\_ROOK** computes the solution to a system of linear equations A \* X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) **Purpose:** ``` !> !> ZHETRS_ROOK solves a system of linear equations A*X = B with a complex !> Hermitian matrix A using the factorization A = U*D*U**H or !> A = L*D*L**H computed by ZHETRF_ROOK. !> ``` **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*D*U**H; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZHETRF_ROOK. !> ``` *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 and the block structure of D !> as determined by ZHETRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **zhetrs\_rook.f**. ### subroutine zsytrs\_rook (character uplo, integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( ldb, \* ) b, integer ldb, integer info) **ZSYTRS\_ROOK** **Purpose:** ``` !> !> ZSYTRS_ROOK solves a system of linear equations A*X = B with !> a complex symmetric matrix A using the factorization A = U*D*U**T or !> A = L*D*L**T computed by ZSYTRF_ROOK. !> ``` **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*D*U**T; !> = 'L': Lower triangular, form is A = L*D*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) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZSYTRF_ROOK. !> ``` *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 and the block structure of D !> as determined by ZSYTRF_ROOK. !> ``` *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). !> ``` *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. **Contributors:** ``` !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **134** of file **zsytrs\_rook.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.