zhesv_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diago- nal pivoting method
SUBROUTINE ZHESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, LDB, LWORK, N, NRHS INTEGER IPIV(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) SUBROUTINE ZHESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, LDB, LWORK, N, NRHS INTEGER*8 IPIV(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) F95 INTERFACE SUBROUTINE HESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B SUBROUTINE HESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void zhesv_rook (char uplo, int n, int nrhs, doublecomplex *a, int lda, int *ipiv, doublecomplex *b, int ldb, int *info); void zhesv_rook_64 (char uplo, long n, long nrhs, doublecomplex *a, long lda, long *ipiv, doublecomplex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library zhesv_rook(3P) NAME zhesv_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diago- nal pivoting method SYNOPSIS SUBROUTINE ZHESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, LDB, LWORK, N, NRHS INTEGER IPIV(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) SUBROUTINE ZHESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, LDB, LWORK, N, NRHS INTEGER*8 IPIV(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) F95 INTERFACE SUBROUTINE HESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B SUBROUTINE HESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void zhesv_rook (char uplo, int n, int nrhs, doublecomplex *a, int lda, int *ipiv, doublecomplex *b, int ldb, int *info); void zhesv_rook_64 (char uplo, long n, long nrhs, doublecomplex *a, long lda, long *ipiv, doublecomplex *b, long ldb, long *info); PURPOSE zhesv_rook computes the solution to a complex system of linear equa- tions A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices. The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) tri- angular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. ZHETRF_ROOK is called to compute the factorization of a complex Hermi- tion matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivot- ing method. The factored form of A is then used to solve the system of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2). ARGUMENTS UPLO (input) UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangu- lar part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by- N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factor- ization A = U*D*U**H or A = L*D*L**H as computed by ZHETRF_ROOK. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (output) IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = 'U': Only the last KB elements of IPIV are set. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L': Only the first KB elements of IPIV are set. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diago- nal block. B (input/output) B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK (output) WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) LWORK is INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF_ROOK. for LWORK < N, TRS will be done with Level BLAS 2; for LWORK >= N, TRS will be done with Level BLAS 3; If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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 (output) INFO is INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. 7 Nov 2015 zhesv_rook(3P)