csysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. CSYTRF_ROOK is called to compute the factoriza- tion of A
SUBROUTINE CSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LWORK, INFO INTEGER IPIV(*) SUBROUTINE CSYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO INTEGER*8 IPIV(*) F95 INTERFACE SUBROUTINE SYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER, DIMENSION(:) :: IPIV UBROUTINE SYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER(8), DIMENSION(:) :: IPIV C INTERFACE #include <sunperf.h> void csysv_rook(char uplo, int n, int nrhs, complex *a, int lda, int *ipiv, complex *b, int ldb, int *info); void csysv_rook_64(char uplo, long n, long nrhs, complex *a, long lda, long *ipiv, complex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library csysv_rook(3P) NAME csysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. CSYTRF_ROOK is called to compute the factoriza- tion of A SYNOPSIS SUBROUTINE CSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LWORK, INFO INTEGER IPIV(*) SUBROUTINE CSYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO INTEGER*8 IPIV(*) F95 INTERFACE SUBROUTINE SYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER, DIMENSION(:) :: IPIV UBROUTINE SYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER(8), DIMENSION(:) :: IPIV C INTERFACE #include <sunperf.h> void csysv_rook(char uplo, int n, int nrhs, complex *a, int lda, int *ipiv, complex *b, int ldb, int *info); void csysv_rook_64(char uplo, long n, long nrhs, complex *a, long lda, long *ipiv, complex *b, long ldb, long *info); PURPOSE csysv_rook computes the solution to a complex system of linear equa- tions A * X = B, where A is an N-by-N symmetric matrix and X and B are N- by-NRHS matrices. The 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 symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. CSYTRF_ROOK is called to compute the factorization of a complex symmet- ric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) On entry, the symmetric 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**T or A = L*D*L**T as computed by CSYTRF_ROOK. LDA (input) The leading dimension of the array A. LDA >= max(1,N). IPIV (output) Details of the interchanges and the block structure of D, as determined by CSYTRF_ROOK. If IPIV(k) > 0, then rows and col- umns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. B (input/output) 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) The leading dimension of the array B. LDB >= max(1,N). WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) The length of WORK. LWORK >= 1, and for best performance LWORK >= N*NB, where NB is the optimal blocksize for CSYTRF_ROOK. 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) = 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 csysv_rook(3P)