csysv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by- NRHS matrices
SUBROUTINE CSYSV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LWORK, INFO INTEGER IPIVOT(*) SUBROUTINE CSYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE SYSV(UPLO, N, NRHS, A, LDA, IPIVOT, 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(:) :: IPIVOT SUBROUTINE SYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, 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(:) :: IPIVOT C INTERFACE #include <sunperf.h> void csysv(char uplo, int n, int nrhs, complex *a, int lda, int *ipivot, complex *b, int ldb, int *info); void csysv_64(char uplo, long n, long nrhs, complex *a, long lda, long *ipivot, complex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library csysv(3P) NAME csysv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by- NRHS matrices SYNOPSIS SUBROUTINE CSYSV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LWORK, INFO INTEGER IPIVOT(*) SUBROUTINE CSYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE SYSV(UPLO, N, NRHS, A, LDA, IPIVOT, 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(:) :: IPIVOT SUBROUTINE SYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, 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(:) :: IPIVOT C INTERFACE #include <sunperf.h> void csysv(char uplo, int n, int nrhs, complex *a, int lda, int *ipivot, complex *b, int ldb, int *info); void csysv_64(char uplo, long n, long nrhs, complex *a, long lda, long *ipivot, complex *b, long ldb, long *info); PURPOSE csysv computes the solution to a complex system of linear equations 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. 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. LDA (input) The leading dimension of the array A. LDA >= max(1,N). IPIVOT (output) Details of the interchanges and the block structure of D, as determined by CSYTRF. If IPIVOT(k) > 0, then rows and col- umns k and IPIVOT(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(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. 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(3P)