• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

csysv - compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS

  SUBROUTINE CSYSV( 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_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( 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

  SUBROUTINE SYSV_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(char uplo, int n, int nrhs, complex *a, int lda, int *ipiv, complex *b, int ldb, int *info);

void csysv_64(char uplo, long n, long nrhs, complex *a, long lda, long *ipiv, 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) triangular 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 triangular 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 factorization 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).

• IPIV (output)
  Details of the interchanges and the block structure of D, as determined by CSYTRF. 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 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.

  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.