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

NAME

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

SYNOPSIS

  SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIVOT, B, LDB, INFO)
  DOUBLE COMPLEX A(LDA,*), B(LDB,*)
  INTEGER N, NRHS, LDA, LDB, INFO
  INTEGER IPIVOT(*)

  SUBROUTINE ZGESV_64( N, NRHS, A, LDA, IPIVOT, B, LDB, INFO)
  DOUBLE COMPLEX A(LDA,*), B(LDB,*)
  INTEGER*8 N, NRHS, LDA, LDB, INFO
  INTEGER*8 IPIVOT(*)

F95 INTERFACE

  SUBROUTINE GESV( [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [INFO])
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER :: N, NRHS, LDA, LDB, INFO
  INTEGER, DIMENSION(:) :: IPIVOT

  SUBROUTINE GESV_64( [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [INFO])
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER(8) :: N, NRHS, LDA, LDB, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT

C INTERFACE

#include <sunperf.h>

void zgesv(int n, int nrhs, doublecomplex *a, int lda, int *ipivot, doublecomplex *b, int ldb, int *info);

void zgesv_64(long n, long nrhs, doublecomplex *a, long lda, long *ipivot, doublecomplex *b, long ldb, long *info);

PURPOSE

zgesv computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as

   A = P * L * U,

where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

• 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 N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,N).

• IPIVOT (output)
  The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIVOT(i).

• B (input/output)
  On entry, the N-by-NRHS matrix of 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).

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   > 0:  if INFO  = i, U(i,i) is exactly zero.  The factorization
  has been completed, but the factor U is exactly
  singular, so the solution could not be computed.