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

NAME

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

SYNOPSIS

  SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NRHS, LDA, LDB, INFO
  REAL A(LDA,*), B(LDB,*)

  SUBROUTINE SPOSV_64( UPLO, N, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NRHS, LDA, LDB, INFO
  REAL A(LDA,*), B(LDB,*)

F95 INTERFACE

  SUBROUTINE POSV( UPLO, [N], [NRHS], A, [LDA], B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, NRHS, LDA, LDB, INFO
  REAL, DIMENSION(:,:) :: A, B

  SUBROUTINE POSV_64( UPLO, [N], [NRHS], A, [LDA], B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NRHS, LDA, LDB, INFO
  REAL, DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void sposv(char uplo, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info);

void sposv_64(char uplo, long n, long nrhs, float *a, long lda, float *b, long ldb, long *info);

PURPOSE

sposv computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as

   A = U**T* U,  if UPLO = 'U', or

   A = L * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. 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 factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.

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

• 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).

• INFO (output)
  

   = 0:  successful exit

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

   > 0:  if INFO  = i, the leading minor of order i of A is not
  positive definite, so the factorization could not be
  completed, and the solution has not been computed.