NAME

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

SYNOPSIS

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

  SUBROUTINE SPPSV_64( UPLO, N, NRHS, A, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NRHS, LDB, INFO
  REAL A(*), B(LDB,*)

F95 INTERFACE

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

  SUBROUTINE PPSV_64( UPLO, N, [NRHS], A, B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NRHS, LDB, INFO
  REAL, DIMENSION(:) :: A
  REAL, DIMENSION(:,:) :: B

C INTERFACE

#include <sunperf.h>

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

void sppsv_64(char uplo, long n, long nrhs, float *a, float *b, long ldb, long *info);

PURPOSE

sppsv computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format 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 upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j < =i < =n. See below for further details.
On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.
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.

FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

   a11 a12 a13 a14

       a22 a23 a24

           a33 a34     (aij  = conjg(aji))

a44

Packed storage of the upper triangle of A:

A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]