sppsv (3p)

Name

sppsv - compute 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

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);

Description

Oracle Solaris Studio Performance Library                            sppsv(3P)



NAME
       sppsv - compute 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


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) REAL array, dimension (N*(N+1)/2)
                 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) REAL array, dimension (LDB,NRHS)
                 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 com-
                 pleted, 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 ]




                                  7 Nov 2015                         sppsv(3P)