sppsv.f man page

subroutine sppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices  

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.

Parameters:

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The number of linear equations, i.e., the order of the
          matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.

AP

          AP is 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 AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(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

          B is 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

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

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:

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

Definition at line 146 of file sppsv.f.