Contents

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

NAME

     spptrf - compute the Cholesky factorization of a  real  sym-
     metric positive definite matrix A stored in packed format

SYNOPSIS

     SUBROUTINE SPPTRF(UPLO, N, A, INFO)

     CHARACTER * 1 UPLO
     INTEGER N, INFO
     REAL A(*)

     SUBROUTINE SPPTRF_64(UPLO, N, A, INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 N, INFO
     REAL A(*)

  F95 INTERFACE
     SUBROUTINE PPTRF(UPLO, [N], A, [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER :: N, INFO
     REAL, DIMENSION(:) :: A

     SUBROUTINE PPTRF_64(UPLO, [N], A, [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER(8) :: N, INFO
     REAL, DIMENSION(:) :: A

  C INTERFACE
     #include <sunperf.h>

     void spptrf(char uplo, int n, float *a, int *info);

     void spptrf_64(char uplo, long n, float *a, long *info);

PURPOSE

     spptrf computes the Cholesky factorization of  a  real  sym-
     metric positive definite matrix A stored in packed format.

     The factorization has the form
        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  lower  tri-
     angular.

ARGUMENTS

     UPLO (input)
               = 'U':  Upper triangle of A is stored;
               = 'L':  Lower triangle of A is stored.

     N (input) The order of the matrix A.  N >= 0.

     A (input/output) REAL array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  sym-
               metric  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 triangular factor U or L
               from  the Cholesky factorization A = U**T*U or A =
               L*L**T, in the same storage format as A.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, the leading minor of order i is
               not positive definite, and the factorization could
               not be completed.

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 = aji)
                    a44

     Packed storage of the upper triangle of A:

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