dsptrf

NAME

dsptrf - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

SYNOPSIS

  SUBROUTINE DSPTRF( UPLO, N, A, IPIVOT, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION A(*)
 
  SUBROUTINE DSPTRF_64( UPLO, N, A, IPIVOT, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION A(*)

F95 INTERFACE

  SUBROUTINE SPTRF( UPLO, [N], A, IPIVOT, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: A
 
  SUBROUTINE SPTRF_64( UPLO, [N], A, IPIVOT, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: A

C INTERFACE

#include <sunperf.h>

void dsptrf(char uplo, int n, double *a, int *ipivot, int *info);

void dsptrf_64(char uplo, long n, double *a, long *ipivot, long *info);

PURPOSE

dsptrf computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:

   A = U*D*U**T  or  A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ARGUMENTS

* UPLO (input)

* N (input)

The order of the matrix A. N >= 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.

On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix overwriting A (see below for further details).

* IPIVOT (output)

Details of the interchanges and the block structure of D. If IPIVOT(k) > 0, then rows and columns k and IPIVOT(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

* INFO (output)