spptri(l) [redhat man page]

SPPTRI(l)								 )								 SPPTRI(l)

NAME

       SPPTRI  - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T com-
       puted by SPPTRF

SYNOPSIS

       SUBROUTINE SPPTRI( UPLO, N, AP, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   REAL 	  AP( * )

PURPOSE

       SPPTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A =  L*L**T  com-
       puted by SPPTRF.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangular factor is stored in AP;
	       = 'L':  Lower triangular factor is stored in AP.

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

       AP      (input/output) REAL array, dimension (N*(N+1)/2)
	       On  entry,  the	triangular  factor  U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise as a linear
	       array.  The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for  1<=i<=j;	if
	       UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

	       On exit, the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.

LAPACK version 3.0						   15 June 2000 							 SPPTRI(l)

SPPTRF(l)								 )								 SPPTRF(l)

NAME

       SPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format

SYNOPSIS

       SUBROUTINE SPPTRF( UPLO, N, AP, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   REAL 	  AP( * )

PURPOSE

       SPPTRF  computes  the Cholesky factorization of a real symmetric 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 triangular.

ARGUMENTS

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

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

       AP      (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 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 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) 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 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:

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

LAPACK version 3.0						   15 June 2000 							 SPPTRF(l)