Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A

**SYNOPSIS**

SUBROUTINE SPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) REAL TOL INTEGER INFO, LDA, N, RANK CHARACTER UPLO REAL A( LDA, * ), WORK( 2*N ) INTEGER PIV( N )

**PURPOSE**

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. The factorization has the form P**T * A * P = U**T * U , if UPLO = 'U', P**T * A * P = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS.

**ARGUMENTS**

UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization as above. PIV (output) INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK (output) INTEGER The rank of A given by the number of steps the algorithm completed. TOL (input) REAL User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). WORK (workspace) REAL array, dimension (2*N) Work space. INFO (output) INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is indefinite. See Section 7 of LAPACK Working Note #161 for further information. LAPACK PROTOTYPE routine (version 3.2.2) April 2011 SPSTF2(3lapack)