1SPSTF2(1)           LAPACK PROTOTYPE routine (version 3.2)           SPSTF2(1)
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NAME

6       SPSTF2  - computes the Cholesky factorization with complete pivoting of
7       a real symmetric positive semidefinite matrix A
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SYNOPSIS

10       SUBROUTINE SPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
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12           REAL           TOL
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14           INTEGER        INFO, LDA, N, RANK
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16           CHARACTER      UPLO
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18           REAL           A( LDA, * ), WORK( 2*N )
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20           INTEGER        PIV( N )
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PURPOSE

23       SPSTF2 computes the Cholesky factorization with complete pivoting of  a
24       real  symmetric  positive semidefinite matrix A.  The factorization has
25       the form
26          P' * A * P = U' * U ,  if UPLO = 'U',
27          P' * A * P = L  * L',  if UPLO = 'L',
28       where U is an upper triangular matrix and L is lower triangular, and  P
29       is stored as vector PIV.
30       This  algorithm  does not attempt to check that A is positive semidefi‐
31       nite. This version of the algorithm calls level 2 BLAS.
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ARGUMENTS

34       UPLO    (input) CHARACTER*1
35               Specifies whether the upper or lower  triangular  part  of  the
36               symmetric matrix A is stored.  = 'U':  Upper triangular
37               = 'L':  Lower triangular
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39       N       (input) INTEGER
40               The order of the matrix A.  N >= 0.
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42       A       (input/output) REAL array, dimension (LDA,N)
43               On entry, the symmetric matrix A.  If UPLO = 'U', the leading n
44               by n upper triangular part of A contains the  upper  triangular
45               part of the matrix A, and the strictly lower triangular part of
46               A is not referenced.  If UPLO = 'L', the leading n by  n  lower
47               triangular  part of A contains the lower triangular part of the
48               matrix A, and the strictly upper triangular part of  A  is  not
49               referenced.   On  exit, if INFO = 0, the factor U or L from the
50               Cholesky factorization as above.
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52       PIV     (output) INTEGER array, dimension (N)
53               PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
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55       RANK    (output) INTEGER
56               The rank of A given by the number of steps the  algorithm  com‐
57               pleted.
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59       TOL     (input) REAL
60               User  defined  tolerance.  If TOL < 0, then N*U*MAX( A( K,K ) )
61               will be used. The algorithm terminates at the (K-1)st  step  if
62               the pivot <= TOL.
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64       LDA     (input) INTEGER
65               The leading dimension of the array A.  LDA >= max(1,N).
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67       WORK    REAL array, dimension (2*N)
68               Work space.
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70       INFO    (output) INTEGER
71               < 0: If INFO = -K, the K-th argument had an illegal value,
72               = 0: algorithm completed successfully, and
73               >  0:  the matrix A is either rank deficient with computed rank
74               as returned in RANK, or is indefinite.  See Section 7 of LAPACK
75               Working Note #161 for further information.
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79 LAPACK PROTOTYPE routine (versionNo3v.e2m)ber 2008                       SPSTF2(1)
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