1ZPSTRF(1)                LAPACK routine (version 3.2)                ZPSTRF(1)
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NAME

6       ZPSTRF  - computes the Cholesky factorization with complete pivoting of
7       a complex Hermitian positive semidefinite matrix A
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SYNOPSIS

10       SUBROUTINE ZPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
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12           DOUBLE         PRECISION TOL
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14           INTEGER        INFO, LDA, N, RANK
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16           CHARACTER      UPLO
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18           COMPLEX*16     A( LDA, * )
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20           DOUBLE         PRECISION WORK( 2*N )
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22           INTEGER        PIV( N )
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PURPOSE

25       ZPSTRF computes the Cholesky factorization with complete pivoting of  a
26       complex  Hermitian  positive  semidefinite matrix A.  The factorization
27       has the form
28          P' * A * P = U' * U ,  if UPLO = 'U',
29          P' * A * P = L  * L',  if UPLO = 'L',
30       where U is an upper triangular matrix and L is lower triangular, and  P
31       is stored as vector PIV.
32       This  algorithm  does not attempt to check that A is positive semidefi‐
33       nite. This version of the algorithm calls level 3 BLAS.
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ARGUMENTS

36       UPLO    (input) CHARACTER*1
37               Specifies whether the upper or lower  triangular  part  of  the
38               symmetric matrix A is stored.  = 'U':  Upper triangular
39               = 'L':  Lower triangular
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41       N       (input) INTEGER
42               The order of the matrix A.  N >= 0.
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44       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
45               On entry, the symmetric matrix A.  If UPLO = 'U', the leading n
46               by n upper triangular part of A contains the  upper  triangular
47               part of the matrix A, and the strictly lower triangular part of
48               A is not referenced.  If UPLO = 'L', the leading n by  n  lower
49               triangular  part of A contains the lower triangular part of the
50               matrix A, and the strictly upper triangular part of  A  is  not
51               referenced.   On  exit, if INFO = 0, the factor U or L from the
52               Cholesky factorization as above.
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54       PIV     (output) INTEGER array, dimension (N)
55               PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
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57       RANK    (output) INTEGER
58               The rank of A given by the number of steps the  algorithm  com‐
59               pleted.
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61       TOL     (input) DOUBLE PRECISION
62               User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) will
63               be used. The algorithm terminates at the (K-1)st  step  if  the
64               pivot <= TOL.
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66       LDA     (input) INTEGER
67               The leading dimension of the array A.  LDA >= max(1,N).
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69       WORK    DOUBLE PRECISION array, dimension (2*N)
70               Work space.
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72       INFO    (output) INTEGER
73               < 0: If INFO = -K, the K-th argument had an illegal value,
74               = 0: algorithm completed successfully, and
75               >  0:  the matrix A is either rank deficient with computed rank
76               as returned in RANK, or is indefinite.  See Section 7 of LAPACK
77               Working Note #161 for further information.
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81 LAPACK routine (version 3.2)    November 2008                       ZPSTRF(1)
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