1CSPCON(1)                LAPACK routine (version 3.1)                CSPCON(1)
2
3
4

NAME

6       CSPCON  -  the  reciprocal of the condition number (in the 1-norm) of a
7       complex symmetric packed matrix A using the factorization A =  U*D*U**T
8       or A = L*D*L**T computed by CSPTRF
9

SYNOPSIS

11       SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
12
13           CHARACTER      UPLO
14
15           INTEGER        INFO, N
16
17           REAL           ANORM, RCOND
18
19           INTEGER        IPIV( * )
20
21           COMPLEX        AP( * ), WORK( * )
22

PURPOSE

24       CSPCON estimates the reciprocal of the condition number (in the 1-norm)
25       of a complex symmetric packed matrix A  using  the  factorization  A  =
26       U*D*U**T or A = L*D*L**T computed by CSPTRF.
27
28       An  estimate  is  obtained  for norm(inv(A)), and the reciprocal of the
29       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
30
31

ARGUMENTS

33       UPLO    (input) CHARACTER*1
34               Specifies whether the details of the factorization  are  stored
35               as an upper or lower triangular matrix.  = 'U':  Upper triangu‐
36               lar, form is A = U*D*U**T;
37               = 'L':  Lower triangular, form is A = L*D*L**T.
38
39       N       (input) INTEGER
40               The order of the matrix A.  N >= 0.
41
42       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
43               The block diagonal matrix D and the multipliers used to  obtain
44               the  factor  U  or  L as computed by CSPTRF, stored as a packed
45               triangular matrix.
46
47       IPIV    (input) INTEGER array, dimension (N)
48               Details of the interchanges and the block  structure  of  D  as
49               determined by CSPTRF.
50
51       ANORM   (input) REAL
52               The 1-norm of the original matrix A.
53
54       RCOND   (output) REAL
55               The  reciprocal  of  the condition number of the matrix A, com‐
56               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
57               mate of the 1-norm of inv(A) computed in this routine.
58
59       WORK    (workspace) COMPLEX array, dimension (2*N)
60
61       INFO    (output) INTEGER
62               = 0:  successful exit
63               < 0:  if INFO = -i, the i-th argument had an illegal value
64
65
66
67 LAPACK routine (version 3.1)    November 2006                       CSPCON(1)
Impressum