1CPPCON(1)                LAPACK routine (version 3.2)                CPPCON(1)
2
3
4

NAME

6       CPPCON  -  estimates  the  reciprocal  of  the condition number (in the
7       1-norm) of a complex Hermitian positive definite  packed  matrix  using
8       the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
9

SYNOPSIS

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

PURPOSE

24       CPPCON estimates the reciprocal of the condition number (in the 1-norm)
25       of a complex  Hermitian  positive  definite  packed  matrix  using  the
26       Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF.  An
27       estimate is obtained for norm(inv(A)), and the reciprocal of the condi‐
28       tion number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
29

ARGUMENTS

31       UPLO    (input) CHARACTER*1
32               = 'U':  Upper triangle of A is stored;
33               = 'L':  Lower triangle of A is stored.
34
35       N       (input) INTEGER
36               The order of the matrix A.  N >= 0.
37
38       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
39               The  triangular factor U or L from the Cholesky factorization A
40               = U**H*U or A = L*L**H, packed columnwise in  a  linear  array.
41               The j-th column of U or L is stored in the array AP as follows:
42               if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if  UPLO
43               = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
44
45       ANORM   (input) REAL
46               The 1-norm (or infinity-norm) of the Hermitian matrix A.
47
48       RCOND   (output) REAL
49               The  reciprocal  of  the condition number of the matrix A, com‐
50               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
51               mate of the 1-norm of inv(A) computed in this routine.
52
53       WORK    (workspace) COMPLEX array, dimension (2*N)
54
55       RWORK   (workspace) REAL array, dimension (N)
56
57       INFO    (output) INTEGER
58               = 0:  successful exit
59               < 0:  if INFO = -i, the i-th argument had an illegal value
60
61
62
63 LAPACK routine (version 3.2)    November 2008                       CPPCON(1)
Impressum