1ZHECON(1) LAPACK routine (version 3.1) ZHECON(1)
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6 ZHECON - the reciprocal of the condition number of a complex Hermitian
7 matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed
8 by ZHETRF
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11 SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO )
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13 CHARACTER UPLO
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15 INTEGER INFO, LDA, N
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17 DOUBLE PRECISION ANORM, RCOND
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19 INTEGER IPIV( * )
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21 COMPLEX*16 A( LDA, * ), WORK( * )
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24 ZHECON estimates the reciprocal of the condition number of a complex
25 Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
26 computed by ZHETRF.
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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))).
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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**H;
37 = 'L': Lower triangular, form is A = L*D*L**H.
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39 N (input) INTEGER
40 The order of the matrix A. N >= 0.
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42 A (input) COMPLEX*16 array, dimension (LDA,N)
43 The block diagonal matrix D and the multipliers used to obtain
44 the factor U or L as computed by ZHETRF.
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46 LDA (input) INTEGER
47 The leading dimension of the array A. LDA >= max(1,N).
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49 IPIV (input) INTEGER array, dimension (N)
50 Details of the interchanges and the block structure of D as
51 determined by ZHETRF.
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53 ANORM (input) DOUBLE PRECISION
54 The 1-norm of the original matrix A.
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56 RCOND (output) DOUBLE PRECISION
57 The reciprocal of the condition number of the matrix A, com‐
58 puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
59 mate of the 1-norm of inv(A) computed in this routine.
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61 WORK (workspace) COMPLEX*16 array, dimension (2*N)
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63 INFO (output) INTEGER
64 = 0: successful exit
65 < 0: if INFO = -i, the i-th argument had an illegal value
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69 LAPACK routine (version 3.1) November 2006 ZHECON(1)