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

6       CTRCON - estimates the reciprocal of the condition number of a triangu‐
7       lar matrix A, in either the 1-norm or the infinity-norm
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SYNOPSIS

10       SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A,  LDA,  RCOND,  WORK,  RWORK,
11                          INFO )
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13           CHARACTER      DIAG, NORM, UPLO
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15           INTEGER        INFO, LDA, N
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17           REAL           RCOND
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19           REAL           RWORK( * )
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21           COMPLEX        A( LDA, * ), WORK( * )
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PURPOSE

24       CTRCON estimates the reciprocal of the condition number of a triangular
25       matrix A, in either the 1-norm or the infinity-norm.  The norm of A  is
26       computed  and an estimate is obtained for norm(inv(A)), then the recip‐
27       rocal of the condition number is computed as
28          RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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ARGUMENTS

31       NORM    (input) CHARACTER*1
32               Specifies whether the 1-norm condition number or the  infinity-
33               norm condition number is required:
34               = '1' or 'O':  1-norm;
35               = 'I':         Infinity-norm.
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37       UPLO    (input) CHARACTER*1
38               = 'U':  A is upper triangular;
39               = 'L':  A is lower triangular.
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41       DIAG    (input) CHARACTER*1
42               = 'N':  A is non-unit triangular;
43               = 'U':  A is unit triangular.
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45       N       (input) INTEGER
46               The order of the matrix A.  N >= 0.
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48       A       (input) COMPLEX array, dimension (LDA,N)
49               The  triangular  matrix  A.   If UPLO = 'U', the leading N-by-N
50               upper triangular part of the array A contains the upper  trian‐
51               gular  matrix,  and  the strictly lower triangular part of A is
52               not referenced.  If UPLO = 'L', the leading N-by-N lower trian‐
53               gular part of the array A contains the lower triangular matrix,
54               and the strictly upper triangular part of A is not  referenced.
55               If  DIAG  = 'U', the diagonal elements of A are also not refer‐
56               enced and are assumed to be 1.
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58       LDA     (input) INTEGER
59               The leading dimension of the array A.  LDA >= max(1,N).
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61       RCOND   (output) REAL
62               The reciprocal of the condition number of the  matrix  A,  com‐
63               puted as RCOND = 1/(norm(A) * norm(inv(A))).
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65       WORK    (workspace) COMPLEX array, dimension (2*N)
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67       RWORK   (workspace) REAL array, dimension (N)
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69       INFO    (output) INTEGER
70               = 0:  successful exit
71               < 0:  if INFO = -i, the i-th argument had an illegal value
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75 LAPACK routine (version 3.2)    November 2008                       CTRCON(1)
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