1CGBCON(1)                LAPACK routine (version 3.1)                CGBCON(1)
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NAME

6       CGBCON  -  the  reciprocal of the condition number of a complex general
7       band matrix A, in either the 1-norm or the infinity-norm,
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SYNOPSIS

10       SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK,
11                          RWORK, INFO )
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13           CHARACTER      NORM
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15           INTEGER        INFO, KL, KU, LDAB, N
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17           REAL           ANORM, RCOND
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19           INTEGER        IPIV( * )
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21           REAL           RWORK( * )
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23           COMPLEX        AB( LDAB, * ), WORK( * )
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PURPOSE

26       CGBCON  estimates  the  reciprocal of the condition number of a complex
27       general band matrix A, in either the 1-norm or the infinity-norm, using
28       the LU factorization computed by CGBTRF.
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30       An  estimate  is  obtained  for norm(inv(A)), and the reciprocal of the
31       condition number is computed as
32          RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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ARGUMENTS

36       NORM    (input) CHARACTER*1
37               Specifies whether the 1-norm condition number or the  infinity-
38               norm condition number is required:
39               = '1' or 'O':  1-norm;
40               = 'I':         Infinity-norm.
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42       N       (input) INTEGER
43               The order of the matrix A.  N >= 0.
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45       KL      (input) INTEGER
46               The number of subdiagonals within the band of A.  KL >= 0.
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48       KU      (input) INTEGER
49               The number of superdiagonals within the band of A.  KU >= 0.
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51       AB      (input) COMPLEX array, dimension (LDAB,N)
52               Details  of  the LU factorization of the band matrix A, as com‐
53               puted by CGBTRF.  U is  stored  as  an  upper  triangular  band
54               matrix  with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
55               multipliers used during the factorization are  stored  in  rows
56               KL+KU+2 to 2*KL+KU+1.
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58       LDAB    (input) INTEGER
59               The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
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61       IPIV    (input) INTEGER array, dimension (N)
62               The  pivot  indices;  for  1 <= i <= N, row i of the matrix was
63               interchanged with row IPIV(i).
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65       ANORM   (input) REAL
66               If NORM = '1' or 'O', the 1-norm of the original matrix A.   If
67               NORM = 'I', the infinity-norm of the original matrix A.
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69       RCOND   (output) REAL
70               The  reciprocal  of  the condition number of the matrix A, com‐
71               puted as RCOND = 1/(norm(A) * norm(inv(A))).
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73       WORK    (workspace) COMPLEX array, dimension (2*N)
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75       RWORK   (workspace) REAL array, dimension (N)
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77       INFO    (output) INTEGER
78               = 0:  successful exit
79               < 0: if INFO = -i, the i-th argument had an illegal value
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83 LAPACK routine (version 3.1)    November 2006                       CGBCON(1)
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