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

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

10       SUBROUTINE SGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK,
11                          IWORK, 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( * ), IWORK( * )
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21           REAL           AB( LDAB, * ), WORK( * )
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PURPOSE

24       SGBCON  estimates the reciprocal of the condition number of a real gen‐
25       eral band matrix A, in either the 1-norm or  the  infinity-norm,  using
26       the LU factorization computed by SGBTRF.
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28       An  estimate  is  obtained  for norm(inv(A)), and the reciprocal of the
29       condition number is computed as
30          RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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ARGUMENTS

34       NORM    (input) CHARACTER*1
35               Specifies whether the 1-norm condition number or the  infinity-
36               norm condition number is required:
37               = '1' or 'O':  1-norm;
38               = 'I':         Infinity-norm.
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40       N       (input) INTEGER
41               The order of the matrix A.  N >= 0.
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43       KL      (input) INTEGER
44               The number of subdiagonals within the band of A.  KL >= 0.
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46       KU      (input) INTEGER
47               The number of superdiagonals within the band of A.  KU >= 0.
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49       AB      (input) REAL array, dimension (LDAB,N)
50               Details  of  the LU factorization of the band matrix A, as com‐
51               puted by SGBTRF.  U is  stored  as  an  upper  triangular  band
52               matrix  with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
53               multipliers used during the factorization are  stored  in  rows
54               KL+KU+2 to 2*KL+KU+1.
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56       LDAB    (input) INTEGER
57               The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
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59       IPIV    (input) INTEGER array, dimension (N)
60               The  pivot  indices;  for  1 <= i <= N, row i of the matrix was
61               interchanged with row IPIV(i).
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63       ANORM   (input) REAL
64               If NORM = '1' or 'O', the 1-norm of the original matrix A.   If
65               NORM = 'I', the infinity-norm of the original matrix A.
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67       RCOND   (output) REAL
68               The  reciprocal  of  the condition number of the matrix A, com‐
69               puted as RCOND = 1/(norm(A) * norm(inv(A))).
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71       WORK    (workspace) REAL array, dimension (3*N)
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73       IWORK   (workspace) INTEGER array, dimension (N)
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75       INFO    (output) INTEGER
76               = 0:  successful exit
77               < 0: if INFO = -i, the i-th argument had an illegal value
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81 LAPACK routine (version 3.1)    November 2006                       SGBCON(1)
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