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

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

10       SUBROUTINE DTBCON( NORM, UPLO, DIAG, N,  KD,  AB,  LDAB,  RCOND,  WORK,
11                          IWORK, INFO )
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13           CHARACTER      DIAG, NORM, UPLO
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15           INTEGER        INFO, KD, LDAB, N
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17           DOUBLE         PRECISION RCOND
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19           INTEGER        IWORK( * )
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21           DOUBLE         PRECISION AB( LDAB, * ), WORK( * )
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PURPOSE

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

33       NORM    (input) CHARACTER*1
34               Specifies  whether the 1-norm condition number or the infinity-
35               norm condition number is required:
36               = '1' or 'O':  1-norm;
37               = 'I':         Infinity-norm.
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39       UPLO    (input) CHARACTER*1
40               = 'U':  A is upper triangular;
41               = 'L':  A is lower triangular.
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43       DIAG    (input) CHARACTER*1
44               = 'N':  A is non-unit triangular;
45               = 'U':  A is unit triangular.
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47       N       (input) INTEGER
48               The order of the matrix A.  N >= 0.
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50       KD      (input) INTEGER
51               The number of superdiagonals or subdiagonals of the  triangular
52               band matrix A.  KD >= 0.
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54       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
55               The  upper  or  lower  triangular  band matrix A, stored in the
56               first kd+1 rows of the array. The j-th column of A is stored in
57               the  j-th  column  of  the  array AB as follows: if UPLO = 'U',
58               AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO  =  'L',
59               AB(1+i-j,j)     = A(i,j) for j<=i<=min(n,j+kd).  If DIAG = 'U',
60               the diagonal elements of A are not referenced and  are  assumed
61               to be 1.
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63       LDAB    (input) INTEGER
64               The leading dimension of the array AB.  LDAB >= KD+1.
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66       RCOND   (output) DOUBLE PRECISION
67               The  reciprocal  of  the condition number of the matrix A, com‐
68               puted as RCOND = 1/(norm(A) * norm(inv(A))).
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70       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
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72       IWORK   (workspace) INTEGER array, dimension (N)
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74       INFO    (output) INTEGER
75               = 0:  successful exit
76               < 0:  if INFO = -i, the i-th argument had an illegal value
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80 LAPACK routine (version 3.1)    November 2006                       DTBCON(1)
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