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

6       CPBCON  -  the  reciprocal of the condition number (in the 1-norm) of a
7       complex Hermitian positive definite band matrix using the Cholesky fac‐
8       torization A = U**H*U or A = L*L**H computed by CPBTRF
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SYNOPSIS

11       SUBROUTINE CPBCON( UPLO,  N,  KD,  AB, LDAB, ANORM, RCOND, WORK, RWORK,
12                          INFO )
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14           CHARACTER      UPLO
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16           INTEGER        INFO, KD, LDAB, N
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18           REAL           ANORM, RCOND
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20           REAL           RWORK( * )
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22           COMPLEX        AB( LDAB, * ), WORK( * )
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PURPOSE

25       CPBCON estimates the reciprocal of the condition number (in the 1-norm)
26       of a complex Hermitian positive definite band matrix using the Cholesky
27       factorization A = U**H*U or A = L*L**H computed by CPBTRF.
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29       An estimate is obtained for norm(inv(A)), and  the  reciprocal  of  the
30       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

34       UPLO    (input) CHARACTER*1
35               = 'U':  Upper triangular factor stored in AB;
36               = 'L':  Lower triangular factor stored in AB.
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38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
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41       KD      (input) INTEGER
42               The  number of superdiagonals of the matrix A if UPLO = 'U', or
43               the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
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45       AB      (input) COMPLEX array, dimension (LDAB,N)
46               The triangular factor U or L from the Cholesky factorization  A
47               =  U**H*U  or  A  =  L*L**H of the band matrix A, stored in the
48               first KD+1 rows of the array.  The j-th column of  U  or  L  is
49               stored  in  the j-th column of the array AB as follows: if UPLO
50               ='U', AB(kd+1+i-j,j) = U(i,j) for  max(1,j-kd)<=i<=j;  if  UPLO
51               ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
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53       LDAB    (input) INTEGER
54               The leading dimension of the array AB.  LDAB >= KD+1.
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56       ANORM   (input) REAL
57               The 1-norm (or infinity-norm) of the Hermitian band matrix A.
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59       RCOND   (output) REAL
60               The  reciprocal  of  the condition number of the matrix A, com‐
61               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
62               mate of the 1-norm of inv(A) computed in this routine.
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64       WORK    (workspace) COMPLEX array, dimension (2*N)
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66       RWORK   (workspace) REAL array, dimension (N)
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68       INFO    (output) INTEGER
69               = 0:  successful exit
70               < 0:  if INFO = -i, the i-th argument had an illegal value
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74 LAPACK routine (version 3.1)    November 2006                       CPBCON(1)
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