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

6       SPBCON  -  estimates  the  reciprocal  of  the condition number (in the
7       1-norm) of a real symmetric positive definite  band  matrix  using  the
8       Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
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SYNOPSIS

11       SUBROUTINE SPBCON( UPLO,  N,  KD,  AB, LDAB, ANORM, RCOND, WORK, IWORK,
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           INTEGER        IWORK( * )
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22           REAL           AB( LDAB, * ), WORK( * )
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PURPOSE

25       SPBCON estimates the reciprocal of the condition number (in the 1-norm)
26       of  a  real  symmetric positive definite band matrix using the Cholesky
27       factorization A = U**T*U or A = L*L**T computed by SPBTRF.  An estimate
28       is  obtained for norm(inv(A)), and the reciprocal of the condition num‐
29       ber is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

32       UPLO    (input) CHARACTER*1
33               = 'U':  Upper triangular factor stored in AB;
34               = 'L':  Lower triangular factor stored in AB.
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36       N       (input) INTEGER
37               The order of the matrix A.  N >= 0.
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39       KD      (input) INTEGER
40               The number of superdiagonals of the matrix A if UPLO = 'U',  or
41               the number of subdiagonals if UPLO = 'L'.  KD >= 0.
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43       AB      (input) REAL array, dimension (LDAB,N)
44               The  triangular factor U or L from the Cholesky factorization A
45               = U**T*U or A = L*L**T of the band  matrix  A,  stored  in  the
46               first  KD+1  rows  of  the array.  The j-th column of U or L is
47               stored in the j-th column of the array AB as follows:  if  UPLO
48               ='U',  AB(kd+1+i-j,j)  =  U(i,j) for max(1,j-kd)<=i<=j; if UPLO
49               ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
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51       LDAB    (input) INTEGER
52               The leading dimension of the array AB.  LDAB >= KD+1.
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54       ANORM   (input) REAL
55               The 1-norm (or infinity-norm) of the symmetric band matrix A.
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57       RCOND   (output) REAL
58               The reciprocal of the condition number of the  matrix  A,  com‐
59               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
60               mate of the 1-norm of inv(A) computed in this routine.
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62       WORK    (workspace) REAL array, dimension (3*N)
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64       IWORK   (workspace) INTEGER array, dimension (N)
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66       INFO    (output) INTEGER
67               = 0:  successful exit
68               < 0:  if INFO = -i, the i-th argument had an illegal value
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72 LAPACK routine (version 3.2)    November 2008                       SPBCON(1)
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