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SUBROUTINE <a name="DPBCON.1"></a><a href="dpbcon.f.html#DPBCON.1">DPBCON</a>( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
$ IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Modified to call <a name="DLACN2.8"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a> in place of <a name="DLACON.8"></a><a href="dlacon.f.html#DLACON.1">DLACON</a>, 5 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION ANORM, RCOND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DPBCON.23"></a><a href="dpbcon.f.html#DPBCON.1">DPBCON</a> estimates the reciprocal of the condition number (in the
</span><span class="comment">*</span><span class="comment"> 1-norm) of a real symmetric positive definite band matrix using the
</span><span class="comment">*</span><span class="comment"> Cholesky factorization A = U**T*U or A = L*L**T computed by <a name="DPBTRF.25"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment"> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular factor stored in AB;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular factor stored in AB.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KD (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> The triangular factor U or L from the Cholesky factorization
</span><span class="comment">*</span><span class="comment"> A = U**T*U or A = L*L**T of the band matrix A, stored in the
</span><span class="comment">*</span><span class="comment"> first KD+1 rows of the array. The j-th column of U or L is
</span><span class="comment">*</span><span class="comment"> stored in the j-th column of the array AB as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KD+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ANORM (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The 1-norm (or infinity-norm) of the symmetric band matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RCOND (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment"> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
</span><span class="comment">*</span><span class="comment"> estimate of the 1-norm of inv(A) computed in this routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
CHARACTER NORMIN
INTEGER IX, KASE
DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> INTEGER ISAVE( 3 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER IDAMAX
DOUBLE PRECISION <a name="DLAMCH.89"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
EXTERNAL <a name="LSAME.90"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, IDAMAX, <a name="DLAMCH.90"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
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