spbcon()

subroutine spbcon	(	character	uplo,
		integer	n,
		integer	kd,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real	anorm,
		real	rcond,
		real, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info
	)

SPBCON

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Purpose:

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

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
[in]	AB	AB is REAL array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[in]	ANORM	ANORM is REAL The 1-norm (or infinity-norm) of the symmetric band matrix A.
[out]	RCOND	RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
[out]	WORK	WORK is REAL array, dimension (3*N)
[out]	IWORK	IWORK is INTEGER array, dimension (N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 130 of file spbcon.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
      REAL               ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      REAL               AB( LDAB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      CHARACTER          NORMIN
      INTEGER            IX, KASE
      REAL               AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ISAMAX
      REAL               SLAMCH
      EXTERNAL           lsame, isamax, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           slacn2, slatbs, srscl, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( kd.LT.0 ) THEN
         info = -3
      ELSE IF( ldab.LT.kd+1 ) THEN
         info = -5
      ELSE IF( anorm.LT.zero ) THEN
         info = -6
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SPBCON', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      rcond = zero
      IF( n.EQ.0 ) THEN
         rcond = one
         RETURN
      ELSE IF( anorm.EQ.zero ) THEN
         RETURN
      END IF
*
      smlnum = slamch( 'Safe minimum' )
*
*     Estimate the 1-norm of the inverse.
*
      kase = 0
      normin = 'N'
   10 CONTINUE
      CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( upper ) THEN
*
*           Multiply by inv(U**T).
*
            CALL slatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
     $                   kd, ab, ldab, work, scalel, work( 2*n+1 ),
     $                   info )
            normin = 'Y'
*
*           Multiply by inv(U).
*
            CALL slatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
     $                   kd, ab, ldab, work, scaleu, work( 2*n+1 ),
     $                   info )
         ELSE
*
*           Multiply by inv(L).
*
            CALL slatbs( 'Lower', 'No transpose', 'Non-unit', normin, n,
     $                   kd, ab, ldab, work, scalel, work( 2*n+1 ),
     $                   info )
            normin = 'Y'
*
*           Multiply by inv(L**T).
*
            CALL slatbs( 'Lower', 'Transpose', 'Non-unit', normin, n,
     $                   kd, ab, ldab, work, scaleu, work( 2*n+1 ),
     $                   info )
         END IF
*
*        Multiply by 1/SCALE if doing so will not cause overflow.
*
         scale = scalel*scaleu
         IF( scale.NE.one ) THEN
            ix = isamax( n, work, 1 )
            IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
     $         GO TO 20
            CALL srscl( n, scale, work, 1 )
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( ainvnm.NE.zero )
     $   rcond = ( one / ainvnm ) / anorm
*
   20 CONTINUE
*
      RETURN
*
*     End of SPBCON
*

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