OpenBLAS/lapack-netlib/SRC/dtbcon.f

*> \brief \b DTBCON
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
*                          IWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, NORM, UPLO
*       INTEGER            INFO, KD, LDAB, N
*       DOUBLE PRECISION   RCOND
*       ..
*       .. Array Arguments ..
*       INTEGER            IWORK( * )
*       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*>
*> The norm of A is computed and an estimate is obtained for
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies whether the 1-norm condition number or the
*>          infinity-norm condition number is required:
*>          = '1' or 'O':  1-norm;
*>          = 'I':         Infinity-norm.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          = 'N':  A is non-unit triangular;
*>          = 'U':  A is unit triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*>          KD is INTEGER
*>          The number of superdiagonals or subdiagonals of the
*>          triangular band matrix A.  KD >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
*>          The upper or lower triangular band matrix A, stored in the
*>          first kd+1 rows of the array. The j-th column of A is stored
*>          in the j-th column of the array AB as follows:
*>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*>          If DIAG = 'U', the diagonal elements of A are not referenced
*>          and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*>          LDAB is INTEGER
*>          The leading dimension of the array AB.  LDAB >= KD+1.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is DOUBLE PRECISION
*>          The reciprocal of the condition number of the matrix A,
*>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (3*N)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
     $                   IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORM, UPLO
      INTEGER            INFO, KD, LDAB, N
      DOUBLE PRECISION   RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, ONENRM, UPPER
      CHARACTER          NORMIN
      INTEGER            IX, KASE, KASE1
      DOUBLE PRECISION   AINVNM, ANORM, SCALE, SMLNUM, XNORM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            IDAMAX
      DOUBLE PRECISION   DLAMCH, DLANTB
      EXTERNAL           LSAME, IDAMAX, DLAMCH, DLANTB
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLACN2, DLATBS, DRSCL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
      NOUNIT = LSAME( DIAG, 'N' )
*
      IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -2
      ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( KD.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DTBCON', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      END IF
*
      RCOND = ZERO
      SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
*
*     Compute the norm of the triangular matrix A.
*
      ANORM = DLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK )
*
*     Continue only if ANORM > 0.
*
      IF( ANORM.GT.ZERO ) THEN
*
*        Estimate the norm of the inverse of A.
*
         AINVNM = ZERO
         NORMIN = 'N'
         IF( ONENRM ) THEN
            KASE1 = 1
         ELSE
            KASE1 = 2
         END IF
         KASE = 0
   10    CONTINUE
         CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
         IF( KASE.NE.0 ) THEN
            IF( KASE.EQ.KASE1 ) THEN
*
*              Multiply by inv(A).
*
               CALL DLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
     $                      AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
            ELSE
*
*              Multiply by inv(A**T).
*
               CALL DLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB,
     $                      LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
            END IF
            NORMIN = 'Y'
*
*           Multiply by 1/SCALE if doing so will not cause overflow.
*
            IF( SCALE.NE.ONE ) THEN
               IX = IDAMAX( N, WORK, 1 )
               XNORM = ABS( WORK( IX ) )
               IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
     $            GO TO 20
               CALL DRSCL( 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 / ANORM ) / AINVNM
      END IF
*
   20 CONTINUE
      RETURN
*
*     End of DTBCON
*
      END