ztbcon.f

          SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
         $                   RWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, NORM, UPLO
          INTEGER            INFO, KD, LDAB, N
          DOUBLE PRECISION   RCOND
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   RWORK( * )
          COMPLEX*16         AB( LDAB, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZTBCON 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)) ).
    *
    *  Arguments
    *  =========
    *
    *  NORM    (input) 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.
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  A is upper triangular;
    *          = 'L':  A is lower triangular.
    *
    *  DIAG    (input) CHARACTER*1
    *          = 'N':  A is non-unit triangular;
    *          = 'U':  A is unit triangular.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  KD      (input) INTEGER
    *          The number of superdiagonals or subdiagonals of the
    *          triangular band matrix A.  KD >= 0.
    *
    *  AB      (input) COMPLEX*16 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.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= KD+1.
    *
    *  RCOND   (output) DOUBLE PRECISION
    *          The reciprocal of the condition number of the matrix A,
    *          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    *
    *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
    *
    *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. 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
          COMPLEX*16         ZDUM
    *     ..
    *     .. Local Arrays ..
          INTEGER            ISAVE( 3 )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            IZAMAX
          DOUBLE PRECISION   DLAMCH, ZLANTB
          EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANTB
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZDRSCL, ZLACN2, ZLATBS
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, DIMAG, MAX
    *     ..
    *     .. Statement Functions ..
          DOUBLE PRECISION   CABS1
    *     ..
    *     .. Statement Function definitions ..
          CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
    *     ..
    *     .. 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( 'ZTBCON', -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( N, 1 ) )
    *
    *     Compute the 1-norm of the triangular matrix A or A'.
    *
          ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK )
    *
    *     Continue only if ANORM > 0.
    *
          IF( ANORM.GT.ZERO ) THEN
    *
    *        Estimate the 1-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 ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
             IF( KASE.NE.0 ) THEN
                IF( KASE.EQ.KASE1 ) THEN
    *
    *              Multiply by inv(A).
    *
                   CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
         $                      AB, LDAB, WORK, SCALE, RWORK, INFO )
                ELSE
    *
    *              Multiply by inv(A').
    *
                   CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
         $                      N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO )
                END IF
                NORMIN = 'Y'
    *
    *           Multiply by 1/SCALE if doing so will not cause overflow.
    *
                IF( SCALE.NE.ONE ) THEN
                   IX = IZAMAX( N, WORK, 1 )
                   XNORM = CABS1( WORK( IX ) )
                   IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
         $            GO TO 20
                   CALL ZDRSCL( 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 ZTBCON
    *
          END