dtrcon.f

          SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
         $                   IWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, NORM, UPLO
          INTEGER            INFO, LDA, N
          DOUBLE PRECISION   RCOND
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   A( LDA, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DTRCON estimates the reciprocal of the condition number of a
    *  triangular 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.
    *
    *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
    *          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
    *          upper triangular part of the array A contains the upper
    *          triangular matrix, and the strictly lower triangular part of
    *          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
    *          triangular part of the array A contains the lower triangular
    *          matrix, and the strictly upper triangular part of A is not
    *          referenced.  If DIAG = 'U', the diagonal elements of A are
    *          also not referenced and are assumed to be 1.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  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) DOUBLE PRECISION array, dimension (3*N)
    *
    *  IWORK   (workspace) INTEGER 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
    *     ..
    *     .. Local Arrays ..
          INTEGER            ISAVE( 3 )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            IDAMAX
          DOUBLE PRECISION   DLAMCH, DLANTR
          EXTERNAL           LSAME, IDAMAX, DLAMCH, DLANTR
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLACN2, DLATRS, 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( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -6
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DTRCON', -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 = DLANTR( NORM, UPLO, DIAG, N, N, A, LDA, 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 DLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
         $                      LDA, WORK, SCALE, WORK( 2*N+1 ), INFO )
                ELSE
    *
    *              Multiply by inv(A').
    *
                   CALL DLATRS( UPLO, 'Transpose', DIAG, NORMIN, N, A, LDA,
         $                      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 DTRCON
    *
          END