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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- 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