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authorSiddhesh Wani2015-05-25 14:46:31 +0530
committerSiddhesh Wani2015-05-25 14:46:31 +0530
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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