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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 DGECON( NORM, N, A, LDA, ANORM, 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 NORM
+ INTEGER INFO, LDA, N
+ DOUBLE PRECISION ANORM, RCOND
+* ..
+* .. Array Arguments ..
+ INTEGER IWORK( * )
+ DOUBLE PRECISION A( LDA, * ), WORK( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DGECON estimates the reciprocal of the condition number of a general
+* real matrix A, in either the 1-norm or the infinity-norm, using
+* the LU factorization computed by DGETRF.
+*
+* An estimate is obtained for norm(inv(A)), and 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.
+*
+* N (input) INTEGER
+* The order of the matrix A. N >= 0.
+*
+* A (input) DOUBLE PRECISION array, dimension (LDA,N)
+* The factors L and U from the factorization A = P*L*U
+* as computed by DGETRF.
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(1,N).
+*
+* ANORM (input) DOUBLE PRECISION
+* If NORM = '1' or 'O', the 1-norm of the original matrix A.
+* If NORM = 'I', the infinity-norm of the original matrix A.
+*
+* 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 (4*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 ONENRM
+ CHARACTER NORMIN
+ INTEGER IX, KASE, KASE1
+ DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU
+* ..
+* .. Local Arrays ..
+ INTEGER ISAVE( 3 )
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER IDAMAX
+ DOUBLE PRECISION DLAMCH
+ EXTERNAL LSAME, IDAMAX, DLAMCH
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
+ IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( ANORM.LT.ZERO ) THEN
+ INFO = -5
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DGECON', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ RCOND = ZERO
+ IF( N.EQ.0 ) THEN
+ RCOND = ONE
+ RETURN
+ ELSE IF( ANORM.EQ.ZERO ) THEN
+ RETURN
+ END IF
+*
+ SMLNUM = DLAMCH( 'Safe minimum' )
+*
+* Estimate the norm of inv(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(L).
+*
+ CALL DLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A,
+ $ LDA, WORK, SL, WORK( 2*N+1 ), INFO )
+*
+* Multiply by inv(U).
+*
+ CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
+ $ A, LDA, WORK, SU, WORK( 3*N+1 ), INFO )
+ ELSE
+*
+* Multiply by inv(U').
+*
+ CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
+ $ LDA, WORK, SU, WORK( 3*N+1 ), INFO )
+*
+* Multiply by inv(L').
+*
+ CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A,
+ $ LDA, WORK, SL, WORK( 2*N+1 ), INFO )
+ END IF
+*
+* Divide X by 1/(SL*SU) if doing so will not cause overflow.
+*
+ SCALE = SL*SU
+ NORMIN = 'Y'
+ IF( SCALE.NE.ONE ) THEN
+ IX = IDAMAX( N, WORK, 1 )
+ IF( SCALE.LT.ABS( WORK( IX ) )*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 / AINVNM ) / ANORM
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of DGECON
+*
+ END