forked from lijiext/lammps
187 lines
5.2 KiB
Fortran
187 lines
5.2 KiB
Fortran
SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
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$ INFO )
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*
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* -- LAPACK routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2006
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*
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* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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INTEGER INFO, LDA, N
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DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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DOUBLE PRECISION A( LDA, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DGECON estimates the reciprocal of the condition number of a general
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* real matrix A, in either the 1-norm or the infinity-norm, using
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* the LU factorization computed by DGETRF.
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*
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* An estimate is obtained for norm(inv(A)), and the reciprocal of the
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* condition number is computed as
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* RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies whether the 1-norm condition number or the
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* infinity-norm condition number is required:
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* = '1' or 'O': 1-norm;
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* = 'I': Infinity-norm.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input) DOUBLE PRECISION array, dimension (LDA,N)
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* The factors L and U from the factorization A = P*L*U
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* as computed by DGETRF.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* ANORM (input) DOUBLE PRECISION
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* If NORM = '1' or 'O', the 1-norm of the original matrix A.
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* If NORM = 'I', the infinity-norm of the original matrix A.
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*
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* RCOND (output) DOUBLE PRECISION
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* The reciprocal of the condition number of the matrix A,
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* computed as RCOND = 1/(norm(A) * norm(inv(A))).
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
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*
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* IWORK (workspace) INTEGER array, dimension (N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL ONENRM
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CHARACTER NORMIN
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INTEGER IX, KASE, KASE1
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DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IDAMAX
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DOUBLE PRECISION DLAMCH
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EXTERNAL LSAME, IDAMAX, DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGECON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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RCOND = ZERO
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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ELSE IF( ANORM.EQ.ZERO ) THEN
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RETURN
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END IF
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*
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SMLNUM = DLAMCH( 'Safe minimum' )
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*
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* Estimate the norm of inv(A).
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*
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AINVNM = ZERO
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NORMIN = 'N'
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KASE = 0
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10 CONTINUE
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CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(L).
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*
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CALL DLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A,
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$ LDA, WORK, SL, WORK( 2*N+1 ), INFO )
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*
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* Multiply by inv(U).
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*
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CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
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$ A, LDA, WORK, SU, WORK( 3*N+1 ), INFO )
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ELSE
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*
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* Multiply by inv(U').
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*
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CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
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$ LDA, WORK, SU, WORK( 3*N+1 ), INFO )
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*
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* Multiply by inv(L').
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*
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CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A,
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$ LDA, WORK, SL, WORK( 2*N+1 ), INFO )
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END IF
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*
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* Divide X by 1/(SL*SU) if doing so will not cause overflow.
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*
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SCALE = SL*SU
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NORMIN = 'Y'
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IF( SCALE.NE.ONE ) THEN
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IX = IDAMAX( N, WORK, 1 )
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IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 20
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CALL DRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / AINVNM ) / ANORM
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*
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20 CONTINUE
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RETURN
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*
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* End of DGECON
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*
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END
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