155 lines
4.2 KiB
FortranFixed
155 lines
4.2 KiB
FortranFixed
SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
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$ EQUED )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER EQUED
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INTEGER LDA, M, N
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DOUBLE PRECISION AMAX, COLCND, ROWCND
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
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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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* DLAQGE equilibrates a general M by N matrix A using the row and
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* column scaling factors in the vectors R and C.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the M by N matrix A.
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* On exit, the equilibrated matrix. See EQUED for the form of
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* the equilibrated matrix.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(M,1).
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*
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* R (input) DOUBLE PRECISION array, dimension (M)
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* The row scale factors for A.
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*
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* C (input) DOUBLE PRECISION array, dimension (N)
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* The column scale factors for A.
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*
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* ROWCND (input) DOUBLE PRECISION
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* Ratio of the smallest R(i) to the largest R(i).
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*
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* COLCND (input) DOUBLE PRECISION
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* Ratio of the smallest C(i) to the largest C(i).
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*
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* AMAX (input) DOUBLE PRECISION
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* Absolute value of largest matrix entry.
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*
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* EQUED (output) CHARACTER*1
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* Specifies the form of equilibration that was done.
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* = 'N': No equilibration
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* = 'R': Row equilibration, i.e., A has been premultiplied by
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* diag(R).
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* = 'C': Column equilibration, i.e., A has been postmultiplied
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* by diag(C).
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* = 'B': Both row and column equilibration, i.e., A has been
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* replaced by diag(R) * A * diag(C).
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*
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* Internal Parameters
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* ===================
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*
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* THRESH is a threshold value used to decide if row or column scaling
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* should be done based on the ratio of the row or column scaling
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* factors. If ROWCND < THRESH, row scaling is done, and if
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* COLCND < THRESH, column scaling is done.
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*
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* LARGE and SMALL are threshold values used to decide if row scaling
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* should be done based on the absolute size of the largest matrix
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* element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, THRESH
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PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION CJ, LARGE, SMALL
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 ) THEN
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EQUED = 'N'
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RETURN
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END IF
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*
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* Initialize LARGE and SMALL.
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*
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SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
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LARGE = ONE / SMALL
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*
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IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
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$ THEN
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*
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* No row scaling
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*
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IF( COLCND.GE.THRESH ) THEN
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*
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* No column scaling
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*
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EQUED = 'N'
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ELSE
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*
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* Column scaling
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*
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DO 20 J = 1, N
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CJ = C( J )
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DO 10 I = 1, M
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A( I, J ) = CJ*A( I, J )
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10 CONTINUE
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20 CONTINUE
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EQUED = 'C'
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END IF
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ELSE IF( COLCND.GE.THRESH ) THEN
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*
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* Row scaling, no column scaling
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*
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DO 40 J = 1, N
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DO 30 I = 1, M
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A( I, J ) = R( I )*A( I, J )
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30 CONTINUE
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40 CONTINUE
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EQUED = 'R'
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ELSE
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*
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* Row and column scaling
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*
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DO 60 J = 1, N
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CJ = C( J )
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DO 50 I = 1, M
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A( I, J ) = CJ*R( I )*A( I, J )
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50 CONTINUE
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60 CONTINUE
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EQUED = 'B'
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END IF
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*
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RETURN
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*
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* End of DLAQGE
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*
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END
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