169 lines
4.9 KiB
FortranFixed
169 lines
4.9 KiB
FortranFixed
SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
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$ AMAX, 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 KL, KU, LDAB, 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 AB( LDAB, * ), 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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* DLAQGB equilibrates a general M by N band matrix A with KL
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* subdiagonals and KU superdiagonals using the row and scaling factors
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* 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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* KL (input) INTEGER
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* The number of subdiagonals within the band of A. KL >= 0.
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*
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* KU (input) INTEGER
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* The number of superdiagonals within the band of A. KU >= 0.
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*
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* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
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* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
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* The j-th column of A is stored in the j-th column of the
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* array AB as follows:
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* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
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*
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* On exit, the equilibrated matrix, in the same storage format
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* as A. See EQUED for the form of the equilibrated matrix.
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDA >= KL+KU+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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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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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 = MAX( 1, J-KU ), MIN( M, J+KL )
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AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, 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 = MAX( 1, J-KU ), MIN( M, J+KL )
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AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, 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 = MAX( 1, J-KU ), MIN( M, J+KL )
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AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, 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 DLAQGB
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*
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END
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