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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
- $ INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER INFO, LDA, M, N
- DOUBLE PRECISION AMAX, COLCND, ROWCND
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DGEEQU computes row and column scalings intended to equilibrate an
-* M-by-N matrix A and reduce its condition number. R returns the row
-* scale factors and C the column scale factors, chosen to try to make
-* the largest element in each row and column of the matrix B with
-* elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
-*
-* R(i) and C(j) are restricted to be between SMLNUM = smallest safe
-* number and BIGNUM = largest safe number. Use of these scaling
-* factors is not guaranteed to reduce the condition number of A but
-* works well in practice.
-*
-* Arguments
-* =========
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix A. N >= 0.
-*
-* A (input) DOUBLE PRECISION array, dimension (LDA,N)
-* The M-by-N matrix whose equilibration factors are
-* to be computed.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* R (output) DOUBLE PRECISION array, dimension (M)
-* If INFO = 0 or INFO > M, R contains the row scale factors
-* for A.
-*
-* C (output) DOUBLE PRECISION array, dimension (N)
-* If INFO = 0, C contains the column scale factors for A.
-*
-* ROWCND (output) DOUBLE PRECISION
-* If INFO = 0 or INFO > M, ROWCND contains the ratio of the
-* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
-* AMAX is neither too large nor too small, it is not worth
-* scaling by R.
-*
-* COLCND (output) DOUBLE PRECISION
-* If INFO = 0, COLCND contains the ratio of the smallest
-* C(i) to the largest C(i). If COLCND >= 0.1, it is not
-* worth scaling by C.
-*
-* AMAX (output) DOUBLE PRECISION
-* Absolute value of largest matrix element. If AMAX is very
-* close to overflow or very close to underflow, the matrix
-* should be scaled.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, and i is
-* <= M: the i-th row of A is exactly zero
-* > M: the (i-M)-th column of A is exactly zero
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE, ZERO
- PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
-* ..
-* .. Local Scalars ..
- INTEGER I, J
- DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
-* ..
-* .. External Functions ..
- DOUBLE PRECISION DLAMCH
- EXTERNAL DLAMCH
-* ..
-* .. External Subroutines ..
- EXTERNAL XERBLA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, MIN
-* ..
-* .. Executable Statements ..
-*
-* Test the input parameters.
-*
- INFO = 0
- IF( M.LT.0 ) THEN
- INFO = -1
- ELSE IF( N.LT.0 ) THEN
- INFO = -2
- ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
- INFO = -4
- END IF
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'DGEEQU', -INFO )
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( M.EQ.0 .OR. N.EQ.0 ) THEN
- ROWCND = ONE
- COLCND = ONE
- AMAX = ZERO
- RETURN
- END IF
-*
-* Get machine constants.
-*
- SMLNUM = DLAMCH( 'S' )
- BIGNUM = ONE / SMLNUM
-*
-* Compute row scale factors.
-*
- DO 10 I = 1, M
- R( I ) = ZERO
- 10 CONTINUE
-*
-* Find the maximum element in each row.
-*
- DO 30 J = 1, N
- DO 20 I = 1, M
- R( I ) = MAX( R( I ), ABS( A( I, J ) ) )
- 20 CONTINUE
- 30 CONTINUE
-*
-* Find the maximum and minimum scale factors.
-*
- RCMIN = BIGNUM
- RCMAX = ZERO
- DO 40 I = 1, M
- RCMAX = MAX( RCMAX, R( I ) )
- RCMIN = MIN( RCMIN, R( I ) )
- 40 CONTINUE
- AMAX = RCMAX
-*
- IF( RCMIN.EQ.ZERO ) THEN
-*
-* Find the first zero scale factor and return an error code.
-*
- DO 50 I = 1, M
- IF( R( I ).EQ.ZERO ) THEN
- INFO = I
- RETURN
- END IF
- 50 CONTINUE
- ELSE
-*
-* Invert the scale factors.
-*
- DO 60 I = 1, M
- R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
- 60 CONTINUE
-*
-* Compute ROWCND = min(R(I)) / max(R(I))
-*
- ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
- END IF
-*
-* Compute column scale factors
-*
- DO 70 J = 1, N
- C( J ) = ZERO
- 70 CONTINUE
-*
-* Find the maximum element in each column,
-* assuming the row scaling computed above.
-*
- DO 90 J = 1, N
- DO 80 I = 1, M
- C( J ) = MAX( C( J ), ABS( A( I, J ) )*R( I ) )
- 80 CONTINUE
- 90 CONTINUE
-*
-* Find the maximum and minimum scale factors.
-*
- RCMIN = BIGNUM
- RCMAX = ZERO
- DO 100 J = 1, N
- RCMIN = MIN( RCMIN, C( J ) )
- RCMAX = MAX( RCMAX, C( J ) )
- 100 CONTINUE
-*
- IF( RCMIN.EQ.ZERO ) THEN
-*
-* Find the first zero scale factor and return an error code.
-*
- DO 110 J = 1, N
- IF( C( J ).EQ.ZERO ) THEN
- INFO = M + J
- RETURN
- END IF
- 110 CONTINUE
- ELSE
-*
-* Invert the scale factors.
-*
- DO 120 J = 1, N
- C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
- 120 CONTINUE
-*
-* Compute COLCND = min(C(J)) / max(C(J))
-*
- COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
- END IF
-*
- RETURN
-*
-* End of DGEEQU
-*
- END