144c6b23bd
Added lapack routines for calculation of condition number and to fill out the QR factorization capability.
226 lines
6 KiB
Fortran
226 lines
6 KiB
Fortran
SUBROUTINE DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
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$ INFO )
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*
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* -- LAPACK routine (version 3.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* March 31, 1993
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*
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* .. Scalar Arguments ..
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INTEGER INFO, 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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* DGEEQU computes row and column scalings intended to equilibrate an
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* M-by-N matrix A and reduce its condition number. R returns the row
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* scale factors and C the column scale factors, chosen to try to make
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* the largest element in each row and column of the matrix B with
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* elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
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*
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* R(i) and C(j) are restricted to be between SMLNUM = smallest safe
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* number and BIGNUM = largest safe number. Use of these scaling
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* factors is not guaranteed to reduce the condition number of A but
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* works well in practice.
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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) DOUBLE PRECISION array, dimension (LDA,N)
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* The M-by-N matrix whose equilibration factors are
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* to be computed.
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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,M).
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*
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* R (output) DOUBLE PRECISION array, dimension (M)
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* If INFO = 0 or INFO > M, R contains the row scale factors
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* for A.
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*
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* C (output) DOUBLE PRECISION array, dimension (N)
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* If INFO = 0, C contains the column scale factors for A.
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*
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* ROWCND (output) DOUBLE PRECISION
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* If INFO = 0 or INFO > M, ROWCND contains the ratio of the
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* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
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* AMAX is neither too large nor too small, it is not worth
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* scaling by R.
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*
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* COLCND (output) DOUBLE PRECISION
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* If INFO = 0, COLCND contains the ratio of the smallest
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* C(i) to the largest C(i). If COLCND >= 0.1, it is not
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* worth scaling by C.
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*
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* AMAX (output) DOUBLE PRECISION
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* Absolute value of largest matrix element. If AMAX is very
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* close to overflow or very close to underflow, the matrix
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* should be scaled.
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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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* > 0: if INFO = i, and i is
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* <= M: the i-th row of A is exactly zero
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* > M: the (i-M)-th column of A is exactly zero
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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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INTEGER I, J
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DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
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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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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN
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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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IF( M.LT.0 ) 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, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGEEQU', -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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IF( M.EQ.0 .OR. N.EQ.0 ) THEN
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ROWCND = ONE
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COLCND = ONE
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AMAX = ZERO
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RETURN
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END IF
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*
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* Get machine constants.
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*
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SMLNUM = DLAMCH( 'S' )
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BIGNUM = ONE / SMLNUM
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*
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* Compute row scale factors.
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*
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DO 10 I = 1, M
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R( I ) = ZERO
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10 CONTINUE
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*
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* Find the maximum element in each row.
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*
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DO 30 J = 1, N
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DO 20 I = 1, M
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R( I ) = MAX( R( I ), ABS( A( I, J ) ) )
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20 CONTINUE
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30 CONTINUE
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*
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* Find the maximum and minimum scale factors.
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*
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RCMIN = BIGNUM
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RCMAX = ZERO
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DO 40 I = 1, M
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RCMAX = MAX( RCMAX, R( I ) )
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RCMIN = MIN( RCMIN, R( I ) )
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40 CONTINUE
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AMAX = RCMAX
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*
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IF( RCMIN.EQ.ZERO ) THEN
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*
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* Find the first zero scale factor and return an error code.
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*
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DO 50 I = 1, M
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IF( R( I ).EQ.ZERO ) THEN
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INFO = I
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RETURN
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END IF
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50 CONTINUE
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ELSE
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*
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* Invert the scale factors.
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*
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DO 60 I = 1, M
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R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
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60 CONTINUE
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*
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* Compute ROWCND = min(R(I)) / max(R(I))
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*
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ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
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END IF
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*
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* Compute column scale factors
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*
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DO 70 J = 1, N
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C( J ) = ZERO
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70 CONTINUE
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*
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* Find the maximum element in each column,
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* assuming the row scaling computed above.
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*
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DO 90 J = 1, N
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DO 80 I = 1, M
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C( J ) = MAX( C( J ), ABS( A( I, J ) )*R( I ) )
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80 CONTINUE
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90 CONTINUE
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*
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* Find the maximum and minimum scale factors.
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*
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RCMIN = BIGNUM
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RCMAX = ZERO
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DO 100 J = 1, N
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RCMIN = MIN( RCMIN, C( J ) )
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RCMAX = MAX( RCMAX, C( J ) )
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100 CONTINUE
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*
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IF( RCMIN.EQ.ZERO ) THEN
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*
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* Find the first zero scale factor and return an error code.
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*
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DO 110 J = 1, N
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IF( C( J ).EQ.ZERO ) THEN
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INFO = M + J
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RETURN
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END IF
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110 CONTINUE
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ELSE
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*
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* Invert the scale factors.
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*
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DO 120 J = 1, N
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C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
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120 CONTINUE
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*
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* Compute COLCND = min(C(J)) / max(C(J))
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*
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COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
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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 DGEEQU
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*
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END
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