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