SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER EQUED, UPLO INTEGER KD, LDAB, N DOUBLE PRECISION AMAX, SCOND * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), S( * ) * .. * * Purpose * ======= * * DLAQSB equilibrates a symmetric band matrix A using the scaling * factors in the vector S. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored. * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of super-diagonals of the matrix A if UPLO = 'U', * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. * * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) * On entry, the upper or lower triangle of the symmetric band * matrix A, stored in the first KD+1 rows of the array. The * j-th column of A is stored in the j-th column of the array AB * as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * * On exit, if INFO = 0, the triangular factor U or L from the * Cholesky factorization A = U'*U or A = L*L' of the band * matrix A, in the same storage format as A. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD+1. * * S (input) DOUBLE PRECISION array, dimension (N) * The scale factors for A. * * SCOND (input) DOUBLE PRECISION * Ratio of the smallest S(i) to the largest S(i). * * AMAX (input) DOUBLE PRECISION * Absolute value of largest matrix entry. * * EQUED (output) CHARACTER*1 * Specifies whether or not equilibration was done. * = 'N': No equilibration. * = 'Y': Equilibration was done, i.e., A has been replaced by * diag(S) * A * diag(S). * * Internal Parameters * =================== * * THRESH is a threshold value used to decide if scaling should be done * based on the ratio of the scaling factors. If SCOND < THRESH, * scaling is done. * * LARGE and SMALL are threshold values used to decide if scaling should * be done based on the absolute size of the largest matrix element. * If AMAX > LARGE or AMAX < SMALL, 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 .. LOGICAL LSAME DOUBLE PRECISION DLAMCH EXTERNAL LSAME, DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN EQUED = 'N' RETURN END IF * * Initialize LARGE and SMALL. * SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) LARGE = ONE / SMALL * IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN * * No equilibration * EQUED = 'N' ELSE * * Replace A by diag(S) * A * diag(S). * IF( LSAME( UPLO, 'U' ) ) THEN * * Upper triangle of A is stored in band format. * DO 20 J = 1, N CJ = S( J ) DO 10 I = MAX( 1, J-KD ), J AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J ) 10 CONTINUE 20 CONTINUE ELSE * * Lower triangle of A is stored. * DO 40 J = 1, N CJ = S( J ) DO 30 I = J, MIN( N, J+KD ) AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J ) 30 CONTINUE 40 CONTINUE END IF EQUED = 'Y' END IF * RETURN * * End of DLAQSB * END