SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V ) * * -- LAPACK auxiliary routine (version 3.2) -- * Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. DOUBLE PRECISION SI1, SI2, SR1, SR2 INTEGER LDH, N * .. * .. Array Arguments .. DOUBLE PRECISION H( LDH, * ), V( * ) * .. * * Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a * scalar multiple of the first column of the product * * (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I) * * scaling to avoid overflows and most underflows. It * is assumed that either * * 1) sr1 = sr2 and si1 = -si2 * or * 2) si1 = si2 = 0. * * This is useful for starting double implicit shift bulges * in the QR algorithm. * * * N (input) integer * Order of the matrix H. N must be either 2 or 3. * * H (input) DOUBLE PRECISION array of dimension (LDH,N) * The 2-by-2 or 3-by-3 matrix H in (*). * * LDH (input) integer * The leading dimension of H as declared in * the calling procedure. LDH.GE.N * * SR1 (input) DOUBLE PRECISION * SI1 The shifts in (*). * SR2 * SI2 * * V (output) DOUBLE PRECISION array of dimension N * A scalar multiple of the first column of the * matrix K in (*). * * ================================================================ * Based on contributions by * Karen Braman and Ralph Byers, Department of Mathematics, * University of Kansas, USA * * ================================================================ * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0d0 ) * .. * .. Local Scalars .. DOUBLE PRECISION H21S, H31S, S * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Executable Statements .. IF( N.EQ.2 ) THEN S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) IF( S.EQ.ZERO ) THEN V( 1 ) = ZERO V( 2 ) = ZERO ELSE H21S = H( 2, 1 ) / S V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )* \$ ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S ) V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) END IF ELSE S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) + \$ ABS( H( 3, 1 ) ) IF( S.EQ.ZERO ) THEN V( 1 ) = ZERO V( 2 ) = ZERO V( 3 ) = ZERO ELSE H21S = H( 2, 1 ) / S H31S = H( 3, 1 ) / S V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) - \$ SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) + \$ H( 2, 3 )*H31S V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) + \$ H21S*H( 3, 2 ) END IF END IF END