SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, 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 .. COMPLEX*16 S1, S2 INTEGER LDH, N * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), V( * ) * .. * * Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a * scalar multiple of the first column of the product * * (*) K = (H - s1*I)*(H - s2*I) * * scaling to avoid overflows and most underflows. * * 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) COMPLEX*16 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 * * S1 (input) COMPLEX*16 * S2 S1 and S2 are the shifts defining K in (*) above. * * V (output) COMPLEX*16 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 .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 CDUM, H21S, H31S DOUBLE PRECISION S * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. IF( N.EQ.2 ) THEN S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) IF( S.EQ.RZERO ) THEN V( 1 ) = ZERO V( 2 ) = ZERO ELSE H21S = H( 2, 1 ) / S V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-S1 )* \$ ( ( H( 1, 1 )-S2 ) / S ) V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) END IF ELSE S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) + \$ CABS1( 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 )-S1 )*( ( H( 1, 1 )-S2 ) / S ) + \$ H( 1, 2 )*H21S + H( 1, 3 )*H31S V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) + H( 2, 3 )*H31S V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-S1-S2 ) + H21S*H( 3, 2 ) END IF END IF END