 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zlaqr1()

 subroutine zlaqr1 ( integer N, complex*16, dimension( ldh, * ) H, integer LDH, complex*16 S1, complex*16 S2, complex*16, dimension( * ) V )

ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

Purpose:
```      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.```
Parameters
 [in] N ``` N is INTEGER Order of the matrix H. N must be either 2 or 3.``` [in] H ``` H is COMPLEX*16 array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*).``` [in] LDH ``` LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N``` [in] S1 ` S1 is COMPLEX*16` [in] S2 ``` S2 is COMPLEX*16 S1 and S2 are the shifts defining K in (*) above.``` [out] V ``` V is COMPLEX*16 array, dimension (N) A scalar multiple of the first column of the matrix K in (*).```
Contributors:
Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 106 of file zlaqr1.f.

107*
108* -- LAPACK auxiliary routine --
109* -- LAPACK is a software package provided by Univ. of Tennessee, --
110* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111*
112* .. Scalar Arguments ..
113 COMPLEX*16 S1, S2
114 INTEGER LDH, N
115* ..
116* .. Array Arguments ..
117 COMPLEX*16 H( LDH, * ), V( * )
118* ..
119*
120* ================================================================
121*
122* .. Parameters ..
123 COMPLEX*16 ZERO
124 parameter( zero = ( 0.0d0, 0.0d0 ) )
125 DOUBLE PRECISION RZERO
126 parameter( rzero = 0.0d0 )
127* ..
128* .. Local Scalars ..
129 COMPLEX*16 CDUM, H21S, H31S
130 DOUBLE PRECISION S
131* ..
132* .. Intrinsic Functions ..
133 INTRINSIC abs, dble, dimag
134* ..
135* .. Statement Functions ..
136 DOUBLE PRECISION CABS1
137* ..
138* .. Statement Function definitions ..
139 cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) )
140* ..
141* .. Executable Statements ..
142*
143* Quick return if possible
144*
145 IF( n.NE.2 .AND. n.NE.3 ) THEN
146 RETURN
147 END IF
148*
149 IF( n.EQ.2 ) THEN
150 s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) )
151 IF( s.EQ.rzero ) THEN
152 v( 1 ) = zero
153 v( 2 ) = zero
154 ELSE
155 h21s = h( 2, 1 ) / s
156 v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-s1 )*
157 \$ ( ( h( 1, 1 )-s2 ) / s )
158 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 )
159 END IF
160 ELSE
161 s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) ) +
162 \$ cabs1( h( 3, 1 ) )
163 IF( s.EQ.zero ) THEN
164 v( 1 ) = zero
165 v( 2 ) = zero
166 v( 3 ) = zero
167 ELSE
168 h21s = h( 2, 1 ) / s
169 h31s = h( 3, 1 ) / s
170 v( 1 ) = ( h( 1, 1 )-s1 )*( ( h( 1, 1 )-s2 ) / s ) +
171 \$ h( 1, 2 )*h21s + h( 1, 3 )*h31s
172 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 ) + h( 2, 3 )*h31s
173 v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-s1-s2 ) + h21s*h( 3, 2 )
174 END IF
175 END IF
Here is the caller graph for this function: