Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?laqr1

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

Syntax

call slaqr1
(
n
,
h
,
ldh
,
sr1
,
si1
,
sr2
,
si2,
v
)
call dlaqr1
(
n
,
h
,
ldh
,
sr1
,
si1
,
sr2
,
si2,
v
)
call claqr1
(
n
,
h
,
ldh
,
s1
,
s2
,
v
)
call zlaqr1
(
n
,
h
,
ldh
,
s1
,
s2
,
v
)
Include Files
  • mkl.fi
Description
Given a 2-by-2 or 3-by-3 matrix
H
, this routine sets
v
to a scalar multiple of the first column of the product
K
= (
H
-
s1
*
I
)*(
H
-
s2
*
I
)
, or
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.
Input Parameters
n
INTEGER
.
The order of the matrix
H
.
n
must be equal to 2 or 3.
sr1
,
si2
,
sr2
,
si2
REAL
for
slaqr1
DOUBLE PRECISION
for
dlaqr1
Shift values that define
K
in the formula above.
s1
,
s2
COMPLEX
for
claqr1
DOUBLE COMPLEX
for
zlaqr1
.
Shift values that define
K
in the formula above.
h
REAL
for
slaqr1
DOUBLE PRECISION
for
dlaqr1
COMPLEX
for
claqr1
DOUBLE COMPLEX
for
zlaqr1
.
Array,
DIMENSION
(
ldh
,
n
), contains 2-by-2 or 3-by-3 matrix
H
in the formula above.
ldh
INTEGER
.
The leading dimension of the array
h
just as declared in the calling routine.
ldh
n
.
Output Parameters
v
REAL
for
slaqr1
DOUBLE PRECISION
for
dlaqr1
COMPLEX
for
claqr1
DOUBLE COMPLEX
for
zlaqr1
.
Array with dimension
(
n
)
.
A scalar multiple of the first column of the matrix
K
in the formula above.