Developer Reference

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

?lagv2

Computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (
A
,
B
) where B is upper triangular.

Syntax

call slagv2
(
a
,
lda
,
b
,
ldb
,
alphar
,
alphai
,
beta
,
csl
,
snl
,
csr
,
snr
)
call dlagv2
(
a
,
lda
,
b
,
ldb
,
alphar
,
alphai
,
beta
,
csl
,
snl
,
csr
,
snr
)
Include Files
  • mkl.fi
Description
The routine computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (
A
,
B
) where
B
is upper triangular. The routine computes orthogonal (rotation) matrices given by
csl
,
snl
and
csr
,
snr
such that:
1) if the pencil (
A
,
B
) has two real eigenvalues (include 0/0 or 1/0 types), then
Equation
Equation
2) if the pencil (
A
,
B
) has a pair of complex conjugate eigenvalues, then
Equation
Equation
where
b
11
b
22
>0.
Input Parameters
a
,
b
REAL
for
slagv2
DOUBLE PRECISION
for
dlagv2
Arrays:
a
(
lda
,
2)
contains the 2-by-2 matrix
A
;
b
(
ldb
,
2)
contains the upper triangular 2-by-2 matrix
B
.
lda
INTEGER
. The leading dimension of the array
a
;
lda
2
.
ldb
INTEGER
. The leading dimension of the array
b
;
ldb
2
.
Output Parameters
a
On exit,
a
is overwritten by the "
A
-part" of the generalized Schur form.
b
On exit,
b
is overwritten by the "
B
-part" of the generalized Schur form.
alphar
,
alphai
,
beta
REAL
for
slagv2
DOUBLE PRECISION
for
dlagv2
.
Arrays, dimension (2) each.
(
alphar
(k) +
i
*
alphai
(k))/
beta
(k)
are the eigenvalues of the pencil (
A
,
B
),
k=1,2
and
i
= sqrt(-1)
.
Note that
beta
(k) may be zero.
csl
,
snl
REAL
for
slagv2
DOUBLE PRECISION
for
dlagv2
The cosine and sine of the left rotation matrix, respectively.
csr
,
snr
REAL
for
slagv2
DOUBLE PRECISION
for
dlagv2
The cosine and sine of the right rotation matrix, respectively.