Developer Reference

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

?latm6

Generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues.

Syntax

call slatm6
(
type
,
n
,
a
,
lda
,
b
,
x
,
ldx
,
y
,
ldy
,
alpha
,
beta
,
wx
,
wy
,
s
,
dif
)
call dlatm6
(
type
,
n
,
a
,
lda
,
b
,
x
,
ldx
,
y
,
ldy
,
alpha
,
beta
,
wx
,
wy
,
s
,
dif
)
call clatm6
(
type
,
n
,
a
,
lda
,
b
,
x
,
ldx
,
y
,
ldy
,
alpha
,
beta
,
wx
,
wy
,
s
,
dif
)
call zlatm6
(
type
,
n
,
a
,
lda
,
b
,
x
,
ldx
,
y
,
ldy
,
alpha
,
beta
,
wx
,
wy
,
s
,
dif
)
Include Files
  • mkl.fi
Description
The
?latm6
routine generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues.
There two kinds of test matrix pairs:
       (
A
,
B
)= inverse(
YH
) * (
Da
,
Db
) * inverse(
X
)
Type 1:
Type 2:
In both cases the same inverse(
YH
) and inverse(X) are used to compute (
A
,
B
), giving the exact eigenvectors to (
A
,
B
) as (
YH
,
X
):
,
where
a
,
b
,
x
and
y
will have all values independently of each other.
Input Parameters
type
INTEGER
.
Specifies the problem type.
n
INTEGER
.
Size of the matrices
A
and
B
.
lda
INTEGER
.
The leading dimension of
a
and of
b
.
ldx
INTEGER
.
The leading dimension of
x
.
ldy
INTEGER
.
The leading dimension of
y
.
alpha
,
beta
REAL
for
slatm6
,
DOUBLE PRECISION
for
dlatm6
,
COMPLEX
for
clatm6
,
DOUBLE COMPLEX
for
zlatm6
,
Weighting constants for matrix
A
.
wx
REAL
for
slatm6
,
DOUBLE PRECISION
for
dlatm6
,
COMPLEX
for
clatm6
,
DOUBLE COMPLEX
for
zlatm6
,
Constant for right eigenvector matrix.
wy
REAL
for