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

Include Files
• mkl.h
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
Specifies the problem type.
n
Size of the matrices
A
and
B
.
lda
a
and of
b
.
ldx
x
.
ldy
y
.
alpha
,
beta
Weighting constants for matrix
A
.
wx
Constant for right eigenvector matrix.
wy
Constant for left eigenvector matrix.
Output Parameters
a
Array, size
lda
*
n
. On exit,
a
contains the
n
-by-
n
matrix initialized according to
type
.
b
Array, size
lda
*
n
. On exit,
b
contains the
n
-by-
n
matrix initialized according to
type
.
x
Array, size
ldx
*
n
. On exit,
x
contains the
n
-by-
n
matrix of right eigenvectors.
y
Array, size
ldy
*
n
. On exit,
y
is the
n
-by-
n
matrix of left eigenvectors.
s
Array, size (
n
).
s
[
i
- 1]
is the reciprocal condition number for eigenvalue
i
.
dif
Array, size(
n
).
dif
[
i
- 1]
is the reciprocal condition number for eigenvector
i
.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804