Contents

# ?latm5

Generates matrices involved in the Generalized Sylvester equation.

## Syntax

Include Files
• mkl.h
Description
The
?latm5
routine generates matrices involved in the Generalized Sylvester equation:
A
*
R
-
L
*
B
=
C
D
*
R
-
L
*
E
=
F
They also satisfy the diagonalization condition:
Input Parameters
prtype
Specifies the type of matrices to generate.
• If
prtype
= 1
,
A
and
B
are Jordan blocks,
D
and
E
are identity matrices.
A
:
If
(
i
==
j
)
then
A
i
,
j
= 1.0
.
If
(
j
==
i
+ 1)
then
A
i
,
j
= -1.0
.
Otherwise
A
i
,
j
= 0.0,
i
,
j
= 1...
m
B
:
If
(
i
==
j
)
then
B
i
,
j
= 1.0 -
alpha
.
If
(
j
==
i
+ 1)
then
B
i
,
j
= 1.0
.
Otherwise
B
i
,
j
= 0.0,
i
,
j
= 1...
n
.
D
:
If
(
i
==
j
)
then
D
i
,
j
= 1.0
.
Otherwise
D
i
,
j
= 0.0,
i
,
j
= 1...
m
.
E:
If
(
i
==
j
)
then
E
i
,
j
= 1.0
Otherwise
E
i
,
j
= 0.0,
i
,
j
= 1...
n
.
L
=
R
are chosen from [-10...10], which specifies the right hand sides (
C
,
F
).
• If
prtype
= 2 or 3
: Triangular and/or quasi- triangular.
A
:
If
(
i
j
)
then
A
i
,
j
= [-1...1]
.
Otherwise
A
i
,
j
= 0.0,
i
,
j
= 1...M
.
If (
prtype
= 3) then
A
k
+ 1,
k
+ 1
=
A
k
,
k
;
A
k
+ 1,
k
= [-1...1]
;
sign(
A
k
,
k
+ 1
) = -(sign(
A
k
+ 1,
k
)
.
k
= 1,
m
- 1,
qblcka
B
:
If
(
i
j
)
then
B
i
,
j
= [-1...1]
.
Otherwise
B
i
,
j
= 0.0,
i
,
j
= 1...
n
.
If (
prtype
= 3) then
B
k
+ 1,
k
+ 1
=
B
k
,
k
B
k
+ 1,
k
= [-1...1]
sign(
B
k
,
k
+ 1
)
= -(sign(
B
k
+ 1,
k
)
k
= 1,
n
- 1,
qblckb
.
D
:
If
(
i
j
)
then
D
i
,
j
= [-1...1]
.
Otherwise
D
i
,
j
= 0.0,
i
,
j
= 1...
m
.
E
:
If
(i <= j)
then
E
i
,
j
= [-1...1]
.
Otherwise
E
i
,
j
= 0.0, i, j = 1...N
.
L
,
R
are chosen from [-10...10], which specifies the right hand sides (
C
,
F
).
• If
prtype
= 4 Full

A
i
,
j
= [-10...10]

D
i
,
j
= [-1...1]
i
,
j
= 1...
m

B
i
,
j
= [-10...10]

E
i
,
j
= [-1...1]
i
,
j
= 1...
n

R
i
,
j
= [-10...10]

L
i
,
j
= [-1...1]
i
= 1..
m
,
j
= 1...
n
L
and
R
specifies the right hand sides (
C
,
F
).
• If
prtype
= 5 special case common and/or close eigs.
m
Specifies the order of
A
and
D
and the number of rows in
C
,
F
,
R
and
L
.
n
Specifies the order of
B
and
E
and the number of columns in
C
,
F
,
R
and
L
.
lda
a
.
ldb
b
.
ldc
c
.
ldd
d
.
lde
e
.
ldf
f
.
ldr
r
.
ldl
l
.
alpha
Parameter used in generating
prtype
= 1 and 5 matrices.
qblcka
When
prtype
= 3, specifies the distance between 2-by-2 blocks on the diagonal in
A
. Otherwise,
qblcka
is not referenced.
qblcka
> 1.
qblckb
When
prtype
= 3, specifies the distance between 2-by-2 blocks on the diagonal in
B
. Otherwise,
qblckb
is not referenced.
qblckb
> 1.
Output Parameters
a
Array, size
lda
*
m
. On exit
a
contains the
m
-by-
m
array
A
initialized according to
prtype
.
b
Array, size
ldb
*
n
. On exit
b
contains the
n
-by-
n
array
B
initialized according to
prtype
.
c
Array, size
ldc
*
n
. On exit
c
contains the
m
-by-
n
array
C
initialized according to
prtype
.
d
Array, size
ldd
*
m
. On exit
d
contains the
m
-by-
m
array
D
initialized according to
prtype
.
e
Array, size
lde
*
n
. On exit
e
contains the
n
-by-
n
array
E
initialized according to
prtype
.
f
Array, size
ldf
*
n
. On exit
f
contains the
m
-by-
n
array
F
initialized according to
prtype
.
r
Array, size
ldr
*
n
. On exit
R
contains the
m
-by-
n
array
R
initialized according to
prtype
.
l
Array, size
ldl
*
n
. On exit
l
contains the
m
-by-
n
array
L
initialized according to
prtype
.

#### 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