Contents

# ?tfsm

Solves a matrix equation (one operand is a triangular matrix in RFP format).

## Syntax

Include Files
• mkl.h
Description
The
?tfsm
routines solve one of the following matrix equations:
`op(A)*X = alpha*B,`
or
`X*op(A) = alpha*B,`
where:
alpha
is a scalar,
X
and
B
are
m
-by-
n
matrices,
A
is a unit, or non-unit, upper or lower triangular matrix in rectangular full packed (RFP) format.
op(
A
)
can be one of the following:
• op(
A
) =
A
or
op(
A
) =
A
T
for real flavors
• op(
A
) =
A
or
op(
A
) =
A
H
for complex flavors
The matrix
B
is overwritten by the solution matrix
X
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
transr
if
transr
= 'N'
or
'n'
, the normal form of RFP
A
is stored;
if
transr
= 'T'
or
't'
, the transpose form of RFP
A
is stored;
if
transr
= 'C'
or
'c'
, the conjugate-transpose form of RFP
A
is stored.
side
Specifies whether
op(
A
)
appears on the left or right of
X
in the equation:
if
side
=
'L'
or
'l'
, then
op(
A
)*
X
=
alpha
*
B
;
if
side
=
'R'
or
'r'
, then
X
*op(
A
) =
alpha
*
B
.
uplo
Specifies whether the RFP matrix
A
is upper or lower triangular:
if
uplo
=
'U'
or
'u'
, then the matrix is upper triangular;
if
uplo
=
'L'
or
'l'
, then the matrix is low triangular.
trans
Specifies the form of
op(
A
)
used in the matrix multiplication:
if
trans
= 'N'
or
'n'
, then
op(
A
) =
A
;
if
trans
= 'T'
or
't'
, then
op(
A
) =
A
'
;
if
trans
= 'C'
or
'c'
, then
op(
A
) = conjg(
A
')
.
diag
Specifies whether the RFP matrix
A
is unit triangular:
if
diag
=
'U'
or
'u'
then the matrix is unit triangular;
if
diag
=
'N'
or
'n'
, then the matrix is not unit triangular.
m
Specifies the number of rows of
B
. The value of
m
must be at least zero.
n
Specifies the number of columns of
B
. The value of
n
must be at least zero.
alpha
Specifies the scalar
alpha
.
When
alpha
is zero, then
a
is not referenced and
b
need not be set before entry.
a
Array, size
(
n
*(
n
+1)/2)
. Contains the matrix
A
in RFP format.
b
Array, size
max(1,
ldb
*
n
)
for column major and
max(1,
ldb
*m
)
for row major.
m
-by-
n
part of the array
b
must contain the right-hand side matrix
B
.
ldb
b
as declared in the calling (sub)program. The value of
ldb
must be at least
max(1,
m
)
for column major and
max(1,
n
)
for row major
.
Output Parameters
b
Overwritten by the solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
< 0
, the
i
-th parameter had an illegal value.
If
info
= -1011
, memory allocation error occurred.

#### 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