Contents

# cblas_?tpsv

Solves a system of linear equations whose coefficients are in a triangular packed matrix.

## Syntax

Include Files
• mkl.h
Description
The
?tpsv
routines solve one of the following systems of equations
A
*
x
=
b
, or
A
'*
x
=
b
, or
conjg(
A
')*
x
=
b
,
where:
b
and
x
are
n
-element vectors,
A
is an
n
-by-
n
unit, or non-unit, upper or lower triangular matrix, supplied in packed form.
This routine does not test for singularity or near-singularity.
Such tests must be performed before calling this routine.
Input Parameters
Layout
Specifies whether two-dimensional array storage is row-major (
CblasRowMajor
) or column-major (
CblasColMajor
).
uplo
Specifies whether the matrix
A
is upper or lower triangular:
uplo
=
CblasUpper
if
uplo
=
CblasLower
, then the matrix is low triangular.
trans
Specifies the system of equations:
if
trans
=
CblasNoTrans
, then
A
*
x
=
b
;
if
trans
=
CblasTrans
, then
A
'*
x
=
b
;
if
trans
=
CblasConjTrans
, then
conjg(
A
')*
x
=
b
.
diag
Specifies whether the matrix
A
is unit triangular:
if
diag
=
CblasUnit
then the matrix is unit triangular;
if
diag
=
CblasNonUnit
, then the matrix is not unit triangular.
n
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
ap
Array, size at least
((
n
*(
n
+ 1))/2)
.
For
Layout
=
CblasColMajor
:
Before entry with
uplo
=
CblasUpper
, the array
ap
must contain the upper triangular part of the triangular matrix packed sequentially, column-by-column, so that
ap
[0]
contains
A
1, 1
,
ap
[1]
and
ap
[2]
contain
A
1, 2
and
A
2, 2
respectively, and so on.
Before entry with
uplo
=
CblasLower
, the array
ap
must contain the lower triangular part of the triangular matrix packed sequentially, column-by-column, so that
ap
[0]
contains
A
1, 1
,
ap
[1]
and
ap
[2]
contain
A
2, 1
and
A
3, 1
respectively, and so on.
For
Layout
=
CblasRowMajor
:
Before entry with
uplo
=
CblasUpper
, the array
ap
must contain the upper triangular part of the triangular matrix packed sequentially, row-by-row,
ap
[0]
contains
A
1, 1
,
ap
[1]
and
ap
[2]
contain
A
1, 2
and
A
1, 3
respectively, and so on. Before entry with
uplo
=
CblasLower
, the array
ap
must contain the lower triangular part of the triangular matrix packed sequentially, row-by-row, so that
ap
[0]
contains
A
1, 1
,
ap
[1]
and
ap
[2]
contain
A
2, 1
and
A
2, 2
respectively, and so on.
When
diag
=
CblasUnit
, the diagonal elements of
a
are not referenced, but are assumed to be unity.
x
Array, size at least
(1 + (
n
- 1)*abs(
incx
))
. Before entry, the incremented array
x
must contain the
n
-element right-hand side vector
b
.
incx
Specifies the increment for the elements of
x
.
The value of
incx
must not be zero.
Output Parameters
x
Overwritten with the solution vector
x
.

#### 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