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

contains
A
1, 1
,
ap

and
ap

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

contains
A
1, 1
,
ap

and
ap

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

contains
A
1, 1
,
ap

and
ap

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

contains
A
1, 1
,
ap

and
ap

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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.