Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

cblas_?tpsv

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

Syntax

void
cblas_stpsv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
CBLAS_TRANSPOSE
trans
,
const
CBLAS_DIAG
diag
,
const
MKL_INT
n
,
const
float
*ap
,
float
*x
,
const
MKL_INT
incx
);
void
cblas_dtpsv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
CBLAS_TRANSPOSE
trans
,
const
CBLAS_DIAG
diag
,
const
MKL_INT
n
,
const
double
*ap
,
double
*x
,
const
MKL_INT
incx
);
void
cblas_ctpsv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
CBLAS_TRANSPOSE
trans
,
const
CBLAS_DIAG
diag
,
const
MKL_INT
n
,
const
void
*ap
,
void
*x
,
const
MKL_INT
incx
);
void
cblas_ztpsv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
CBLAS_TRANSPOSE
trans
,
const
CBLAS_DIAG
diag
,
const
MKL_INT
n
,
const
void
*ap
,
void
*x
,
const
MKL_INT
incx
);
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

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