Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?gtsv

Computes the solution to the system of linear equations with a tridiagonal coefficient matrix A and multiple right-hand sides.

Syntax

lapack_int
LAPACKE_sgtsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
float
*
dl
,
float
*
d
,
float
*
du
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dgtsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
double
*
dl
,
double
*
d
,
double
*
du
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cgtsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_float
*
dl
,
lapack_complex_float
*
d
,
lapack_complex_float
*
du
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zgtsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_double
*
dl
,
lapack_complex_double
*
d
,
lapack_complex_double
*
du
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
 the system of linear equations
A*X
 =
B
, where
A
 is an
n
-by-
n
 tridiagonal matrix, the columns of matrix
B
 are individual right-hand sides, and the columns of
X
 are the corresponding solutions. The routine uses Gaussian elimination with partial pivoting.
Note that the equation
A
T
*X
 =
B
 may be solved by interchanging the order of the arguments
du
 and
dl
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
n
The order of
A
, the number of rows in
B
;
n
≥
 0.
nrhs
The number of right-hand sides, the number of columns in
B
;
nrhs
≥
 0
.
dl
The array
dl
 (size
n
 - 1) contains the
(
n
 - 1)
 subdiagonal elements of
A
.
d
The array
d
 (size
n
) contains the diagonal elements of
A
.
du
The array
du
 (size
n
 - 1) contains the
(
n
 - 1)
 superdiagonal elements of
A
.
b
The array
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout
 contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
Output Parameters
dl
Overwritten by the
(
n
-2)
 elements of the second superdiagonal of the upper triangular matrix
U
 from the
LU
 factorization of A. These elements are stored in
dl
[0], ...,
dl
[
n
 - 3]
.
d
Overwritten by the
n
 diagonal elements of
U
.
du
Overwritten by the
(
n
-1)
 elements of the first superdiagonal of
U
.
b
Overwritten by the solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.
If
info
 =
i
,
U
i
,
i
 is exactly zero, and the solution has not been computed. The factorization has not been completed unless
i
 =
n
.

Product and Performance Information

1

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