Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.10
  • 10/21/2020
  • 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

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