Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?ptsv

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

Syntax

lapack_int LAPACKE_sptsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
float*
d
,
float*
e
,
float*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_dptsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
double*
d
,
double*
e
,
double*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_cptsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
float*
d
,
lapack_complex_float*
e
,
lapack_complex_float*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_zptsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
double*
d
,
lapack_complex_double*
e
,
lapack_complex_double*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
 the real or complex system of linear equations
A*X
 =
B
, where
A
 is an
n
-by-
n
 symmetric/Hermitian positive-definite tridiagonal matrix, the columns of matrix
B
 are individual right-hand sides, and the columns of
X
 are the corresponding solutions.
A
 is factored as
A
 =
L*D*L
T
 (real flavors) or
A
 =
L*D*L
H
 (complex flavors), and the factored form of
A
 is then used to solve the system of equations
A*X
 =
B
.
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 matrix
A
;
n
≥
 0.
nrhs
The number of right-hand sides, the number of columns in
B
;
nrhs
≥
 0
.
d
Array, dimension at least
max(1,
n
)
. Contains the diagonal elements of the tridiagonal matrix
A
.
e
,
b
Arrays:
e
 (size
n
 - 1),
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout
. The array
e
 contains the
(
n
 - 1)
 subdiagonal elements of
A
.
The array
b
 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
d
Overwritten by the
n
 diagonal elements of the diagonal matrix
D
 from the
L*D*L
T
 (real)/
L*D*L
H
 (complex) factorization of
A
.
e
Overwritten by the
(
n
 - 1)
 subdiagonal elements of the unit bidiagonal factor
L
 from the factorization of
A
.
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
, the leading minor of order
i
 (and therefore the matrix
A
 itself) is not positive-definite, 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.