Developer Reference

Contents

?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by
?pttrf
.

Syntax

lapack_int LAPACKE_spttrs
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
d
,
const float*
e
,
float*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_dpttrs
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
d
,
const double*
e
,
double*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_cpttrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
d
,
const lapack_complex_float*
e
,
lapack_complex_float*
b
,
lapack_int
ldb
);
lapack_int LAPACKE_zpttrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
d
,
const lapack_complex_double*
e
,
lapack_complex_double*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
a system of linear equations
A*X
=
B
with a symmetric (Hermitian) positive-definite tridiagonal matrix
A
. Before calling this routine, call
?pttrf
to compute the
L*D*L
T
or
U
T
*D*U
for real data and the
L*D*L
H
or
U
H
*D*U
factorization of
A
for complex data.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Used for
cpttrs
/
zpttrs
only. Must be
'U'
or
'L'
.
Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix
A
is stored and how
A
is factored:
If
uplo
=
'U'
, the array
e
stores the conjugated values of the superdiagonal of
U
, and
A
is factored as
U
H
*D*U
.
If
uplo
=
'L'
, the array
e
stores the subdiagonal of
L
, and
A
is factored as
L*D*L
H
.
n
The order of
A
;
n
0.
nrhs
The number of right-hand sides, that is, the number of columns of the matrix
B
;
nrhs
0.
d
Array, dimension (
n
). Contains the diagonal elements of the diagonal matrix
D
from the factorization computed by
?pttrf
.
e
Array
e
is of size (
n
-1).
The array
e
contains the (
n
- 1) sub-diagonal elements of the unit bidiagonal factor
L
or the conjugated values of the superdiagonal of
U
from the factorization computed by
?pttrf
(see
uplo
).
e
,
b
The array
b
contains the matrix
B
whose columns are the right-hand sides for the systems of equations.
The size of
b
is at least max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout.
ldb
The leading dimension of
b
;
ldb
max(1,
n
) for column major layout and
ldb
nrhs
for row major layout
.
Output Parameters
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.

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