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

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
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
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

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