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

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