## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?pttrf

Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine forms the factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite tridiagonal matrix
A
:
A
=
L*D*L
T
for real flavors, or
A
=
L*D*L
H
for complex flavors,
where
D
is diagonal and
L
is unit lower bidiagonal. The factorization may also be regarded as having the form
A
=
U
T
*D*U
for real flavors, or
A
=
U
H
*D*U
for complex flavors, where
U
is unit upper bidiagonal.
Input Parameters
n
INTEGER
.
The order of the matrix
A
;
n
0.
d
REAL
for
spttrf
,
cpttrf
DOUBLE PRECISION
for
dpttrf
,
zpttrf
.
Array, dimension (
n
). Contains the diagonal elements of
A
.
e
REAL
for
spttrf
DOUBLE PRECISION
for
dpttrf
COMPLEX
for
cpttrf
DOUBLE COMPLEX
for
zpttrf
.
Array, dimension (
n
-1). Contains the subdiagonal elements of
A
.
Output Parameters
d
Overwritten by the
n
diagonal elements of the diagonal matrix
D
from the
L*D*L
T
(for real flavors) or
L*D*L
H
(for complex flavors) factorization of
A
.
e
Overwritten by the
(
n
- 1)
sub-diagonal elements of the unit bidiagonal factor
L
or
U
from the factorization of
A
.
info
INTEGER
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
If
info
=
i
, the leading minor of order
i
(and therefore the matrix
A
itself) is not positive-definite; if
i
<
n
, the factorization could not be completed, while if
i
=
n
, the factorization was completed, but
d
(
n
) ≤ 0
.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine
pttrf
interface are as follows:
d
Holds the vector of length
n
.
e
Holds the vector of length (
n
-1).