Developer Reference

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

?ptsvx

Uses factorization to compute the solution to the system of linear equations with a symmetric (Hermitian) positive definite tridiagonal coefficient matrix
A
, and provides error bounds on the solution.

Syntax

call sptsvx
(
fact
,
n
,
nrhs
,
d
,
e
,
df
,
ef
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
info
)
call dptsvx
(
fact
,
n
,
nrhs
,
d
,
e
,
df
,
ef
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
info
)
call cptsvx
(
fact
,
n
,
nrhs
,
d
,
e
,
df
,
ef
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
rwork
,
info
)
call zptsvx
(
fact
,
n
,
nrhs
,
d
,
e
,
df
,
ef
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
rwork
,
info
)
call ptsvx
(
d
,
e
,
b
,
x
[
,
df
]
[
,
ef
]
[
,
fact
]
[
,
ferr
]
[
,
berr
]
[
,
rcond
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine uses the Cholesky factorization
A
=
L*D*L
T
(real)/
A
=
L*D*L
H
(complex) to compute the solution to a real or complex system of linear equations
A*X
=
B
, where
A
is a
n
-by-
n
symmetric or Hermitian positive definite tridiagonal matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
Error bounds on the solution and a condition estimate are also provided.
The routine
?ptsvx
performs the following steps:
  1. If
    fact
    =
    'N'
    , the matrix
    A
    is factored as
    A
    =
    L*D*L
    T
    (real flavors)/
    A
    =
    L*D*L
    H
    (complex flavors), where
    L
    is a unit lower bidiagonal matrix and
    D
    is diagonal. The factorization can also be regarded as having the form
    A
    =
    U
    T
    *D*U
    (real flavors)/
    A
    =
    U
    H
    *D*U
    (complex flavors).
  2. If the leading
    i
    -by-
    i
    principal minor is not positive-definite, then the routine returns with