## Developer Reference

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

# ?pbsv

Computes the solution to the system of linear equations with a symmetric or Hermitian positive-definite band coefficient matrix A and multiple right-hand sides.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
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 band matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
The Cholesky decomposition is used to factor
A
as
A
=
U
T
*U
(real flavors) and
A
=
U
H
*U
(complex flavors), if
uplo
=
'U'
or
A
=
L*L
T
(real flavors) and
A
=
L*L
H
(complex flavors), if
uplo
=
'L'
,
where
U
is an upper triangular band matrix and
L
is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as
A
. The factored form of
A
is then used to solve the system of equations
A*X
=
B
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is stored:
If
uplo
=
'U'
, the upper triangle of
A
is stored.
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
INTEGER
.
The order of matrix
A
;
n
0.
kd
INTEGER
.
The number of superdiagonals of the matrix
A
if
uplo
=
'U'
, or the number of subdiagonals if
uplo
=
'L'
;
kd
0.
nrhs
INTEGER
.
The number of right-hand sides, the number of columns in
B
;
nrhs
0
.
ab
,
b
REAL
for
spbsv
DOUBLE PRECISION
for
dpbsv
COMPLEX
for
cpbsv
DOUBLE COMPLEX
for
zpbsv
.
Arrays:
ab
(size
ldab
by *)
,
b
(size
ldb
by *)
. The array
ab
contains the upper or the lower triangular part of the matrix
A