Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

p?gbtrs

Solves a system of distributed linear equations with a general band matrix, using the
LU
 factorization computed by
p?gbtrf
.

Syntax

void
psgbtrs
(
char
*trans
,
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
float
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
float
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
float
*af
,
MKL_INT
*laf
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgbtrs
(
char
*trans
,
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
double
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
double
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
double
*af
,
MKL_INT
*laf
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgbtrs
(
char
*trans
,
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
MKL_Complex8
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex8
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex8
*af
,
MKL_INT
*laf
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzgbtrs
(
char
*trans
,
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
MKL_Complex16
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex16
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex16
*af
,
MKL_INT
*laf
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?gbtrs
function
solves a system of distributed linear equations with a general band distributed matrix sub(
A
) =
A
(1:
n
,
ja
:
ja
+
n
-1) using the
LU
 factorization computed by p?gbtrf.
The system has one of the following forms specified by
trans
:
sub(
A
)*
X
 = sub(
B
) (no transpose),
sub(
A
)
T
*X = sub(
B
) (transpose),
sub(
A
)
H
*
X
 = sub(
B
) (conjugate transpose),
where sub(
B
) =
B
(
ib
:
ib
+
n
-1, 1:
nrhs
).
Before calling this
function
,you must call
p?gbtrf
 to compute the
LU
 factorization of sub(
A
).
Input Parameters
trans
(global) Must be
'N'
 or
'T'
 or
'C'
.
Indicates the form of the equations:
If
trans
 =
'N'
, then sub(
A
)*
X
 = sub(
B
) is solved for
X
.
If
trans
 =
'T'
, then sub(
A
)
T
*
X
 = sub(
B
) is solved for
X
.
If
trans
 =
'C'
, then sub(
A
)
H
 *
X
 = sub(
B
) is solved for
X
.
n
(global) The number of linear equations; the order of the distributed matrix sub(
A
)
(
n
≥
 0)
.
bwl
(global) The number of sub-diagonals within the band of
A
( 0 ≤
bwl
 ≤
n-1
 )
.
bwu
(global) The number of super-diagonals within the band of
A
( 0 ≤
bwu
 ≤
n-1
 )
.
nrhs
(global) The number of right hand sides; the number of columns of the distributed matrix sub(
B
)
(
nrhs
≥
 0)
.
a
,
b
(local)
Pointers into the local memory to arrays of local sizes
lld_a
*
LOCc
(
ja
+
n
-1)
 and
lld_b
*
LOCc
(
nrhs
)
, respectively.
The array
a
 contains details of the
LU
 factorization of the distributed band matrix
A
.
On entry, the array
b
 contains the local pieces of the right hand sides
B
(
ib
:
ib
+
n
-1, 1:
nrhs
).
ja
(global) The index in the global matrix
A
 indicating the start of the matrix to be operated on ( which may be either all of
A
 or a submatrix of
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
If
dtype_a
 = 501
, then
dlen_
≥
 7
;
else if
dtype_a
 = 1
, then
dlen_
≥
 9
.
ib
(global) The index in the global matrix
A
 indicating the start of the matrix to be operated on (which may be either all of
A
 or a submatrix of
A
).
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
If
dtype_b
 = 502
, then
dlen_
≥
 7
;
else if
dtype_b
 = 1
, then
dlen_
≥
 9
.
laf
(local) The size of the array
af
.
Must be
laf
≥
nb_a
*(
bwl
+
bwu
)+6*(
bwl
+
bwu
)*(
bwl
+2*
bwu
).
If
laf
 is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af
[0]
.
work
(local) Same type as
a
. Workspace array of size
lwork
.
lwork
(local or global) The size of the
work
 array, must be at least
lwork
≥
nrhs
*(
nb_a
+2
*bwl
+4
*bwu
)
.
Output Parameters
ipiv
(local) array.
The size of
ipiv
 must be
≥
nb_a
.
Contains pivot indices for local factorizations. Note that you should not alter the contents of this array between factorization and solve.
b
On exit, overwritten by the local pieces of the solution distributed matrix
X
.
af
(local)
Array of size
laf
.
Auxiliary Fill-in space. The fill-in space is created in a call to the factorization
function
p?gbtrf
 and is stored in
af
.
Note that if a linear system is to be solved using p?gbtrs after the factorization
function
,
af
 must not be altered after the factorization.
work
[0]
On exit,
work
[0]
 contains the minimum value of
lwork
 required for optimum performance.
info
If
info
=0
, the execution is successful.
info
 < 0
:
If the
i
-th argument is an array and the
j-
th entry
, indexed
j
 - 1,
 had an illegal value, then
info
 = -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
 =
-i
.

Product and Performance Information

1

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