Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?getrs

Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.

Syntax

lapack_int
LAPACKE_sgetrs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const
float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dgetrs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const
double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cgetrs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zgetrs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
 the following systems of linear equations:
A*X
 =
B
if
trans
=
'N'
,
A
T
*X
 =
B
if
trans
=
'T'
,
A
H
*X
 =
B
if
trans
=
'C'
 (for complex matrices only).
Before calling this routine, you must call
?getrf
 to compute the
LU
 factorization of
A
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
trans
Must be
'N'
 or
'T'
 or
'C'
.
Indicates the form of the equations:
If
trans
 =
'N'
, then
A*X
 =
B
 is solved for
X
.
If
trans
 =
'T'
, then
A
T
*X
 =
B
 is solved for
X
.
If
trans
 =
'C'
, then
A
H
*X
 =
B
 is solved for
X
.
n
The order of
A
; the number of rows in
B
(
n
≥
 0)
.
nrhs
The number of right-hand sides;
nrhs
≥
 0.
a
Array of size max(1,
lda
*
n
).
The array
a
 contains
LU
 factorization of matrix
A
 resulting from the call of
?getrf
.
b
Array of size max(1,
ldb
*
nrhs
) for column major layout, and max(1,
ldb
*
n
) for row major layout.
The array
b
 contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
lda
The leading dimension of
a
;
lda
≥
 max(1,
n
)
.
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
ipiv
Array, size at least
max(1,
n
)
. The
ipiv
 array, as returned by
?getrf
.
Output Parameters
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
 had an illegal value.
Application Notes
For each right-hand side
b
, the computed solution is the exact solution of a perturbed system of equations
(
A
 +
E
)
x
 =
b
, where 
|E| ≤ c(n)ε P|L||U|
c
(
n
)
 is a modest linear function of
n
, and
ε
 is the machine precision.
If
x
0
 is the true solution, the computed solution
x
 satisfies this error bound:
Equation
where
cond(
A
,
x
)= || |
A
-1
||
A
| |
x
| ||
∞
 / ||
x
||
∞
≤
 ||
A
-1
||
∞
 ||
A
||
∞
 =
κ
∞
(
A
)
.
Note that
cond(
A
,
x
)
 can be much smaller than
κ
∞
(
A
)
; the condition number of
A
T
 and
A
H
 might or might not be equal to
κ
∞
(
A
)
.
The approximate number of floating-point operations for one right-hand side vector
b
 is
2
n
2
 for real flavors and
8
n
2
 for complex flavors.
To estimate the condition number
κ
∞
(
A
)
, call
?gecon
.
To refine the solution and estimate the error, call
?gerfs
.

Product and Performance Information

1

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