Contents

# ?getrs

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

## Syntax

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
a
;
lda
max(1,
n
)
.
ldb
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
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)εP|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:
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804