Contents

# ?pftrs

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix using the Rectangular Full Packed (RFP) format.

## Syntax

Include Files
• mkl.h
Description
The routine solves a system of linear equations
A*X
=
B
with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix
A
using the Cholesky factorization of
A
:
 A = UT*U for real data, A = UH*U for complex data if uplo='U' A = L*LT for real data, A = L*LH for complex data if uplo='L'
Before calling
?pftrs
, you must call
?pftrf
to compute the Cholesky factorization of
A
.
L
stands for a lower triangular matrix and
U
for an upper triangular matrix.
The matrix
A
is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
transr
Must be
'N'
,
'T'
(for real data) or
'C'
(for complex data).
If
transr
=
'N'
, the untransposed factor of
A
is stored in RFP format.
If
transr
=
'T'
, the transposed factor of
A
is stored in RFP format.
If
transr
=
'C'
, the conjugate-transposed factor of
A
is stored in RFP format.
uplo
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
,
U
is stored, where
A
=
U
T
*
U
for real data,
A
=
U
H
*
U
for complex data.
If
uplo
=
'L'
,
L
is stored, where
A
=
L
*
L
T
for real data,
A
=
L
*
L
H
for complex data
n
The order of the matrix
A
;
n
0.
nrhs
The number of right-hand sides, that is, the number of columns of the matrix
B
;
nrhs
0.
a
Array
a
of size max(1,
n
*(
n
+ 1)/2).
The array
a
contains, in the RFP format, the factor
U
or
L
obtained by factorization of matrix
A
.
b
The array
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout contains the matrix
B
whose columns are the right-hand sides for the systems of equations.
ldb
b
;
ldb
max(1,
n
) for column major layout and
ldb
nrhs
for row major layout
.
Output Parameters
b
The solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, parameter
i