?pftrs
?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
lapack_int
LAPACKE_spftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
float
*
a
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
double
*
a
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
a
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
a
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
- mkl.h
Description
The routine solves a system of linear equations with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix
A*X
= B
A
using the Cholesky factorization of A
:A = U T *U A = U H *U | if uplo ='U' |
A = L*L T A = L*L H | 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).Iftransr='N', the untransposed factor ofAis stored in RFP format.Iftransr='T', the transposed factor ofAis stored in RFP format.Iftransr='C', the conjugate-transposed factor ofAis stored in RFP format.
- uplo
- Must be'U'or'L'.Indicates how the input matrixAhas been factored:If,uplo='U'Uis stored, whereA=UT*Ufor real data,A=UH*Ufor complex data.If,uplo='L'Lis stored, whereA=L*LTfor real data,A=L*LHfor complex data
- n
- The order of the matrixA;n≥0.
- nrhs
- The number of right-hand sides, that is, the number of columns of the matrixB;nrhs≥0.
- a
- Arrayaof size max(1,n*(n+ 1)/2).The arrayacontains, in the RFP format, the factorUorLobtained by factorization of matrixA.
- b
- The arraybof size max(1,ldb*nrhs) for column major layout and max(1,ldb*n) for row major layout contains the matrixBwhose columns are the right-hand sides for the systems of equations.
- ldb
- The leading dimension ofb;.ldb≥max(1,n) for column major layout andldb≥nrhsfor row major layout
Output Parameters
- b
- The solution matrixX.
Return Values
This function returns a value
info
.If , the execution is successful.
info
=0If , parameter
info
= -i
i
had an illegal value.