Developer Reference for Intel® oneAPI Math Kernel Library for C
?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_intLAPACKE_spftrs ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_intnrhs , constfloat*a , float*b , lapack_intldb );
lapack_intLAPACKE_dpftrs ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_intnrhs , constdouble*a , double*b , lapack_intldb );
lapack_intLAPACKE_cpftrs ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_intnrhs , constlapack_complex_float*a , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zpftrs ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_intnrhs , constlapack_complex_double*a , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
spftrs dpftrs cpftrs zpftrs
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 = U^{T}*U for real data, A = U^{H}*U for complex data |
if uplo='U' |
A = L*L^{T} for real data, A = L*L^{H} for complex data |
if uplo='L' |
Before calling ?pftrs , you must call ?pftrf (Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .) 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 = UT * U for real data, A = UH * U for complex data.
If uplo = 'L' , L is stored, where A = L * LT for real data, A = L * LH 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 , b
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
The leading dimension of b ; ldb≥ max(1, n)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 had an illegal value.