Developer Reference for Intel® oneAPI Math Kernel Library for C
?ppsv
Computes the solution to the system of linear equations with a symmetric (Hermitian) positive definite packed coefficient matrix A and multiple right-hand sides.
Syntax
lapack_intLAPACKE_sppsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , float*ap , float*b , lapack_intldb );
lapack_intLAPACKE_dppsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , double*ap , double*b , lapack_intldb );
lapack_intLAPACKE_cppsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_float*ap , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zppsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_double*ap , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
sppsv dppsv cppsv zppsv ppsv
The routine solves for X the real or complex system of linear equations A*X = B , where A is an n -by- n real symmetric/Hermitian positive-definite matrix stored in packed format, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.
The Cholesky decomposition is used to factor A as
A = U:code:`T`*U (real flavors) and A = U:code:`H`*U (complex flavors), if uplo = 'U'
or A = L*L^{T} (real flavors) and A = L*L^{H} (complex flavors), if uplo = 'L' ,
where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A*X = B .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
uplo
Must be ‘U’ or ‘L’ .
Indicates whether the upper or lower triangular part of A is stored:
If uplo = 'U' , the upper triangle of A is stored.
If uplo = 'L' , the lower triangle of A is stored.
n
The order of matrix A ; n ≥ 0.
nrhs
The number of right-hand sides, the number of columns in B; nrhs≥ 0 .
ap , b
Arrays: ap (size max(1, n *( n +1)/2) , b , size max( ldb * nrhs ) for column major layout and max( ldb * n ) for row major layout, . The array ap contains the upper or the lower triangular part of the matrix A (as specified by uplo ) in packed storage (see Matrix Storage Schemes ). .
The array b 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
ap
If info = 0, the upper or lower triangular part of A in packed storage is overwritten by the Cholesky factor U or L , as specified by uplo .
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.
If info = i , the leading minor of order i (and therefore the matrix A itself) is not positive-definite, so the factorization could not be completed, and the solution has not been computed.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.