Developer Reference for Intel® oneAPI Math Kernel Library for C
?hpsv
Computes the solution to the system of linear equations with a Hermitian coefficient matrix A stored in packed format, and multiple right-hand sides.
Syntax
lapack_intLAPACKE_chpsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_float*ap , lapack_int*ipiv , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zhpsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_double*ap , lapack_int*ipiv , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
chpsv zhpsv hpsv
The routine solves for X the system of linear equations A*X = B , where A is an n -by- n Hermitian 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 diagonal pivoting method is used to factor A as A = U*D*U^{H} or A = L*D*L^{H} , where U (or L ) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
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 of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout .
The array ap contains the factor U or L , 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
The block-diagonal matrix D and the multipliers used to obtain the factor U (or L ) from the factorization of A as computed by ?hptrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix using packed storage.) , stored as a packed triangular matrix in the same storage format as A .
b
If info = 0, b is overwritten by the solution matrix X .
ipiv
Array, size at least max(1, n) . Contains details of the interchanges and the block structure of D , as determined by ?hptrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix using packed storage.) .
If ipiv[i-1] = k > 0 , then dii is a 1-by-1 block, and the i -th row and column of A was interchanged with the k -th row and column.
If uplo = 'U' and ipiv [ i ]= ipiv [ i -1] = - m < 0, then D has a 2-by-2 block in rows/columns i and i +1, and i -th row and column of A was interchanged with the m -th row and column.
If uplo = 'L' and ipiv [ i -1] = ipiv [ i ] = - m < 0, then D has a 2-by-2 block in rows/columns i and i +1, and ( i +1)-th row and column of A was interchanged with the m -th row and column.
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 , d_{ii} is 0. The factorization has been completed, but D is exactly singular, so the solution could not be 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.