Developer Reference for Intel® oneAPI Math Kernel Library for C
?hesv
Computes the solution to the system of linear equations with a Hermitian matrix A and multiple right-hand sides.
Syntax
lapack_intLAPACKE_chesv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_float*a , lapack_intlda , lapack_int*ipiv , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zhesv ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_double*a , lapack_intlda , lapack_int*ipiv , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
chesv zhesv hesv
The routine solves for X the complex system of linear equations A*X = B , where A is an n -by- n symmetric matrix, 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 and how A is factored:
If uplo = 'U' , the array a stores the upper triangular part of the matrix A , and A is factored as U*D*U^{H} .
If uplo = 'L' , the array a stores the lower triangular part of the matrix A , and A is factored as L*D*L^{H} .
n
The order of matrix A ; n ≥ 0.
nrhs
The number of right-hand sides, the number of columns in B; nrhs≥ 0 .
a , b , work
Arrays: a (size max(1, lda * n )) , bb(size ldb by *) of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout . The array a contains the upper or the lower triangular part of the Hermitian matrix A (see uplo ).
The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.
lda
The leading dimension of a ; lda≥ max(1, n) .
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 .
lwork
The size of the work array ( lwork ≥ 1).
If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla . See Application Notes below for details and for the suggested value of lwork .
Output Parameters
a
If info = 0 , a is overwritten by the block-diagonal matrix D and the multipliers used to obtain the factor U (or L ) from the factorization of A as computed by ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) .
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 ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) .
If ipiv[i-1] = k > 0 , then d_{ii} is a 1-by-1 diagonal 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 ] = ipiv [ i -1] = - 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.
work(1)
If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
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.
Application Notes
For better performance, try using lwork = n*blocksize , where blocksize is a machine-dependent value (typically, 16 to 64) required for optimum performance of the blocked algorithm .
If you are in doubt how much workspace to supply, use a generous value of lwork for the first run or set lwork = -1 .
If you choose the first option and set any of admissible lwork sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value ( work(1) ) for subsequent runs.
If you set lwork = -1 , the routine returns immediately and provides the recommended workspace in the first element of the corresponding array ( work ). This operation is called a workspace query.
Note that if you set lwork to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.