Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?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
call chpsv ( uplo , n , nrhs , ap , ipiv , b , ldb , info )
call zhpsv ( uplo , n , nrhs , ap , ipiv , b , ldb , info )
call hpsv ( ap , b [ , uplo ] [ , ipiv ] [ , info ] )
Include Files
mkl.fi , mkl_lapack.f90
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
uplo
CHARACTER*1 . 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
INTEGER . The order of matrix A ; n ≥ 0.
nrhs
INTEGER . The number of right-hand sides; the number of columns in B; nrhs≥ 0 .
ap , b
COMPLEX for chpsv
DOUBLE COMPLEX for zhpsv .
Arrays: ap (size *) , b (size ldb by *) .
The dimension of ap must be at least max(1,n(n+1)/2) . 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. The second dimension of b must be at least max(1,nrhs) .
ldb
INTEGER . The leading dimension of b ; ldb≥ max(1, n) .
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
INTEGER .
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) = k > 0 , then d_{ii} 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-1 )-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.
info
INTEGER .
If info = 0 , the execution is successful.
If info = -i , the i -th parameter 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.
Return Values
No return value, info is an Output Parameter.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions .
Specific details for the routine hpsv interface are as follows:
ap
Holds the array A of size ( n*(n+1)/2 ).
b
Holds the matrix B of size ( n,nrhs ).
ipiv
Holds the vector with the number of elements n .
uplo
Must be ‘U’ or ‘L’ . The default value is ‘U’ .