Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
p?her2k
Performs a rank-2k update of a Hermitian distributed matrix.
Syntax
call pcher2k ( uplo , trans , n , k , alpha , a , ia , ja , desca , b , ib , jb , descb , beta , c , ic , jc , descc )
call pzher2k ( uplo , trans , n , k , alpha , a , ia , ja , desca , b , ib , jb , descb , beta , c , ic , jc , descc )
Include Files
mkl_pblas.h
Description
The p?her2k routines perform a distributed matrix-matrix operation defined as sub( C ):= alpha *sub( A )*conjg(sub( B )’)+ conjg( alpha )*sub( B )*conjg(sub( A )’)+ beta *sub( C ),
or sub( C ):= alpha *conjg(sub( A )’)*sub( A )+ conjg( alpha )*conjg(sub( B )’)*sub( A ) + beta *sub( C ),
where:
alpha and beta are scalars,
sub(C) is an n -by- n Hermitian distributed matrix, sub(C) = C(ic:ic+n-1, jc:jc+n-1) .
sub(A) is a distributed matrix, sub(A)=A(ia:ia+n-1, ja:ja+k-1) , if trans = 'N' or 'n' , and sub(A) = A(ia:ia+k-1, ja:ja+n-1) otherwise.
sub(B) is a distributed matrix, sub(B) = B(ib:ib+n-1, jb:jb+k-1) , if trans = 'N' or 'n' , and sub(B)=B(ib:ib+k-1, jb:jb+n-1) otherwise.
Input Parameters
uplo
(global) CHARACTER*1 . Specifies whether the upper or lower triangular part of the Hermitian distributed matrix sub(C) is used:
If uplo = 'U' or ‘u’ , then the upper triangular part of the sub(C) is used. If uplo = 'L' or ‘l’ , then the low triangular part of the sub(C) is used.
trans
(global) CHARACTER*1 . Specifies the operation:
if trans = 'N' or 'n' , then sub(C) := alpha*sub(A)*conjg(sub(B)')+ conjg(alpha)*sub(B)*conjg(sub(A)') + beta*sub(C) ; if trans = 'C' or 'c' , then sub(C) := alpha*conjg(sub(A)')*sub(A)+ conjg(alpha)*conjg(sub(B)')*sub(A) + beta*sub(C) .
n
(global) INTEGER . Specifies the order of the distributed matrix sub(C) , n ≥ 0.
k
(global) INTEGER . On entry with trans = 'N' or ‘n’ , k specifies the number of columns of the distributed matrices sub(A) and sub(B) , and on entry with trans = 'C' or ‘c’ , k specifies the number of rows of the distributed matrices sub(A) and sub(B) , k ≥ 0.
alpha
(global) COMPLEX for pcher2k
DOUBLE COMPLEX for pzher2k Specifies the scalar alpha .
a
(local) COMPLEX for pcher2k
DOUBLE COMPLEX for pzher2k Array, size (lld_a, kla) , where kla is LOCq(ja+k-1) when trans = 'N' or ‘n’ , and is LOCq(ja+n-1) otherwise. Before entry with trans = 'N' or ‘n’ , this array contains the local pieces of the distributed matrix sub(A) .
ia , ja
(global) INTEGER . The row and column indices in the distributed matrix A indicating the first row and the first column of the submatrix sub(A) , respectively.
desca
(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix A .
b
(local) COMPLEX for pcher2k
DOUBLE COMPLEX for pzher2k Array, size (lld_b, klb) , where klb is LOCq(jb+k-1) when trans = 'N' or ‘n’ , and is LOCq(jb+n-1) otherwise. Before entry with trans = 'N' or ‘n’ , this array contains the local pieces of the distributed matrix sub(B) .
ib , jb
(global) INTEGER . The row and column indices in the distributed matrix B indicating the first row and the first column of the submatrix sub(B) , respectively.
descb
(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix B .
beta
(global) REAL for pcher2k
DOUBLE PRECISION for pzher2k Specifies the scalar beta .
c
(local) COMPLEX for pcher2k
DOUBLE COMPLEX for pzher2k Array, size (lld_c, LOCq(jc+n-1)) . Before entry with uplo = 'U' or ‘u’ , this array contains n -by- n upper triangular part of the symmetric distributed matrix sub(C) and its strictly lower triangular part is not referenced. Before entry with uplo = 'L' or ‘l’ , this array contains n -by- n lower triangular part of the symmetric distributed matrix sub(C) and its strictly upper triangular part is not referenced.
ic , jc
(global) INTEGER . The row and column indices in the distributed matrix C indicating the first row and the first column of the submatrix sub(C) , respectively.
descc
(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix C .
Output Parameters
- c
-
With uplo = 'U' or ‘u’ , the upper triangular part of sub(C) is overwritten by the upper triangular part of the updated distributed matrix. With uplo = 'L' or ‘l’ , the lower triangular part of sub(C) is overwritten by the upper triangular part of the updated distributed matrix.