Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
p?larft
Forms the triangular vector T of a block reflector H=I-V*T*V^{H} .
Syntax
call pslarft ( direct , storev , n , k , v , iv , jv , descv , tau , t , work )
call pdlarft ( direct , storev , n , k , v , iv , jv , descv , tau , t , work )
call pclarft ( direct , storev , n , k , v , iv , jv , descv , tau , t , work )
call pzlarft ( direct , storev , n , k , v , iv , jv , descv , tau , t , work )
Include Files
mkl_scalapack.h
Description
pslarft pdlarft pclarft pzlarft The p?larft routine function forms the triangular factor T of a real/complex block reflector H of order n , which is defined as a product of k elementary reflectors.
If direct = 'F', H = H(1)*H(2)...*H(k) , and T is upper triangular;
If direct = 'B', H = H(k)*...*H(2)*H(1) , and T is lower triangular.
If storev = 'C' , the vector which defines the elementary reflector H(i) is stored in the i -th column of the distributed matrix V , and
H = I-V*T*V'
If storev = 'R' , the vector which defines the elementary reflector H(i) is stored in the i -th row of the distributed matrix V , and
H = I-V'*T*V .
Input Parameters
direct
(global) CHARACTER*1 .
Specifies the order in which the elementary reflectors are multiplied to form the block reflector: if direct = 'F': H = H(1)*H(2)*...*H(k) (forward) if direct = 'B': H = H(k)*...*H(2)*H(1) (backward).
storev
(global) CHARACTER*1 .
Specifies how the vectors that define the elementary reflectors are stored (See Application Notes below) : if storev = 'C' : columnwise; if storev = 'R' : rowwise.
n
(global) INTEGER .
The order of the block reflector H . n ≥ 0 .
k
(global) INTEGER .
The order of the triangular factor T , is equal to the number of elementary reflectors. 1 ≤ k ≤ mb_v (= nb_v) .
- v
-
REAL for pslarft DOUBLE PRECISION for pdlarft COMPLEX for pclarft COMPLEX*16 for pzlarft . Pointer into the local memory to an array of local size
(LOCr(iv+n-1) , LOCc(jv+k-1)) if storev = 'C' , and
(LOCr(iv+k-1) , LOCc(jv+n-1)) if storev = 'R' .
The distributed matrix V contains the Householder vectors. (See Application Notes below).
iv , jv
(global) INTEGER .
The row and column indices in the global matrix V indicating the first row and the first column of the matrix sub( V ), respectively.
descv
(local) INTEGER array of size dlen_ . The array descriptor for the distributed matrix V .
- tau
-
(local) REAL for pslarft DOUBLE PRECISION for pdlarft COMPLEX for pclarft COMPLEX*16 for pzlarft . Array of size LOCr(iv+k-1) if incv = m_v , and LOCc(jv+k-1) otherwise. This array contains the Householder scalars related to the Householder vectors. tau is tied to the distributed matrix V .
- work
-
(local). REAL for pslarft DOUBLE PRECISION for pdlarft COMPLEX for pclarft COMPLEX*16 for pzlarft . Workspace array of size k *( k -1)/2.
Output Parameters
- v
-
REAL for pslarft DOUBLE PRECISION for pdlarft COMPLEX for pclarft COMPLEX*16 for pzlarft .
- t
-
(local) REAL for pslarft DOUBLE PRECISION for pdlarft COMPLEX for pclarft COMPLEX*16 for pzlarft .
Array of size ( nb_v , nb_v ) if storev = 'C' , and ( mb_v , mb_v ) otherwise. It contains the k -by- k triangular factor of the block reflector associated with v . If direct = 'F' , t is upper triangular;
if direct = 'B' , t is lower triangular.
Application Notes
The shape of the matrix V and the storage of the vectors that define the H(i) is best illustrated by the following example with n = 5 and k = 3 . The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.
