Developer Reference for Intel® oneAPI Math Kernel Library for C
p?unmhr
Multiplies a general matrix by the unitary transformation matrix from a reduction to Hessenberg form determined by p?gehrd .
Syntax
voidpcunmhr ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*ilo , MKL_INT*ihi , MKL_Complex8*a , MKL_INT*ia , MKL_INT*ja , MKL_INT*desca , MKL_Complex8*tau , MKL_Complex8*c , MKL_INT*ic , MKL_INT*jc , MKL_INT*descc , MKL_Complex8*work , MKL_INT*lwork , MKL_INT*info );
voidpzunmhr ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*ilo , MKL_INT*ihi , MKL_Complex16*a , MKL_INT*ia , MKL_INT*ja , MKL_INT*desca , MKL_Complex16*tau , MKL_Complex16*c , MKL_INT*ic , MKL_INT*jc , MKL_INT*descc , MKL_Complex16*work , MKL_INT*lwork , MKL_INT*info );
Include Files
mkl_scalapack.h
Description
pcunmhr pzunmhr This routine function overwrites the general complex distributed m -by- n matrix sub( C ) = C ( iс : iс + m -1, jс : jс + n -1) with
side = ‘L’ |
side = ‘R’ |
|
trans = ‘N’ : |
Q *sub( C ) |
sub( C )* Q |
trans = ‘H’ : |
Q:code:`H` *sub( C ) |
sub( C )* Q:code:`H` |
where Q is a complex unitary distributed matrix of order nq , with nq = m if side = 'L' and nq = n if side = 'R' .
Q is defined as the product of ihi - ilo elementary reflectors, as returned by p?gehrd (Reduces a general matrix to upper Hessenberg form.) .
Q = H ( ilo ) H ( ilo +1)… H ( ihi -1).
Input Parameters
- side
-
(global) CHARACTER ='L' : Q or Q:code:`H` is applied from the left. ='R' : Q or Q:code:`H` is applied from the right.
- trans
-
(global) CHARACTER ='N' , no transpose, Q is applied. ='C' , conjugate transpose, Q:code:`H` is applied.
m
(global) The number of rows in the distributed matrix sub ( C ) (m≥0) .
n
(global) The number of columns in the distributed matrix sub ( C ) (n≥0) .
- ilo , ihi
-
(global) INTEGER These must be the same parameters ilo and ihi , respectively, as supplied to p?gehrd . Q is equal to the unit matrix except in the distributed submatrix Q ( ia + ilo : ia + ihi -1, ja + ilo : ja + ihi -1). If side ='L' , then 1≤ilo≤ihi≤max(1,m) . If side = 'R' , then 1≤ilo≤ihi≤max(1,n)ilo and ihi are relative indexes.
- a
-
(local) COMPLEX for pcunmhr DOUBLE COMPLEX for pzunmhr .
Pointer into the local memory to an array of size (lld_a,LOCc(ja+m-1))lld_a * LOCc ( ja + m -1) if side = 'L' , and (lld_a,LOCc(ja+n-1))lld_a * LOCc ( ja + n -1) if side = 'R' .
Contains the vectors which define the elementary reflectors, as returned by p?gehrd .
ia , ja
(global) The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A , respectively.
desca
(global and local) array of size dlen_ . The array descriptor for the distributed matrix A .
- tau
-
(local) COMPLEX for pcunmhr DOUBLE COMPLEX for pzunmhr . Array of size LOCc(ja+m-2) , if side = 'L' , and LOCc(ja+n-2) if side = 'R' .
tau [ j ] contains the scalar factor of the elementary reflector H ( j +1) as returned by p?gehrd (0 ≤ j < size( tau )) . tau is tied to the distributed matrix A .
- c
-
(local) COMPLEX for pcunmhr DOUBLE COMPLEX for pzunmhr .
Pointer into the local memory to an array of size (lld_c,LOCc(jc+n-1))lld_c * LOCc ( jc + n -1) .
Contains the local pieces of the distributed matrix sub( C ).
ic , jc
(global) The row and column indices in the global matrix C indicating the first row and the first column of the submatrix C , respectively.
descc
(global and local) array of size dlen_ . The array descriptor for the distributed matrix C .
- work
-
(local) COMPLEX for pcunmhr DOUBLE COMPLEX for pzunmhr . Workspace array with size lwork .
- lwork
-
(local or global) The size of the array work . lwork must be at least iaa = ia + ilo;jaa = ja+ilo-1; If side = 'L' , mi = ihi-ilo ; ni = n ; icc = ic + ilo ; jcc = jc ; lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+mpc0)*nb_a) + nb_a*nb_a else if side = 'R' , mi = m ; ni = ihi-ilo ; icc = ic ; jcc = jc + ilo ; lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0 + max(npa0+numroc(numroc(ni+icoffc, nb_a, 0, 0, NPCOL), nb_a, 0, 0, lcmq ), mpc0))*nb_a) + nb_a*nb_a end if where lcmq = lcm/NPCOL with lcm = ilcm(NPROW, NPCOL) , iroffa = mod(iaa-1, mb_a),icoffa = mod(jaa-1, nb_a) , iarow = indxg2p(iaa, mb_a, MYROW, rsrc_a, NPROW) , npa0 = numroc(ni+iroffa, mb_a, MYROW, iarow, NPROW) , iroffc = mod(icc-1, mb_c) , icoffc = mod(jcc-1, nb_c) , icrow = indxg2p(icc, mb_c, MYROW, rsrc_c, NPROW) , iccol = indxg2p(jcc, nb_c, MYCOL, csrc_c, NPCOL) , mpc0 = numroc(mi+iroffc, mb_c, MYROW, icrow, NPROW) , nqc0 = numroc(ni+icoffc, nb_c, MYCOL, iccol, NPCOL) ,
ilcm , indxg2p and numroc are ScaLAPACK tool functions; MYROW , MYCOL , NPROW and NPCOL can be determined by calling the function blacs_gridinfo .
If lwork = -1 , then lwork is global input and a workspace query is assumed; the function only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by pxerbla .
Output Parameters
- c
-
C is overwritten by Q * sub( C ) or Q' *sub( C ) or sub( C )* Q' or sub( C )* Q .
work(1)[0])
On exit work(1)[0] contains the minimum value of lwork required for optimum performance.
info
(global)
= 0 : the execution is successful.
< 0 : if the i -th argument is an array and the j- th entry , indexed j - 1, had an illegal value, then info = -( i *100+ j ); if the i- th argument is a scalar and had an illegal value, then info = -i .