Developer Reference for Intel® oneAPI Math Kernel Library for C
p?unmtr
Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by p?hetrd .
Syntax
voidpcunmtr ( char*side , char*uplo , char*trans , MKL_INT*m , MKL_INT*n , 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 );
voidpzunmtr ( char*side , char*uplo , char*trans , MKL_INT*m , MKL_INT*n , 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
pcunmtr pzunmtr 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 = ‘C’ : |
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 nq -1 elementary reflectors, as returned by p?hetrd (Reduces a Hermitian matrix to Hermitian tridiagonal form by a unitary similarity transformation.) .
If uplo = 'U' , Q = H ( nq -1)… H (2) H (1);
If uplo = 'L' , Q = H (1) H (2)… H ( nq -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.
uplo
(global)
= 'U' : Upper triangle of A(ia:*, ja:*) contains elementary reflectors from p?hetrd ; = 'L' : Lower triangle of A(ia:*,ja:*) contains elementary reflectors from p?hetrd
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) .
- a
-
(local) REAL for pcunmtr DOUBLE PRECISION for pzunmtr .
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?hetrd . If side='L' , lld_a ≥ max(1,LOCr(ia+m-1)) ; If side ='R' , lld_a ≥ max(1,LOCr(ia+n-1)) .
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 pcunmtr DOUBLE COMPLEX for pzunmtr . Array of size of ltau where If side = 'L' and uplo = 'U' , ltau = LOCc(m_a) , if side = 'L' and uplo = 'L' , ltau = LOCc(ja+m-2) , if side = 'R' and uplo = 'U' , ltau = LOCc(n_a) , if side = 'R' and uplo = 'L' , ltau = LOCc(ja+n-2) .
tau [ i ] must contain the scalar factor of the elementary reflector H ( i +1) , as returned by p?hetrd (0 ≤ i < ltau ) . tau is tied to the distributed matrix A .
c
(local)
DOUBLE COMPLEX for pzunmtr .
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 pcunmtr DOUBLE COMPLEX for pzunmtr . Workspace array of size lwork .
lwork
(local or global) size of work , must be at least:
If uplo = 'U' , iaa= ia; jaa= ja+1, icc= ic; jcc= jc ; else uplo = 'L' , iaa= ia+1, jaa= ja ; If side = 'L' , icc= ic+1; jcc= jc ; else icc= ic; jcc= jc+1 ; end if end if If side = 'L' , mi= m-1; ni= nlwork ≥ max((nb_a*(nb_a-1))/2, (nqc0 + mpc0)*nb_a) + nb_a*nb_a else If side = 'R' , mi= m; mi = n-1 ; 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) , npa 0 = 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
-
Overwritten by the product 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 .