Developer Reference for Intel® oneAPI Math Kernel Library for C
p?orm2r/p?unm2r
Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by p?geqrf (unblocked algorithm).
Syntax
voidpsorm2r ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*k , float*a , MKL_INT*ia , MKL_INT*ja , MKL_INT*desca , float*tau , float*c , MKL_INT*ic , MKL_INT*jc , MKL_INT*descc , float*work , MKL_INT*lwork , MKL_INT*info );
voidpdorm2r ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*k , double*a , MKL_INT*ia , MKL_INT*ja , MKL_INT*desca , double*tau , double*c , MKL_INT*ic , MKL_INT*jc , MKL_INT*descc , double*work , MKL_INT*lwork , MKL_INT*info );
voidpcunm2r ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*k , 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 );
voidpzunm2r ( char*side , char*trans , MKL_INT*m , MKL_INT*n , MKL_INT*k , 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
psorm2r pdorm2r pcunm2r pzunm2r The p?orm2r/p?unm2r routine function overwrites the general real/complex m -by- n distributed matrix sub (C)=C(ic:ic+m-1, jc:jc+n-1) with
Q *sub( C ) if side = 'L' and trans = 'N' , or
Q:code:`T` *sub( C ) / Q^{H}*sub(C) if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or
sub( C )* Q if side = 'R ‘ and trans = 'N' , or
sub( C )* Q:code:`T` / sub( C )* Q:code:`H` if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).
where Q is a real orthogonal or complex unitary matrix defined as the product of k elementary reflectors
Q = H(k)*...*H(2)*H(1) as returned by p?geqrf (Computes the QR factorization of a general m-by-n matrix.) . Q is of order m if side = 'L' and of order n if side = 'R' .
Input Parameters
side
(global)
= ‘L’ : apply Q or Q:code:`T` for real flavors ( Q:code:`H` for complex flavors) from the left, = ‘R’ : apply Q or Q:code:`T` for real flavors ( Q:code:`H` for complex flavors) from the right.
trans
(global)
= ‘N’ : apply Q (no transpose) = ‘T’ : apply Q:code:`T` (transpose, for real flavors) = ‘C’ : apply Q:code:`H` (conjugate transpose, for complex flavors)
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 .
k
(global)
The number of elementary reflectors whose product defines the matrix Q . If side = 'L' , m ≥ k ≥ 0 ; if side = 'R' , n ≥ k ≥ 0 .
- a
-
(local) REAL for psorm2r DOUBLE PRECISION for pdorm2r COMPLEX for pcunm2r COMPLEX*16 for pzunm2r .
Pointer into the local memory to an array of size (lld_a, LOCc(ja+k-1))lld_a * LOCc ( ja + k -1) .
On entry, the j -th column of the matrix stored in a must contain the vector that defines the elementary reflector H ( j ), ja ≤ j ≤ ja + k -1, as returned by GUID-C9186306-C07B-43AF-A0DE-575A1D91C5F2.xml#GUID-C9186306-C07B-43AF-A0DE-575A1D91C5F2 in the k columns of its distributed matrix argument A(ia:*,ja:ja+k-1) . The argument A(ia:*,ja:ja+k-1) is modified by the function but restored on exit.
If side = 'L' , lld_a ≥ max(1, LOCr(ia+m-1)) , if side = 'R' , lld_a ≥ max(1, LOCr(ia+n-1)) .
ia
(global)
The row index in the global matrix A indicating the first row of sub( A ).
ja
(global)
The column index in the global matrix A indicating the first column of sub( A ).
desca
(global and local) array of size dlen_ . The array descriptor for the distributed matrix A .
- tau
-
(local) REAL for psorm2r DOUBLE PRECISION for pdorm2r COMPLEX for pcunm2r COMPLEX*16 for pzunm2r .
Array of size LOCc(ja+k-1) . tau [ j ] contains the scalar factor of the elementary reflector H ( j +1), j = 0, 1, …, LOCc(ja+k-1) -1 , as returned by GUID-C9186306-C07B-43AF-A0DE-575A1D91C5F2.xml#GUID-C9186306-C07B-43AF-A0DE-575A1D91C5F2 . This array is tied to the distributed matrix A .
- c
-
(local) REAL for psorm2r DOUBLE PRECISION for pdorm2r COMPLEX for pcunm2r COMPLEX*16 for pzunm2r .
Pointer into the local memory to an array of size (lld_c, LOCc(jc+n-1))lld_c * LOCc ( jc + n -1) .
On entry, the local pieces of the distributed matrix sub ( C ).
ic
(global)
The row index in the global matrix C indicating the first row of sub( C ).
jc
(global)
The column index in the global matrix C indicating the first column of sub( C ).
descc
(global and local) array of size dlen_ .
The array descriptor for the distributed matrix C .
- work
-
(local) REAL for psorm2r DOUBLE PRECISION for pdorm2r COMPLEX for pcunm2r COMPLEX*16 for pzunm2r . Workspace array of size lwork .
lwork
(local or global)
The size of the array work . lwork is local input and must be at least if side = 'L' , lwork ≥ mpc0 + max(1, nqc0) , if side = 'R' , lwork ≥ nqc0 + max(max(1, mpc0), numroc(numroc(n+icoffc, nb_a, 0, 0, npcol), nb_a, 0, 0, lcmq)) , where lcmq = lcm/npcol , lcm = iclm(nprow, npcol) , iroffc = mod(ic-1, mb_c) , icoffc = mod(jc-1, nb_c) , icrow = indxg2p(ic, mb_c, myrow, rsrc_c, nprow) , iccol = indxg2p(jc, nb_c, mycol, csrc_c, npcol) , Mqc0 = numroc(m+icoffc, nb_c, mycol, icrow, nprow) , Npc0 = numroc(n+iroffc, mb_c, myrow, 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 GUID-E523C816-D553-4D4E-8458-5404828CC07B.xml .
Output Parameters
- c
-
On exit, c is overwritten by Q *sub( C ), or Q:code:`T` *sub( C )/ Q:code:`H` *sub( C ), or sub( C )* Q , or sub( C )* Q:code:`T` / sub( C )* Q:code:`H`
work
On exit, work(1)[0] returns the minimal and optimal lwork .
info
(local)
= 0 : successful exit
< 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 .
If side = 'L' , (mb_a.eq.mb_c .AND. iroffa.eq.iroffc .AND. iarow.eq.icrow)(mb_a == mb_c) && (iroffa == iroffc) && (iarow == icrow) .
If side = 'R' , (mb_a.eq.nb_c .AND. iroffa.eq.iroffc)(mb_a == nb_c) && (iroffa == iroffc) .