Developer Reference for Intel® oneAPI Math Kernel Library for C
p?orm2l/p?unm2l
Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by p?geqlf (unblocked algorithm).
Syntax
voidpsorm2l ( 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 );
voidpdorm2l ( 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 );
voidpcunm2l ( 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 );
voidpzunm2l ( 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
psorm2l pdorm2l pcunm2l pzunm2l The p?orm2l/p?unm2l 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:code:`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 distributed matrix defined as the product of k elementary reflectors
Q = H ( k )*…* H (2)* H (1) as returned by p?geqlf (Computes the QL factorization of a general 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 psorm2l DOUBLE PRECISION for pdorm2l COMPLEX for pcunm2l COMPLEX*16 for pzunm2l .
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 row 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-DAA2D124-C6B2-48F0-AE29-60F115CC5EF0.xml#GUID-DAA2D124-C6B2-48F0-AE29-60F115CC5EF0 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 psorm2l DOUBLE PRECISION for pdorm2l COMPLEX for pcunm2l COMPLEX*16 for pzunm2l .
Array of size LOCc(ja+n-1) . tau [ j ] contains the scalar factor of the elementary reflector H ( j +1), j = 0, 1, …, LOCc(ja+n-1) -1 , as returned by GUID-DAA2D124-C6B2-48F0-AE29-60F115CC5EF0.xml#GUID-DAA2D124-C6B2-48F0-AE29-60F115CC5EF0 . This array is tied to the distributed matrix A .
- c
-
(local) REAL for psorm2l DOUBLE PRECISION for pdorm2l COMPLEX for pcunm2l COMPLEX*16 for pzunm2l .
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 psorm2l DOUBLE PRECISION for pdorm2l COMPLEX for pcunm2l COMPLEX*16 for pzunm2l . Workspace array of size lwork . On exit, work(1) returns the minimal and optimal 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 ) .