p?gerqf
p?gerqf
Computes the
RQ
factorization of a general rectangular matrix.Syntax
void
psgerqf
(
MKL_INT
*m
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*tau
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgerqf
(
MKL_INT
*m
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*tau
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgerqf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*tau
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzgerqf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*tau
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
- mkl_scalapack.h
Description
The
p?gerqf
function
forms the Q
R
factorization of a general m
-by-n
distributed matrix sub(A
)= A
(ia
:ia
+m
-1, ja
:ja
+n
-1) asA
= R
*Q
Input Parameters
- m
- (global) The number of rows in the distributed matrix sub(A);(.m≥0)
- n
- (global) The number of columns in the distributed matrix sub(A);(.n≥0)
- a
- (local)Pointer into the local memory to an array of local size.lld_a*LOCc(ja+n-1)Contains the local pieces of the distributed matrix sub(A) to be factored.
- ia,ja
- (global) The row and column indices in the global matrixAindicating the first row and the first column of the submatrixA(ia:ia+m-1,ja:ja+n-1), respectively.
- desca
- (global and local) array of sizedlen_. The array descriptor for the distributed matrixA
- work
- (local).Workspace array of sizelwork.
- lwork
- (local or global) size ofwork, must be at least, wherelwork≥mb_a*(mp0+nq0+mb_a),iroff=mod(ia-1,mb_a),icoff=mod(ja-1,nb_a),iarow=indxg2p(ia,mb_a,MYROW,rsrc_a,NPROW),iacol=indxg2p(ja,nb_a,MYCOL,csrc_a,NPCOL),mp0 =numroc(m+iroff,mb_a,MYROW,iarow,NPROW)mod(is the integer remainder ofx,y).x/yandnq0 =numroc(n+icoff,nb_a,MYCOL,iacol,NPCOL)numroc,indxg2pare ScaLAPACK tool functions;MYROW,MYCOL,NPROWandNPCOLcan be determined by calling thefunctionblacs_gridinfo.If, thenlwork= -1lworkis global input and a workspace query is assumed; thefunctiononly 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
- a
- On exit, if, the upper triangle ofm≤nA(ia:ia+m-1,ja:ja+n-1) contains them-by-mupper triangular matrixR; if, the elements on and above the (m≥nm-n)-th subdiagonal contain them-by-nupper trapezoidal matrixR; the remaining elements, with the arraytau, represent the orthogonal/unitary matrixQas a product of elementary reflectors(see.Application Notesbelow)
- tau
- (local)Array of size.LOCr(ia+m-1)Contains the scalar factor of elementary reflectors.tauis tied to the distributed matrixA.
- work[0]
- On exit,contains the minimum value ofwork[0]lworkrequired for optimum performance.
- info
- (global)= 0, the execution is successful.< 0, if thei-th argument is an array and thej-th entry, indexedhad an illegal value, thenj- 1,info= -(i*100+j); if thei-th argument is a scalar and had an illegal value, theninfo=-i.
Application Notes
The matrix
Q
is represented as a product of elementary reflectors Q
= H
(ia
)*H
(ia
+1)*...*H
(ia
+k
-1),where
k
= min(
. m
,n
)Each
H
(i
) has the form H
(i
) = I
- tau
*v
*v'
where
tau
is a real/complex scalar, and v
is a real/complex vector with v
(n
-k
+i
+1:n
) = 0 and v
(n
-k
+i
) = 1; v
(1:n
-k
+i
-1) is stored on exit in A
(ia
+m
-k
+i
-1,ja
:ja
+n
-k
+i
-2), and tau
in tau
[
.ia
+m
-k
+i
-2]