p?gerq2
p?gerq2
Computes an RQ factorization of a general rectangular matrix (unblocked algorithm).
Syntax
void
psgerq2
(
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
pdgerq2
(
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
pcgerq2
(
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
pzgerq2
(
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?gerq2
function
computes an RQ
factorization of a real/complex distributed m
-by-n
matrix sub(
, A
) = A
(ia
:ia
+m
-1ja
:ja
+n
-1) = 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 size.*lld_aLOC(cja+n-1)On entry, this array contains the local pieces of them-by-ndistributed matrix sub(A) which is to be factored.
- ia,ja
- (global) The row and column indices in the global matrixAindicating the first row and the first column of sub(A), respectively.
- desca
- (global and local) array of sizedlen_. The array descriptor for the distributed matrix A.
- work
- (local).This is a workspace array of sizelwork.
- lwork
- (local or global)The size of the arraywork.lworkis local input and must be at least, wherelwork≥nq0 + max(1,mp0),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),nq0 =numroc(n+icoff,nb_a,mycol,iacol,npcol)indxg2pandnumrocare ScaLAPACK tool functions;myrow,mycol,nprow, andnpcolcan be determined by calling thefunctionblacs_gridinfo.Iflwork= -1, thenlworkis 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 bypxerbla.
Output Parameters
- a
- (local).On exit,if, the upper triangle ofm≤nA(ia+m-n:ia+m-1,ja:ja+n-1) contains them-by-mupper triangular matrixR;ifm≥n, the elements on and above the (m-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 sizeLOCr(ia+m-1). This array contains the scalar factors of the elementary reflectors.tauis tied to the distributed matrixA.
- work
- On exit,returns the minimal and optimalwork[0]lwork.
- info
- (local)Ifinfo= 0, the execution is successful.ifinfo< 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 reflectorsQ
= H
(ia
)*H
(ia
+1)*...*H
(ia
+k
-1)Q
= (H
(ia
))H
H
(ia
+1))H
H
(ia
+k
-1))H
where .
k
= min(m
, n
)Each has the form
H
(i
)H
(i
) = I
- tau
*v
*v'
where and ; for real flavors or for complex flavors is stored on exit in , and .
tau
is a real/complex scalar, and v
is a real/complex vector with v
(n-k
+i
+1:n
) = 0v
(n
-k
+i
) = 1v
(1:n
-k
+i
-1)conjg
(v
(1:n
-k
+i
-1))A
(ia
+m-k
+i
-1, ja
:ja
+n-k
+i
-2)tau
in tau
[
ia
+m-k
+i
-2]