p?gelqf
p?gelqf
Computes the
LQ
factorization of a general rectangular matrix.Syntax
void
psgelqf
(
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
pdgelqf
(
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
pcgelqf
(
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
pzgelqf
(
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?gelqf
function
computes the LQ
factorization of a real/complex distributed m
-by-n
matrix sub(A
)= A
(ia
:ia
+m
-1,ja
:ja
+n
-1) = L
*Q
.Input Parameters
- m
- (global) The number of rows in the distributed submatrix sub(A)(.m≥0)
- n
- (global) The number of columns in the distributed submatrix 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 arrayAindicating 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 size oflwork.
- 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)nq0 =numroc(n+icoff,nb_a,MYCOL,iacol,NPCOL)indxg2pandnumrocare ScaLAPACK tool functions;MYROW,MYCOL,NPROWandNPCOLcan be determined by calling thefunctionblacs_gridinfo.mod(is the integer remainder ofx,y).x/yIf, 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
- The elements on and below the diagonal of sub(A) contain them-by-min(m,n) lower trapezoidal matrixL(Lis lower trapezoidal ifm≤n); the elements above the diagonal, with the arraytau, represent the orthogonal/unitary matrixQas a product of elementary reflectors(see.Application Notesbelow)
- tau
- (local)Array of size.LOCr(ia+min(m,n)-1)Contains the scalar factors 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
+k
-1)*H
(ia
+k
-2)*...*H
(ia
),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
(1:i
-1) = 0 and v
(i
) = 1; v
(i
+1:n
) is stored on exit in A
(ia
+i
-1,ja
+i
:ja
+n
-1), and tau
in tau
[
.ia
+i
-2]