p?geqpf
p?geqpf
Computes the
QR
factorization of a general m-by-n matrix with pivoting.Syntax
void
psgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
float
*tau
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
double
*tau
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex8
*tau
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
float
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
void
pzgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex16
*tau
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
double
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
Include Files
- mkl_scalapack.h
Description
The
p?geqpf
function
forms the QR
factorization with column pivoting of a general m
-by-n
distributed matrix sub(A
)= A
(ia
:ia
+m
-1, ja
:ja
+n
-1) as sub(
A
)*P
=Q
*R
.Input Parameters
- m
- (global) The number of rows in the matrix sub(A)(.m≥0)
- n
- (global) The number of columns in the 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 leastFor real flavors:.lwork≥max(3,mp0+nq0) +LOCc(ja+n-1) +nq0For complex flavors:.lwork≥max(3,mp0+nq0)Here,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), andLOCc(ja+n-1) =numroc(ja+n-1,nb_a,MYCOL,csrc_a,NPCOL)numroc,indxg2pare ScaLAPACK tool functions.You can determineMYROW,MYCOL,NPROWandNPCOLby calling theblacs_gridinfofunction.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.
- rwork
- (local).Workspace array of sizelrwork(complex flavors only).
- lrwork
- (local or global) size ofrwork(complex flavors only). The value oflrworkmust be at least.lwork≥LOCc(ja+n-1) +nq0Here,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), andLOCc(ja+n-1) =numroc(ja+n-1,nb_a,MYCOL,csrc_a,NPCOL)numroc,indxg2pare ScaLAPACK tool functions.You can determineMYROW,MYCOL,NPROWandNPCOLby calling theblacs_gridinfofunction.If, thenlrwork= -1lrworkis 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 above the diagonal of sub(A)contain the min(m,n)-by-nupper trapezoidal matrixR(Ris upper triangular if); the elements below the diagonal, with the arraym≥ntau, represent the orthogonal/unitary matrixQas a product of elementary reflectors(see.Application Notesbelow)
- ipiv
- (local) Array of size.LOCc(ja+n-1)column of sub(ipiv[i] =k, the local (i+1)-thA)*Pwas the globalk-th column of sub(A)(0 ≤.i<LOCc(ja+n-1)ipivis tied to the distributed matrixA.
- tau
- (local)Array of size.LOCc(ja+min(m,n)-1)Contains the scalar factortauof elementary reflectors.tauis tied to the distributed matrixA.
- work[0]
- On exit,contains the minimum value ofwork[0]lworkrequired for optimum performance.
- rwork[0]
- On exit,contains the minimum value ofrwork[0]lrworkrequired 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
(1)*H
(2)*...*H
(k
)where
k
= min(m
,n
).Each
H
(i
) has the form H
= 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
:m
) is stored on exit in A
(ia
+i
:ia
+m-1, ja
+i
-1).The matrix canonical unit vector
P
is represented in ipiv
as follows: if ipiv
[j
]= i
then the (j
+1)-th column of P
is the i
-th (0 ≤
. j
< LOCc
(ja
+n
-1)