Visible to Intel only — GUID: GUID-DBD590BD-86E0-4A78-927F-C8D85B7BC388
Visible to Intel only — GUID: GUID-DBD590BD-86E0-4A78-927F-C8D85B7BC388
?unmbr
Multiplies an arbitrary complex matrix by the unitary matrix Q or P determined by ?gebrd.
Syntax
call cunmbr(vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
call zunmbr(vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
call unmbr(a, tau, c [,vect] [,side] [,trans] [,info])
Include Files
- mkl.fi, lapack.f90
Description
Given an arbitrary complex matrix C, this routine forms one of the matrix products Q*C, QH*C, C*Q, C*QH, P*C, PH*C, C*P, or C*PH, where Q and P are unitary matrices computed by a call to gebrd/gebrd. The routine overwrites the product on C.
Input Parameters
In the descriptions below, r denotes the order of Q or PH:
If side = 'L', r = m; if side = 'R', r = n.
- vect
-
CHARACTER*1. Must be 'Q' or 'P'.
If vect = 'Q', then Q or QH is applied to C.
If vect = 'P', then P or PH is applied to C.
- side
-
CHARACTER*1. Must be 'L' or 'R'.
If side = 'L', multipliers are applied to C from the left.
If side = 'R', they are applied to C from the right.
- trans
-
CHARACTER*1. Must be 'N' or 'C'.
If trans = 'N', then Q or P is applied to C.
If trans = 'C', then QH or PH is applied to C.
- m
-
INTEGER. The number of rows in C.
- n
-
INTEGER. The number of columns in C.
- k
-
INTEGER. One of the dimensions of A in ?gebrd:
If vect = 'Q', the number of columns in A;
If vect = 'P', the number of rows in A.
Constraints: m≥ 0, n≥ 0, k≥ 0.
- a, c, work
-
COMPLEX for cunmbr
DOUBLE COMPLEX for zunmbr.
Arrays:
a(lda,*) is the array a as returned by ?gebrd.
Its second dimension must be at least max(1, min(r,k)) for vect = 'Q', or max(1, r)) for vect = 'P'.
c(ldc,*) holds the matrix C.
Its second dimension must be at least max(1, n).
work is a workspace array, its dimension max(1, lwork).
- lda
-
INTEGER. The leading dimension of a. Constraints:
lda≥ max(1, r) if vect = 'Q';
lda≥ max(1, min(r,k)) if vect = 'P'.
- ldc
-
INTEGER. The leading dimension of c; ldc≥ max(1, m).
- tau
-
COMPLEX for cunmbr
DOUBLE COMPLEX for zunmbr.
Array, size at least max (1, min(r, k)).
For vect = 'Q', the array tauq as returned by ?gebrd. For vect = 'P', the array taup as returned by ?gebrd.
- lwork
-
INTEGER. The size of the work array.
lwork≥ max(1, n) if side = 'L';
lwork≥ max(1, m) if side = 'R'.
lwork≥ 1 if n=0 or m=0.
For optimum performance lwork ≥ max(1,n*nb) if side = 'L', and lwork ≥ max(1,m*nb) if side = 'R', where nb is the optimal blocksize. (nb = 0 if m = 0 or n = 0.)
If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.
See Application Notes for the suggested value of lwork.
Output Parameters
- c
-
Overwritten by the product Q*C, QH*C, C*Q, C*QH, P*C, PH*C, C*P, or C*PH, as specified by vect, side, and trans.
- work(1)
-
If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine unmbr interface are the following:
- a
-
Holds the matrix A of size (r,min(nq,k)) where
r = nq, if vect = 'Q',
r = min(nq,k), if vect = 'P',
nq = m, if side = 'L',
nq = n, if side = 'R',
k = m, if vect = 'P',
k = n, if vect = 'Q'.
- tau
-
Holds the vector of length min(nq,k).
- c
-
Holds the matrix C of size (m,n).
- vect
-
Must be 'Q' or 'P'. The default value is 'Q'.
- side
-
Must be 'L' or 'R'. The default value is 'L'.
- trans
-
Must be 'N' or 'C'. The default value is 'N'.
Application Notes
For better performance, use
lwork = n*blocksize for side = 'L', or
lwork = m*blocksize for side = 'R',
where blocksize is a machine-dependent value (typically, 16 to 64) required for optimum performance of the blocked algorithm.
If it is not clear how much workspace to supply, use a generous value of lwork for the first run, or set lwork = -1.
In first case the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value (work(1)) for subsequent runs.
If lwork = -1, then the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work). This operation is called a workspace query.
Note that if lwork is less than the minimal required value and is not equal to -1, then the routine returns immediately with an error exit and does not provide any information on the recommended workspace.
The computed product differs from the exact product by a matrix E such that ||E||2 = O(ε)*||C||2.
The total number of floating-point operations is approximately
8*n*k(2*m - k) if side = 'L' and m≥k;
8*m*k(2*n - k) if side = 'R' and n≥k;
8*m2*n if side = 'L' and m < k;
8*n2*m if side = 'R' and n < k.
The real counterpart of this routine is ormbr.