Visible to Intel only — GUID: GUID-2A117A42-951E-4E6D-8806-01B24FB7B8D4
Visible to Intel only — GUID: GUID-2A117A42-951E-4E6D-8806-01B24FB7B8D4
?orm2r/?unm2r
Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by ?geqrf (unblocked algorithm).
Syntax
call sorm2r( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call dorm2r( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call cunm2r( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call zunm2r( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
Include Files
- mkl.fi
Description
The routine ?orm2r/?unm2r overwrites the general real/complex m-by-n matrix C with
Q*C if side = 'L' and trans = 'N', or
QT*C / QH*C if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or
C*Q if side = 'R' and trans = 'N', or
C*QT / C*QH if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).
Here Q is a real orthogonal or complex unitary matrix defined as the product of k elementary reflectors
Q = H(1)*H(2)*...*H(k) as returned by ?geqrf.
Q is of order m if side = 'L' and of order n if side = 'R'.
Input Parameters
- side
-
CHARACTER*1.
= 'L': apply Q or QT / QH from the left
= 'R': apply Q or QT / QH from the right
- trans
-
CHARACTER*1.
= 'N': apply Q (no transpose)
= 'T': apply QT (transpose, for real flavors)
= 'C': apply QH (conjugate transpose, for complex flavors)
- m
-
INTEGER. The number of rows of the matrix C. m≥ 0.
- n
-
INTEGER. The number of columns of the matrix C. n≥ 0.
- k
-
INTEGER. The number of elementary reflectors whose product defines the matrix Q.
If side = 'L', m≥k≥ 0;
if side = 'R', n≥k≥ 0.
- a
-
REAL for sorm2r
DOUBLE PRECISION for dorm2r
COMPLEX for cunm2r
DOUBLE COMPLEX for zunm2r.
Array, DIMENSION (lda,k).
The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,..., k, as returned by ?geqrf in the first k columns of its array argument a. The array a is modified by the routine but restored on exit.
- lda
-
INTEGER. The leading dimension of the array a.
If side = 'L', lda≥ max(1, m);
if side = 'R', lda≥ max(1, n).
- tau
-
REAL for sorm2r
DOUBLE PRECISION for dorm2r
COMPLEX for cunm2r
DOUBLE COMPLEX for zunm2r.
Array, DIMENSION (k).
tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?geqrf.
- c
-
REAL for sorm2r
DOUBLE PRECISION for dorm2r
COMPLEX for cunm2r
DOUBLE COMPLEX for zunm2r.
Array, DIMENSION (ldc, n).
On entry, the m-by-n matrix C.
- ldc
-
INTEGER. The leading dimension of the array c. ldc≥ max(1,m).
- work
-
REAL for sorm2r
DOUBLE PRECISION for dorm2r
COMPLEX for cunm2r
DOUBLE COMPLEX for zunm2r.
Workspace array, DIMENSION
(n) if side = 'L',
(m) if side = 'R'.
Output Parameters
- c
-
On exit, c is overwritten by Q*C or QT*C / QH*C, or C*Q, or C*QT / C*QH.
- info
-
INTEGER.
= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value