Visible to Intel only — GUID: GUID-C7CF6BD8-C976-44E4-9C13-93CEF22016D7
Visible to Intel only — GUID: GUID-C7CF6BD8-C976-44E4-9C13-93CEF22016D7
?orml2/?unml2
Multiplies a general matrix by the orthogonal/unitary matrix from a LQ factorization determined by ?gelqf (unblocked algorithm).
Syntax
call sorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call dorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call cunml2( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
call zunml2( side, trans, m, n, k, a, lda, tau, c, ldc, work, info )
Include Files
- mkl.fi
Description
The routine ?orml2/?unml2 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(k)*...*H(2)*H(1)for real flavors, or Q = (H(k))H*...*(H(2))H*(H(1))H for complex flavors as returned by ?gelqf.
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 sorml2
DOUBLE PRECISION for dorml2
COMPLEX for cunml2
DOUBLE COMPLEX for zunml2.
Array, DIMENSION
(lda, m) if side = 'L',
(lda, n) if side = 'R'
The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,..., k, as returned by ?gelqf in the first k rows 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. lda≥ max(1,k).
- tau
-
REAL for sorml2
DOUBLE PRECISION for dorml2
COMPLEX for cunml2
DOUBLE COMPLEX for zunml2.
Array, DIMENSION (k).
tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?gelqf.
- c
-
REAL for sorml2
DOUBLE PRECISION for dorml2
COMPLEX for cunml2
DOUBLE COMPLEX for zunml2.
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 sorml2
DOUBLE PRECISION for dorml2
COMPLEX for cunml2
DOUBLE COMPLEX for zunml2.
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