Visible to Intel only — GUID: GUID-7A1EF7E8-333F-430A-B5C7-3EE1A4EBC2D4
Visible to Intel only — GUID: GUID-7A1EF7E8-333F-430A-B5C7-3EE1A4EBC2D4
?ormr3/?unmr3
Multiplies a general matrix by the orthogonal/unitary matrix from a RZ factorization determined by ?tzrzf (unblocked algorithm).
Syntax
call sormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )
call dormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )
call cunmr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )
call zunmr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )
Include Files
- mkl.fi
Description
The routine ?ormr3/?unmr3 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 ?tzrzf.
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.
- l
-
INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors.
If side = 'L', m≥l≥ 0,
if side = 'R', n≥l≥ 0.
- a
-
REAL for sormr3
DOUBLE PRECISION for dormr3
COMPLEX for cunmr3
DOUBLE COMPLEX for zunmr3.
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 ?tzrzf in the last 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 sormr3
DOUBLE PRECISION for dormr3
COMPLEX for cunmr3
DOUBLE COMPLEX for zunmr3.
Array, DIMENSION (k).
tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?tzrzf.
- c
-
REAL for sormr3
DOUBLE PRECISION for dormr3
COMPLEX for cunmr3
DOUBLE COMPLEX for zunmr3.
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 sormr3
DOUBLE PRECISION for dormr3
COMPLEX for cunmr3
DOUBLE COMPLEX for zunmr3.
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