Visible to Intel only — GUID: GUID-9C4CD970-E664-42C2-B728-F588BBFAB3AD
Visible to Intel only — GUID: GUID-9C4CD970-E664-42C2-B728-F588BBFAB3AD
?gerq2
Computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
Syntax
call sgerq2( m, n, a, lda, tau, work, info )
call dgerq2( m, n, a, lda, tau, work, info )
call cgerq2( m, n, a, lda, tau, work, info )
call zgerq2( m, n, a, lda, tau, work, info )
Include Files
- mkl.fi
Description
The routine computes a RQ factorization of a real/complex m-by-n matrix A as A = R*Q.
The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors :
Q = H(1)*H(2)* ... *H(k) for real flavors, or
Q = H(1)H*H(2)H* ... *H(k)H for complex flavors
where k = min(m, n).
Each H(i) has the form
H(i) = I - tau*v*vT for real flavors, or
H(i) = I - tau*v*vH for complex flavors
where tau is a real/complex scalar stored in tau(i), and v is a real/complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1.
On exit, v(1:n-k+i-1) is stored in a(m-k+i, 1:n-k+i-1).
Input Parameters
- m
-
INTEGER. The number of rows in the matrix A (m≥ 0).
- n
-
INTEGER. The number of columns in A (n≥ 0).
- a, work
-
REAL for sgerq2
DOUBLE PRECISION for dgerq2
COMPLEX for cgerq2
DOUBLE COMPLEX for zgerq2.
Arrays:
a(lda,*) contains the m-by-n matrix A.
The second dimension of a must be at least max(1, n).
work(m) is a workspace array.
- lda
-
INTEGER. The leading dimension of a; at least max(1, m).
Output Parameters
- a
-
Overwritten by the factorization data as follows:
on exit, if m ≤ n, the upper triangle of the subarray a(1:m, n-m+1:n ) contains the m-by-m upper triangular matrix R; if m > n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
- tau
-
REAL for sgerq2
DOUBLE PRECISION for dgerq2
COMPLEX for cgerq2
DOUBLE COMPLEX for zgerq2.
Array, DIMENSION at least max(1, min(m, n)).
Contains scalar factors of the elementary reflectors.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.