Visible to Intel only — GUID: GUID-E524DD07-617C-441E-A8E1-517701EEEBF8
Visible to Intel only — GUID: GUID-E524DD07-617C-441E-A8E1-517701EEEBF8
?geql2
Computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
Syntax
call sgeql2( m, n, a, lda, tau, work, info )
call dgeql2( m, n, a, lda, tau, work, info )
call cgeql2( m, n, a, lda, tau, work, info )
call zgeql2( m, n, a, lda, tau, work, info )
Include Files
- mkl.fi
Description
The routine computes a QL factorization of a real/complex m-by-n matrix A as A = Q*L.
The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors :
Q = H(k)* ... *H(2)*H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1.
On exit, v(1:m-k+i-1) is stored in a(1:m-k+i-1, n-k+i).
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 sgeql2
DOUBLE PRECISION for dgeql2
COMPLEX for cgeql2
DOUBLE COMPLEX for zgeql2.
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 lower triangle of the subarray a(m-n+1:m, 1:n) contains the n-by-n lower triangular matrix L; if m < n, the elements on and below the (n-m)th superdiagonal contain the m-by-n lower trapezoidal matrix L; the remaining elements, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
- tau
-
REAL for sgeql2
DOUBLE PRECISION for dgeql2
COMPLEX for cgeql2
DOUBLE COMPLEX for zgeql2.
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.