Visible to Intel only — GUID: GUID-F6BDFFB0-D806-405C-8101-E326E5C4BBEE
Visible to Intel only — GUID: GUID-F6BDFFB0-D806-405C-8101-E326E5C4BBEE
?gelq2
Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
Syntax
call sgelq2( m, n, a, lda, tau, work, info )
call dgelq2( m, n, a, lda, tau, work, info )
call cgelq2( m, n, a, lda, tau, work, info )
call zgelq2( m, n, a, lda, tau, work, info )
Include Files
- mkl.fi
Description
The routine computes an LQ factorization of a real/complex m-by-n matrix A as A = L*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(k) ... H(2) H(1) (or Q = H(k)H ... H(2)HH(1)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 v1:i-1 = 0 and vi = 1.
On exit, vi+1:n (for real functions) and conjg(vi+1:n) (for complex functions) are stored in a(i, i+1:n).
Input Parameters
The data types are given for the Fortran interface.
- 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 sgelq2
DOUBLE PRECISION for dgelq2
COMPLEX for cgelq2
DOUBLE COMPLEX for zgelq2.
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, the elements on and below the diagonal of the array a contain the m-by-min(n,m) lower trapezoidal matrix L (L is lower triangular if n≥m); the elements above the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of min(n,m) elementary reflectors.
- tau
-
REAL for sgelq2
DOUBLE PRECISION for dgelq2
COMPLEX for cgelq2
DOUBLE COMPLEX for zgelq2.
Array, size 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.
If info = -1011, memory allocation error occurred.