Visible to Intel only — GUID: GUID-B280F74F-4F92-4D91-AE1A-A23A60589514
Visible to Intel only — GUID: GUID-B280F74F-4F92-4D91-AE1A-A23A60589514
?geqr2
Computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
Syntax
call sgeqr2( m, n, a, lda, tau, work, info )
call dgeqr2( m, n, a, lda, tau, work, info )
call cgeqr2( m, n, a, lda, tau, work, info )
call zgeqr2( m, n, a, lda, tau, work, info )
Include Files
- mkl.fi
Description
The routine computes a QR factorization of a real/complex m-by-n matrix A as A = Q*R.
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), 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:m is stored in a(i+1:m, i).
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 sgeqr2
DOUBLE PRECISION for dgeqr2
COMPLEX for cgeqr2
DOUBLE COMPLEX for zgeqr2.
Arrays:
a(lda,*) contains the m-by-n matrix A.
The second dimension of a must be at least max(1, n).
work(n) 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 above the diagonal of the array a contain the min(n,m)-by-n upper trapezoidal matrix R (R is upper triangular if m≥n); the elements below the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
- tau
-
REAL for sgeqr2
DOUBLE PRECISION for dgeqr2
COMPLEX for cgeqr2
DOUBLE COMPLEX for zgeqr2.
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.