Visible to Intel only — GUID: GUID-BB848113-8369-4C56-B6A8-CD9B83477D88
Visible to Intel only — GUID: GUID-BB848113-8369-4C56-B6A8-CD9B83477D88
?geqr2p
Computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
Syntax
call sgeqr2p( m, n, a, lda, tau, work, info )
call dgeqr2p( m, n, a, lda, tau, work, info )
call cgeqr2p( m, n, a, lda, tau, work, info )
call zgeqr2p( 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 diagonal entries of R are real and nonnegative.
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 v(1:i-1) = 0 and v(i) = 1.
On exit, v(i+1:m) is stored in a(i+1:m, 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 sgeqr2p
DOUBLE PRECISION for d
COMPLEX for cgeqr2p
DOUBLE COMPLEX for zgeqr2p.
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 diagonal entries of R are real and nonnegative; the elements below the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
- tau
-
REAL for sgeqr2p
DOUBLE PRECISION for dgeqr2p
COMPLEX for cgeqr2p
DOUBLE COMPLEX for zgeqr2p.
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.