?geqr2p

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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

sgeqr2p dgeqr2p cgeqr2p zgeqr2p

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*v^{T} for real flavors, or

H(i) = I - tau*v*v^{H} 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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?geqr2p

Syntax

Include Files

Description

Input Parameters

Output Parameters