?geqr2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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

sgeqr2 dgeqr2 cgeqr2 zgeqr2

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*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)[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

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.
a: Array, size at least max(1, lda*n) for column major and max(1, lda*m) for row major layout. Array a contains the m -by- n matrix A .

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.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?geqr2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values