Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
lapack_int LAPACKE_sgelq2 (int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, float* tau);
lapack_int LAPACKE_dgelq2 (int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, double * tau);
lapack_int LAPACKE_cgelq2 (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_complex_float* tau);
lapack_int LAPACKE_zgelq2 (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_complex_double* tau);
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, the j-th (i+1 ≤j≤n) component of vector v (for real functions) or its conjugate (for complex functions) is stored in a[i - 1 + lda*(j - 1)] for column major layout or in a[j - 1 + lda*(i - 1)] for row major layout.
A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
The number of rows in the matrix A (m≥ 0).
The number of columns in A (n≥ 0).
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.
The leading dimension of a; at least max(1, m) for column major layout and max(1,n) for row major layout.
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.
Array, size at least max(1, min(m, n)).
Contains scalar factors of the elementary reflectors.
This function returns a value info.
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.