Reduces the upper trapezoidal matrix A to upper triangular form.
lapack_int LAPACKE_stzrzf (int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, float* tau);
lapack_int LAPACKE_dtzrzf (int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, double* tau);
lapack_int LAPACKE_ctzrzf (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_complex_float* tau);
lapack_int LAPACKE_ztzrzf (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_complex_double* tau);
The routine reduces the m-by-n (m≤n) real/complex upper trapezoidal matrix A to upper triangular form by means of orthogonal/unitary transformations. The upper trapezoidal matrix A = [A1 A2] = [A1:m, 1:m, A1:m, m+1:n] is factored as
A = [R0]*Z,
where Z is an n-by-n orthogonal/unitary matrix, R is an m-by-m upper triangular matrix, and 0 is the m-by-(n-m) zero matrix.
The ?tzrzf routine replaces the deprecated ?tzrqf routine.
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
The number of rows in the matrix A (m≥ 0).
The number of columns in A (n≥m).
Array a is of size max(1, lda*n) for column major layout and max(1, lda*m) for row major layout.
The leading m-by-n upper trapezoidal part of the array a contains the matrix A to be factorized.
The leading dimension of a; at least max(1, m)for column major layout and max(1, n) for row major layout.
Overwritten on exit by the factorization data as follows:
the leading m-by-m upper triangular part of a contains the upper triangular matrix R, and elements m +1 to n of the first m rows of a, with the array tau, represent the orthogonal matrix Z as a product of m elementary reflectors.
Array, size at least max (1, m). Contains scalar factors of the elementary reflectors for the matrix Z.
This function returns a value info.
If info=0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
The factorization is obtained by Householder's method. The k-th transformation matrix, Z(k), which is used to introduce zeros into the (m - k + 1)-th row of A, is given in the form
where for real flavors
and for complex flavors
tau is a scalar and z(k) is an l-element vector. tau and z(k) are chosen to annihilate the elements of the k-th row of A2.
The scalar tau is returned in the k-th element of tau and the vector u(k) in the k-th row of A, such that the elements of z(k) are stored in the last m - n elements of the k-th row of array a.
The elements of R are returned in the upper triangular part of A.
The matrix Z is given by
Z = Z(1)*Z(2)*...*Z(m).
Related routines include: