zgeqr2.f - Man Page
SRC/zgeqr2.f
Synopsis
Functions/Subroutines
subroutine zgeqr2 (m, n, a, lda, tau, work, info)
ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
Function/Subroutine Documentation
subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)
ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
Purpose:
ZGEQR2 computes a QR factorization of a complex m-by-n matrix A: A = Q * ( R ), ( 0 ) where: Q is a m-by-m orthogonal matrix; R is an upper-triangular n-by-n matrix; 0 is a (m-n)-by-n zero matrix, if m > n.
- Parameters
M
M is INTEGER The number of rows of the matrix A. M >= 0.
N
N is INTEGER The number of columns of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
WORK
WORK is COMPLEX*16 array, dimension (N)
INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The matrix Q is represented as a product of 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**H where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
Definition at line 129 of file zgeqr2.f.
Author
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Referenced By
The man page zgeqr2(3) is an alias of zgeqr2.f(3).
Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK