CGERQ2(3F) CGERQ2(3F)
CGERQ2  compute an RQ factorization of a complex m by n matrix A
SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R
* Q.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the m by n matrix A. On exit, if m <= n, the upper
triangle of the subarray A(1:m,nm+1:n) contains the m by m upper
triangular matrix R; if m >= n, the elements on and above the
(mn)th subdiagonal contain the m by n upper trapezoidal matrix
R; the remaining elements, with the array TAU, represent the
unitary matrix Q as a product of elementary reflectors (see
Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX array, dimension (M)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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'
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CGERQ2(3F) CGERQ2(3F)
where tau is a complex scalar, and v is a complex vector with v(nk+i+1:n)
= 0 and v(nk+i) = 1; conjg(v(1:nk+i1)) is stored on exit in
A(mk+i,1:nk+i1), and tau in TAU(i).
CGERQ2(3F) CGERQ2(3F)
CGERQ2  compute an RQ factorization of a complex m by n matrix A
SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R
* Q.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the m by n matrix A. On exit, if m <= n, the upper
triangle of the subarray A(1:m,nm+1:n) contains the m by m upper
triangular matrix R; if m >= n, the elements on and above the
(mn)th subdiagonal contain the m by n upper trapezoidal matrix
R; the remaining elements, with the array TAU, represent the
unitary matrix Q as a product of elementary reflectors (see
Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX array, dimension (M)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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'
Page 1
CGERQ2(3F) CGERQ2(3F)
where tau is a complex scalar, and v is a complex vector with v(nk+i+1:n)
= 0 and v(nk+i) = 1; conjg(v(1:nk+i1)) is stored on exit in
A(mk+i,1:nk+i1), and tau in TAU(i).
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