CGERQF(3F) CGERQF(3F)
CGERQF - compute an RQ factorization of a complex M-by-N matrix A
SUBROUTINE CGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
CGERQF 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,n-m+1:n) contains the M-by-M upper
triangular matrix R; if m >= n, the elements on and above the
(m-n)-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 min(m,n) 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/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M). For optimum
performance LWORK >= M*NB, where NB is the optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th 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).
Page 1
CGERQF(3F) CGERQF(3F)
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(nk+i+1:n)
= 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
CGERQF(3F) CGERQF(3F)
CGERQF - compute an RQ factorization of a complex M-by-N matrix A
SUBROUTINE CGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
CGERQF 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,n-m+1:n) contains the M-by-M upper
triangular matrix R; if m >= n, the elements on and above the
(m-n)-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 min(m,n) 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/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M). For optimum
performance LWORK >= M*NB, where NB is the optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th 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).
Page 1
CGERQF(3F) CGERQF(3F)
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(nk+i+1:n)
= 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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