ZGELQF(3F) ZGELQF(3F)
ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK )
ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
* 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*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, the elements on and
below the diagonal of the array contain the m-by-min(m,n) lower
trapezoidal matrix L (L is lower triangular if m <= n); the
elements above the diagonal, 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*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 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(k)' . . . H(2)' H(1)', where k = min(m,n).
Each H(i) has the form
Page 1
ZGELQF(3F) ZGELQF(3F)
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) =
0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau
in TAU(i).
ZGELQF(3F) ZGELQF(3F)
ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK )
ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
* 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*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, the elements on and
below the diagonal of the array contain the m-by-min(m,n) lower
trapezoidal matrix L (L is lower triangular if m <= n); the
elements above the diagonal, 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*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 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(k)' . . . H(2)' H(1)', where k = min(m,n).
Each H(i) has the form
Page 1
ZGELQF(3F) ZGELQF(3F)
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) =
0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau
in TAU(i).
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