DGEQLF(3F) DGEQLF(3F)
DGEQLF - compute a QL factorization of a real M-by-N matrix A
SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
DGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L.
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) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, if m >= n, the lower
triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower
triangular matrix L; if m <= n, the elements on and below the
(n-m)-th superdiagonal contain the M-by-N lower trapezoidal
matrix L; the remaining elements, with the array TAU, represent
the orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE PRECISION 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,N). For optimum
performance LWORK >= N*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
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DGEQLF(3F) DGEQLF(3F)
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
DGEQLF(3F) DGEQLF(3F)
DGEQLF - compute a QL factorization of a real M-by-N matrix A
SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
DGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L.
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) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, if m >= n, the lower
triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower
triangular matrix L; if m <= n, the elements on and below the
(n-m)-th superdiagonal contain the M-by-N lower trapezoidal
matrix L; the remaining elements, with the array TAU, represent
the orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE PRECISION 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,N). For optimum
performance LWORK >= N*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
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DGEQLF(3F) DGEQLF(3F)
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
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