CGEQLF(3F) CGEQLF(3F)
CGEQLF - compute a QL factorization of a complex M-by-N matrix A
SUBROUTINE CGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
CGEQLF computes a QL factorization of a complex 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) COMPLEX 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 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/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,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).
Page 1
CGEQLF(3F) CGEQLF(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(mk+i+1:m)
= 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:mk+i-1,n-k+i),
and tau in TAU(i).
CGEQLF(3F) CGEQLF(3F)
CGEQLF - compute a QL factorization of a complex M-by-N matrix A
SUBROUTINE CGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
CGEQLF computes a QL factorization of a complex 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) COMPLEX 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 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/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,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).
Page 1
CGEQLF(3F) CGEQLF(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(mk+i+1:m)
= 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:mk+i-1,n-k+i),
and tau in TAU(i).
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