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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine cgeql2 | ( | integer | M, |
integer | N, | ||
complex, dimension( lda, * ) | A, | ||
integer | LDA, | ||
complex, dimension( * ) | TAU, | ||
complex, dimension( * ) | WORK, | ||
integer | INFO | ||
) |
CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
Download CGEQL2 + dependencies [TGZ] [ZIP] [TXT]
CGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L.
[in] | M | M is INTEGER The number of rows of the matrix A. M >= 0. |
[in] | N | N is INTEGER The number of columns of the matrix A. N >= 0. |
[in,out] | A | A is 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). |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | TAU | TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | WORK | WORK is COMPLEX array, dimension (N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
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 H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex 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).
Definition at line 125 of file cgeql2.f.