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zgeql2.f(3) LAPACK zgeql2.f(3)

zgeql2.f -


subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO)
 
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
Purpose:
 ZGEQL2 computes a QL factorization of a complex m by n matrix A:
 A = Q * L.
Parameters:
M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
A
          A is COMPLEX*16 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
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
TAU
          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
WORK
          WORK is COMPLEX*16 array, dimension (N)
INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
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
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 124 of file zgeql2.f.

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