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NAMEzgerq2.f -SYNOPSISFunctions/Subroutinessubroutine zgerq2 (M, N, A, LDA, TAU, WORK, INFO) Function/Subroutine Documentationsubroutine zgerq2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose:ZGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q. M
Author:
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 upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; 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 (M)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 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(1)**H H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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