- SUBROUTINE ZGERQF(
- M, N, A, LDA, TAU, WORK, LWORK, INFO )
- INTEGER INFO, LDA, LWORK, M, N
- COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSEZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
- 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*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 min(m,n) elementary reflectors (see Further Details). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M).
- TAU (output) COMPLEX*16 array, dimension (min(M,N))
- The scalar factors of the elementary reflectors (see Further Details).
- WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
- On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
- LWORK (input) INTEGER
- The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
- INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILSThe matrix Q is represented as a product of elementary reflectors
Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
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(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).