zgeqrf (l) - Linux Manuals
zgeqrf: computes a QR factorization of a complex M-by-N matrix A
NAMEZGEQRF - computes a QR factorization of a complex M-by-N matrix A
- SUBROUTINE ZGEQRF(
- M, N, A, LDA, TAU, WORK, LWORK, INFO )
- INTEGER INFO, LDA, LWORK, M, N
- COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSEZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
- 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, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, 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,N). For optimum performance LWORK >= N*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
Each H(i) has the form
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).