zgeqrf (l)  Linux Manuals
zgeqrf: computes a QR factorization of a complex MbyN matrix A
NAME
ZGEQRF  computes a QR factorization of a complex MbyN matrix ASYNOPSIS
 SUBROUTINE ZGEQRF(
 M, N, A, LDA, TAU, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LWORK, M, N
 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGEQRF computes a QR factorization of a complex MbyN matrix A: A = Q * R.ARGUMENTS
 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 MbyN matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)byN 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 ith argument had an illegal value
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectorsQ
Each H(i) has the form
H(i)
where tau is a complex scalar, and v is a complex vector with v(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).