zgeqrfp.f - Man Page




subroutine zgeqrfp (m, n, a, lda, tau, work, lwork, info)

Function/Subroutine Documentation

subroutine zgeqrfp (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)



 ZGEQR2P computes a QR factorization of a complex M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )


    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix with nonnegative diagonal
    0 is a (M-N)-by-N zero matrix, if M > N.


          M is INTEGER
          The number of rows of the matrix A.  M >= 0.


          N is INTEGER
          The number of columns of the matrix A.  N >= 0.


          A is 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 diagonal entries of R
          are real and nonnegative; 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


          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).


          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further


          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


          LWORK is 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 is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

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Further Details:

  The 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**H

  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).

 See Lapack Working Note 203 for details

Definition at line 148 of file zgeqrfp.f.


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Referenced By

The man page zgeqrfp(3) is an alias of zgeqrfp.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK