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ctzrqf.f(3)			    LAPACK			   ctzrqf.f(3)

       ctzrqf.f -

       subroutine ctzrqf (M, N, A, LDA, TAU, INFO)

Function/Subroutine Documentation
   subroutine ctzrqf (integerM, integerN, complex, dimension( lda, * )A,
       integerLDA, complex, dimension( * )TAU, integerINFO)


	    This routine is deprecated and has been replaced by routine CTZRZF.

	    CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
	    to upper triangular form by means of unitary transformations.

	    The upper trapezoidal matrix A is factored as

	       A = ( R	0 ) * Z,

	    where Z is an N-by-N unitary matrix and R is an M-by-M upper
	    triangular matrix.


		     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 >= M.


		     A is COMPLEX array, dimension (LDA,N)
		     On entry, the leading M-by-N upper trapezoidal part of the
		     array A must contain the matrix to be factorized.
		     On exit, the leading M-by-M upper triangular part of A
		     contains the upper triangular matrix R, and elements M+1 to
		     N of the first M rows of A, with the array TAU, represent the
		     unitary matrix Z as a product of M elementary reflectors.


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


		     TAU is COMPLEX array, dimension (M)
		     The scalar factors of the elementary reflectors.


		     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.

	   November 2011

       Further Details:

	     The  factorization is obtained by Householder's method.  The kth
	     transformation matrix, Z( k ), whose conjugate transpose is used to
	     introduce zeros into the (m - k + 1)th row of A, is given in the form

		Z( k ) = ( I	 0   ),
			 ( 0  T( k ) )


		T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (	  1    ),
							      (	  0    )
							      ( z( k ) )

	     tau is a scalar and z( k ) is an ( n - m ) element vector.
	     tau and z( k ) are chosen to annihilate the elements of the kth row
	     of X.

	     The scalar tau is returned in the kth element of TAU and the vector
	     u( k ) in the kth row of A, such that the elements of z( k ) are
	     in	 a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
	     the upper triangular part of A.

	     Z is given by

		Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

       Definition at line 139 of file ctzrqf.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			   ctzrqf.f(3)

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