slarft.f(3)							      LAPACK							       slarft.f(3)

NAME

       slarft.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
	   SLARFT

Function/Subroutine Documentation
   subroutine slarft (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real,
       dimension( ldt, * )T, integerLDT)
       SLARFT

       Purpose:

	    SLARFT forms the triangular factor T of a real block reflector H
	    of order n, which is defined as a product of k elementary reflectors.

	    If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;

	    If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.

	    If STOREV = 'C', the vector which defines the elementary reflector
	    H(i) is stored in the i-th column of the array V, and

	       H  =  I - V * T * V**T

	    If STOREV = 'R', the vector which defines the elementary reflector
	    H(i) is stored in the i-th row of the array V, and

	       H  =  I - V**T * T * V

       Parameters:
	   DIRECT

		     DIRECT is CHARACTER*1
		     Specifies the order in which the elementary reflectors are
		     multiplied to form the block reflector:
		     = 'F': H = H(1) H(2) . . . H(k) (Forward)
		     = 'B': H = H(k) . . . H(2) H(1) (Backward)

	   STOREV

		     STOREV is CHARACTER*1
		     Specifies how the vectors which define the elementary
		     reflectors are stored (see also Further Details):
		     = 'C': columnwise
		     = 'R': rowwise

	   N

		     N is INTEGER
		     The order of the block reflector H. N >= 0.

	   K

		     K is INTEGER
		     The order of the triangular factor T (= the number of
		     elementary reflectors). K >= 1.

	   V

		     V is REAL array, dimension
					  (LDV,K) if STOREV = 'C'
					  (LDV,N) if STOREV = 'R'
		     The matrix V. See further details.

	   LDV

		     LDV is INTEGER
		     The leading dimension of the array V.
		     If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

	   TAU

		     TAU is REAL array, dimension (K)
		     TAU(i) must contain the scalar factor of the elementary
		     reflector H(i).

	   T

		     T is REAL array, dimension (LDT,K)
		     The k by k triangular factor T of the block reflector.
		     If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
		     lower triangular. The rest of the array is not used.

	   LDT

		     LDT is INTEGER
		     The leading dimension of the array T. LDT >= K.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       Further Details:

	     The shape of the matrix V and the storage of the vectors which define
	     the H(i) is best illustrated by the following example with n = 5 and
	     k = 3. The elements equal to 1 are not stored.

	     DIRECT = 'F' and STOREV = 'C':	    DIRECT = 'F' and STOREV = 'R':

			  V = (  1	 )		   V = (  1 v1 v1 v1 v1 )
			      ( v1  1	 )		       (     1 v2 v2 v2 )
			      ( v1 v2  1 )		       (	1 v3 v3 )
			      ( v1 v2 v3 )
			      ( v1 v2 v3 )

	     DIRECT = 'B' and STOREV = 'C':	    DIRECT = 'B' and STOREV = 'R':

			  V = ( v1 v2 v3 )		   V = ( v1 v1	1	)
			      ( v1 v2 v3 )		       ( v2 v2 v2  1	)
			      (  1 v2 v3 )		       ( v3 v3 v3 v3  1 )
			      (     1 v3 )
			      (        1 )

       Definition at line 164 of file slarft.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       slarft.f(3)