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slarzt.f(3)				      LAPACK				      slarzt.f(3)

NAME
       slarzt.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
	   SLARZT forms the triangular factor T of a block reflector H = I - vtvH.

Function/Subroutine Documentation
   subroutine slarzt (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv,
       * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT)
       SLARZT forms the triangular factor T of a block reflector H = I - vtvH.

       Purpose:

	    SLARZT 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

	    Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

       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, not supported yet)
		     = '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			      (not supported yet)
		     = '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:
	   September 2012

       Contributors:
	   A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       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; the corresponding
	     array elements are modified but restored on exit. The rest of the
	     array is not used.

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

							 ______V_____
		    ( v1 v2 v3 )			/		      ( v1 v2 v3 )			( v1 v1 v1 v1 v1 . . . . 1 )
		V = ( v1 v2 v3 )		      ( v2 v2 v2 v2 v2 . . . 1	 )
		    ( v1 v2 v3 )		      ( v3 v3 v3 v3 v3 . . 1	 )
		    ( v1 v2 v3 )
		       .  .  .
		       .  .  .
		       1  .  .
			  1  .
			     1

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

								   ______V_____
		       1					  /			   .  1 			  ( 1 . . . . v1 v1 v1 v1 v1 )
		       .  .  1			      ( . 1 . . . v2 v2 v2 v2 v2 )
		       .  .  .			      ( . . 1 . . v3 v3 v3 v3 v3 )
		       .  .  .
		    ( v1 v2 v3 )
		    ( v1 v2 v3 )
		V = ( v1 v2 v3 )
		    ( v1 v2 v3 )
		    ( v1 v2 v3 )

       Definition at line 186 of file slarzt.f.

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

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