Annotation of rpl/lapack/lapack/dlatrz.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b DLATRZ
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLATRZ + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrz.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrz.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrz.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER L, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
! 37: *> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means
! 38: *> of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
! 39: *> matrix and, R and A1 are M-by-M upper triangular matrices.
! 40: *> \endverbatim
! 41: *
! 42: * Arguments:
! 43: * ==========
! 44: *
! 45: *> \param[in] M
! 46: *> \verbatim
! 47: *> M is INTEGER
! 48: *> The number of rows of the matrix A. M >= 0.
! 49: *> \endverbatim
! 50: *>
! 51: *> \param[in] N
! 52: *> \verbatim
! 53: *> N is INTEGER
! 54: *> The number of columns of the matrix A. N >= 0.
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in] L
! 58: *> \verbatim
! 59: *> L is INTEGER
! 60: *> The number of columns of the matrix A containing the
! 61: *> meaningful part of the Householder vectors. N-M >= L >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in,out] A
! 65: *> \verbatim
! 66: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 67: *> On entry, the leading M-by-N upper trapezoidal part of the
! 68: *> array A must contain the matrix to be factorized.
! 69: *> On exit, the leading M-by-M upper triangular part of A
! 70: *> contains the upper triangular matrix R, and elements N-L+1 to
! 71: *> N of the first M rows of A, with the array TAU, represent the
! 72: *> orthogonal matrix Z as a product of M elementary reflectors.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] LDA
! 76: *> \verbatim
! 77: *> LDA is INTEGER
! 78: *> The leading dimension of the array A. LDA >= max(1,M).
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[out] TAU
! 82: *> \verbatim
! 83: *> TAU is DOUBLE PRECISION array, dimension (M)
! 84: *> The scalar factors of the elementary reflectors.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[out] WORK
! 88: *> \verbatim
! 89: *> WORK is DOUBLE PRECISION array, dimension (M)
! 90: *> \endverbatim
! 91: *
! 92: * Authors:
! 93: * ========
! 94: *
! 95: *> \author Univ. of Tennessee
! 96: *> \author Univ. of California Berkeley
! 97: *> \author Univ. of Colorado Denver
! 98: *> \author NAG Ltd.
! 99: *
! 100: *> \date November 2011
! 101: *
! 102: *> \ingroup doubleOTHERcomputational
! 103: *
! 104: *> \par Contributors:
! 105: * ==================
! 106: *>
! 107: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 108: *
! 109: *> \par Further Details:
! 110: * =====================
! 111: *>
! 112: *> \verbatim
! 113: *>
! 114: *> The factorization is obtained by Householder's method. The kth
! 115: *> transformation matrix, Z( k ), which is used to introduce zeros into
! 116: *> the ( m - k + 1 )th row of A, is given in the form
! 117: *>
! 118: *> Z( k ) = ( I 0 ),
! 119: *> ( 0 T( k ) )
! 120: *>
! 121: *> where
! 122: *>
! 123: *> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ),
! 124: *> ( 0 )
! 125: *> ( z( k ) )
! 126: *>
! 127: *> tau is a scalar and z( k ) is an l element vector. tau and z( k )
! 128: *> are chosen to annihilate the elements of the kth row of A2.
! 129: *>
! 130: *> The scalar tau is returned in the kth element of TAU and the vector
! 131: *> u( k ) in the kth row of A2, such that the elements of z( k ) are
! 132: *> in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
! 133: *> the upper triangular part of A1.
! 134: *>
! 135: *> Z is given by
! 136: *>
! 137: *> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
! 138: *> \endverbatim
! 139: *>
! 140: * =====================================================================
1.1 bertrand 141: SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
142: *
1.10 ! bertrand 143: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 144: * -- LAPACK is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 146: * November 2011
1.1 bertrand 147: *
148: * .. Scalar Arguments ..
149: INTEGER L, LDA, M, N
150: * ..
151: * .. Array Arguments ..
152: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
153: * ..
154: *
155: * =====================================================================
156: *
157: * .. Parameters ..
158: DOUBLE PRECISION ZERO
159: PARAMETER ( ZERO = 0.0D+0 )
160: * ..
161: * .. Local Scalars ..
162: INTEGER I
163: * ..
164: * .. External Subroutines ..
1.5 bertrand 165: EXTERNAL DLARFG, DLARZ
1.1 bertrand 166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input arguments
170: *
171: * Quick return if possible
172: *
173: IF( M.EQ.0 ) THEN
174: RETURN
175: ELSE IF( M.EQ.N ) THEN
176: DO 10 I = 1, N
177: TAU( I ) = ZERO
178: 10 CONTINUE
179: RETURN
180: END IF
181: *
182: DO 20 I = M, 1, -1
183: *
184: * Generate elementary reflector H(i) to annihilate
185: * [ A(i,i) A(i,n-l+1:n) ]
186: *
1.5 bertrand 187: CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) )
1.1 bertrand 188: *
189: * Apply H(i) to A(1:i-1,i:n) from the right
190: *
191: CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
192: $ TAU( I ), A( 1, I ), LDA, WORK )
193: *
194: 20 CONTINUE
195: *
196: RETURN
197: *
198: * End of DLATRZ
199: *
200: END
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