Annotation of rpl/lapack/lapack/zlatzm.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZLATZM
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLATZM + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatzm.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatzm.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatzm.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER SIDE
! 25: * INTEGER INCV, LDC, M, N
! 26: * COMPLEX*16 TAU
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> This routine is deprecated and has been replaced by routine ZUNMRZ.
! 39: *>
! 40: *> ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
! 41: *>
! 42: *> Let P = I - tau*u*u**H, u = ( 1 ),
! 43: *> ( v )
! 44: *> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
! 45: *> SIDE = 'R'.
! 46: *>
! 47: *> If SIDE equals 'L', let
! 48: *> C = [ C1 ] 1
! 49: *> [ C2 ] m-1
! 50: *> n
! 51: *> Then C is overwritten by P*C.
! 52: *>
! 53: *> If SIDE equals 'R', let
! 54: *> C = [ C1, C2 ] m
! 55: *> 1 n-1
! 56: *> Then C is overwritten by C*P.
! 57: *> \endverbatim
! 58: *
! 59: * Arguments:
! 60: * ==========
! 61: *
! 62: *> \param[in] SIDE
! 63: *> \verbatim
! 64: *> SIDE is CHARACTER*1
! 65: *> = 'L': form P * C
! 66: *> = 'R': form C * P
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] M
! 70: *> \verbatim
! 71: *> M is INTEGER
! 72: *> The number of rows of the matrix C.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] N
! 76: *> \verbatim
! 77: *> N is INTEGER
! 78: *> The number of columns of the matrix C.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] V
! 82: *> \verbatim
! 83: *> V is COMPLEX*16 array, dimension
! 84: *> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
! 85: *> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
! 86: *> The vector v in the representation of P. V is not used
! 87: *> if TAU = 0.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] INCV
! 91: *> \verbatim
! 92: *> INCV is INTEGER
! 93: *> The increment between elements of v. INCV <> 0
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] TAU
! 97: *> \verbatim
! 98: *> TAU is COMPLEX*16
! 99: *> The value tau in the representation of P.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in,out] C1
! 103: *> \verbatim
! 104: *> C1 is COMPLEX*16 array, dimension
! 105: *> (LDC,N) if SIDE = 'L'
! 106: *> (M,1) if SIDE = 'R'
! 107: *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
! 108: *> if SIDE = 'R'.
! 109: *>
! 110: *> On exit, the first row of P*C if SIDE = 'L', or the first
! 111: *> column of C*P if SIDE = 'R'.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in,out] C2
! 115: *> \verbatim
! 116: *> C2 is COMPLEX*16 array, dimension
! 117: *> (LDC, N) if SIDE = 'L'
! 118: *> (LDC, N-1) if SIDE = 'R'
! 119: *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
! 120: *> m x (n - 1) matrix C2 if SIDE = 'R'.
! 121: *>
! 122: *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
! 123: *> if SIDE = 'R'.
! 124: *> \endverbatim
! 125: *>
! 126: *> \param[in] LDC
! 127: *> \verbatim
! 128: *> LDC is INTEGER
! 129: *> The leading dimension of the arrays C1 and C2.
! 130: *> LDC >= max(1,M).
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[out] WORK
! 134: *> \verbatim
! 135: *> WORK is COMPLEX*16 array, dimension
! 136: *> (N) if SIDE = 'L'
! 137: *> (M) if SIDE = 'R'
! 138: *> \endverbatim
! 139: *
! 140: * Authors:
! 141: * ========
! 142: *
! 143: *> \author Univ. of Tennessee
! 144: *> \author Univ. of California Berkeley
! 145: *> \author Univ. of Colorado Denver
! 146: *> \author NAG Ltd.
! 147: *
! 148: *> \date November 2011
! 149: *
! 150: *> \ingroup complex16OTHERcomputational
! 151: *
! 152: * =====================================================================
1.1 bertrand 153: SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
154: *
1.9 ! bertrand 155: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 156: * -- LAPACK is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 158: * November 2011
1.1 bertrand 159: *
160: * .. Scalar Arguments ..
161: CHARACTER SIDE
162: INTEGER INCV, LDC, M, N
163: COMPLEX*16 TAU
164: * ..
165: * .. Array Arguments ..
166: COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
167: * ..
168: *
169: * =====================================================================
170: *
171: * .. Parameters ..
172: COMPLEX*16 ONE, ZERO
173: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
174: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
175: * ..
176: * .. External Subroutines ..
177: EXTERNAL ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
178: * ..
179: * .. External Functions ..
180: LOGICAL LSAME
181: EXTERNAL LSAME
182: * ..
183: * .. Intrinsic Functions ..
184: INTRINSIC MIN
185: * ..
186: * .. Executable Statements ..
187: *
188: IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
189: $ RETURN
190: *
191: IF( LSAME( SIDE, 'L' ) ) THEN
192: *
1.8 bertrand 193: * w := ( C1 + v**H * C2 )**H
1.1 bertrand 194: *
195: CALL ZCOPY( N, C1, LDC, WORK, 1 )
196: CALL ZLACGV( N, WORK, 1 )
197: CALL ZGEMV( 'Conjugate transpose', M-1, N, ONE, C2, LDC, V,
198: $ INCV, ONE, WORK, 1 )
199: *
1.8 bertrand 200: * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
1.1 bertrand 201: * [ C2 ] [ C2 ] [ v ]
202: *
203: CALL ZLACGV( N, WORK, 1 )
204: CALL ZAXPY( N, -TAU, WORK, 1, C1, LDC )
205: CALL ZGERU( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
206: *
207: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
208: *
209: * w := C1 + C2 * v
210: *
211: CALL ZCOPY( M, C1, 1, WORK, 1 )
212: CALL ZGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
213: $ WORK, 1 )
214: *
1.8 bertrand 215: * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
1.1 bertrand 216: *
217: CALL ZAXPY( M, -TAU, WORK, 1, C1, 1 )
218: CALL ZGERC( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
219: END IF
220: *
221: RETURN
222: *
223: * End of ZLATZM
224: *
225: END
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