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reflections.h
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1 /*************************************************************************
2 Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
3 
4 Contributors:
5  * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
6  pseudocode.
7 
8 See subroutines comments for additional copyrights.
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37 *************************************************************************/
38 
39 #ifndef _reflections_h
40 #define _reflections_h
41 
42 #include "ap.h"
43 #include "amp.h"
44 namespace reflections
45 {
46  template<unsigned int Precision>
48  int n,
50  template<unsigned int Precision>
54  int m1,
55  int m2,
56  int n1,
57  int n2,
59  template<unsigned int Precision>
63  int m1,
64  int m2,
65  int n1,
66  int n2,
68 
69 
70  /*************************************************************************
71  Generation of an elementary reflection transformation
72 
73  The subroutine generates elementary reflection H of order N, so that, for
74  a given X, the following equality holds true:
75 
76  ( X(1) ) ( Beta )
77  H * ( .. ) = ( 0 )
78  ( X(n) ) ( 0 )
79 
80  where
81  ( V(1) )
82  H = 1 - Tau * ( .. ) * ( V(1), ..., V(n) )
83  ( V(n) )
84 
85  where the first component of vector V equals 1.
86 
87  Input parameters:
88  X - vector. Array whose index ranges within [1..N].
89  N - reflection order.
90 
91  Output parameters:
92  X - components from 2 to N are replaced with vector V.
93  The first component is replaced with parameter Beta.
94  Tau - scalar value Tau. If X is a null vector, Tau equals 0,
95  otherwise 1 <= Tau <= 2.
96 
97  This subroutine is the modification of the DLARFG subroutines from
98  the LAPACK library. It has a similar functionality except for the
99  fact that it doesn’t handle errors when the intermediate results
100  cause an overflow.
101 
102 
103  MODIFICATIONS:
104  24.12.2005 sign(Alpha) was replaced with an analogous to the Fortran SIGN code.
105 
106  -- LAPACK auxiliary routine (version 3.0) --
107  Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
108  Courant Institute, Argonne National Lab, and Rice University
109  September 30, 1994
110  *************************************************************************/
111  template<unsigned int Precision>
113  int n,
115  {
116  int j;
118  amp::ampf<Precision> xnorm;
122 
123 
124 
125  //
126  // Executable Statements ..
127  //
128  if( n<=1 )
129  {
130  tau = 0;
131  return;
132  }
133 
134  //
135  // XNORM = DNRM2( N-1, X, INCX )
136  //
137  alpha = x(1);
138  mx = 0;
139  for(j=2; j<=n; j++)
140  {
141  mx = amp::maximum<Precision>(amp::abs<Precision>(x(j)), mx);
142  }
143  xnorm = 0;
144  if( mx!=0 )
145  {
146  for(j=2; j<=n; j++)
147  {
148  xnorm = xnorm+amp::sqr<Precision>(x(j)/mx);
149  }
150  xnorm = amp::sqrt<Precision>(xnorm)*mx;
151  }
152  if( xnorm==0 )
153  {
154 
155  //
156  // H = I
157  //
158  tau = 0;
159  return;
160  }
161 
162  //
163  // general case
164  //
165  mx = amp::maximum<Precision>(amp::abs<Precision>(alpha), amp::abs<Precision>(xnorm));
166  beta = -mx*amp::sqrt<Precision>(amp::sqr<Precision>(alpha/mx)+amp::sqr<Precision>(xnorm/mx));
167  if( alpha<0 )
168  {
169  beta = -beta;
170  }
171  tau = (beta-alpha)/beta;
172  v = 1/(alpha-beta);
173  ap::vmul(x.getvector(2, n), v);
174  x(1) = beta;
175  }
176 
177 
178  /*************************************************************************
179  Application of an elementary reflection to a rectangular matrix of size MxN
180 
181  The algorithm pre-multiplies the matrix by an elementary reflection transformation
182  which is given by column V and scalar Tau (see the description of the
183  GenerateReflection procedure). Not the whole matrix but only a part of it
184  is transformed (rows from M1 to M2, columns from N1 to N2). Only the elements
185  of this submatrix are changed.
186 
187  Input parameters:
188  C - matrix to be transformed.
189  Tau - scalar defining the transformation.
190  V - column defining the transformation.
191  Array whose index ranges within [1..M2-M1+1].
192  M1, M2 - range of rows to be transformed.
193  N1, N2 - range of columns to be transformed.
194  WORK - working array whose indexes goes from N1 to N2.
195 
196  Output parameters:
197  C - the result of multiplying the input matrix C by the
198  transformation matrix which is given by Tau and V.
199  If N1>N2 or M1>M2, C is not modified.
200 
201  -- LAPACK auxiliary routine (version 3.0) --
202  Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
203  Courant Institute, Argonne National Lab, and Rice University
204  September 30, 1994
205  *************************************************************************/
206  template<unsigned int Precision>
210  int m1,
211  int m2,
212  int n1,
213  int n2,
215  {
217  int i;
218  int vm;
219 
220 
221  if( tau==0 || n1>n2 || m1>m2 )
222  {
223  return;
224  }
225 
226  //
227  // w := C' * v
228  //
229  vm = m2-m1+1;
230  for(i=n1; i<=n2; i++)
231  {
232  work(i) = 0;
233  }
234  for(i=m1; i<=m2; i++)
235  {
236  t = v(i+1-m1);
237  ap::vadd(work.getvector(n1, n2), c.getrow(i, n1, n2), t);
238  }
239 
240  //
241  // C := C - tau * v * w'
242  //
243  for(i=m1; i<=m2; i++)
244  {
245  t = v(i-m1+1)*tau;
246  ap::vsub(c.getrow(i, n1, n2), work.getvector(n1, n2), t);
247  }
248  }
249 
250 
251  /*************************************************************************
252  Application of an elementary reflection to a rectangular matrix of size MxN
253 
254  The algorithm post-multiplies the matrix by an elementary reflection transformation
255  which is given by column V and scalar Tau (see the description of the
256  GenerateReflection procedure). Not the whole matrix but only a part of it
257  is transformed (rows from M1 to M2, columns from N1 to N2). Only the
258  elements of this submatrix are changed.
259 
260  Input parameters:
261  C - matrix to be transformed.
262  Tau - scalar defining the transformation.
263  V - column defining the transformation.
264  Array whose index ranges within [1..N2-N1+1].
265  M1, M2 - range of rows to be transformed.
266  N1, N2 - range of columns to be transformed.
267  WORK - working array whose indexes goes from M1 to M2.
268 
269  Output parameters:
270  C - the result of multiplying the input matrix C by the
271  transformation matrix which is given by Tau and V.
272  If N1>N2 or M1>M2, C is not modified.
273 
274  -- LAPACK auxiliary routine (version 3.0) --
275  Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
276  Courant Institute, Argonne National Lab, and Rice University
277  September 30, 1994
278  *************************************************************************/
279  template<unsigned int Precision>
283  int m1,
284  int m2,
285  int n1,
286  int n2,
288  {
290  int i;
291  int vm;
292 
293 
294  if( tau==0 || n1>n2 || m1>m2 )
295  {
296  return;
297  }
298 
299  //
300  // w := C * v
301  //
302  vm = n2-n1+1;
303  for(i=m1; i<=m2; i++)
304  {
305  t = ap::vdotproduct(c.getrow(i, n1, n2), v.getvector(1, vm));
306  work(i) = t;
307  }
308 
309  //
310  // C := C - w * v'
311  //
312  for(i=m1; i<=m2; i++)
313  {
314  t = work(i)*tau;
315  ap::vsub(c.getrow(i, n1, n2), v.getvector(1, vm), t);
316  }
317  }
318 } // namespace
319 
320 #endif
reflections
Definition: reflections.h:45
j
int j
Definition: facHensel.cc:105
x
Variable x
Definition: cfModGcd.cc:4023
ap::vadd
void vadd(raw_vector< T > vdst, const_raw_vector< T > vsrc)
Definition: ap.h:418
ap::template_1d_array
Definition: ap.h:662
ap::template_2d_array
Definition: ap.h:812
amp::ampf
Definition: amp.h:83
reflections::applyreflectionfromtheleft
void applyreflectionfromtheleft(ap::template_2d_array< amp::ampf< Precision > > &c, amp::ampf< Precision > tau, const ap::template_1d_array< amp::ampf< Precision > > &v, int m1, int m2, int n1, int n2, ap::template_1d_array< amp::ampf< Precision > > &work)
Definition: reflections.h:243
ap::vmul
void vmul(raw_vector< T > vdst, T2 alpha)
Definition: ap.h:608
reflections::generatereflection
void generatereflection(ap::template_1d_array< amp::ampf< Precision > > &x, int n, amp::ampf< Precision > &tau)
Definition: reflections.h:148
ap.h
i
int i
Definition: cfEzgcd.cc:125
alpha
Variable alpha
Definition: facAbsBiFact.cc:52
ap::vsub
void vsub(raw_vector< T > vdst, const_raw_vector< T > vsrc)
Definition: ap.h:538
beta
Variable beta
Definition: facAbsFact.cc:99
reflections::applyreflectionfromtheright
void applyreflectionfromtheright(ap::template_2d_array< amp::ampf< Precision > > &c, amp::ampf< Precision > tau, const ap::template_1d_array< amp::ampf< Precision > > &v, int m1, int m2, int n1, int n2, ap::template_1d_array< amp::ampf< Precision > > &work)
Definition: reflections.h:316
tau
void tau(int **points, int sizePoints, int k)
Definition: cfNewtonPolygon.cc:461
ap::vdotproduct
T vdotproduct(const_raw_vector< T > v1, const_raw_vector< T > v2)
Definition: ap.h:186
v
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
amp.h