SAGA API  v9.5
mat_regression_multiple.cpp
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1 
3 // //
4 // SAGA //
5 // //
6 // System for Automated Geoscientific Analyses //
7 // //
8 // Application Programming Interface //
9 // //
10 // Library: SAGA_API //
11 // //
12 //-------------------------------------------------------//
13 // //
14 // mat_regression_multiple.cpp //
15 // //
16 // Copyright (C) 2005 by Olaf Conrad //
17 // //
18 //-------------------------------------------------------//
19 // //
20 // This file is part of 'SAGA - System for Automated //
21 // Geoscientific Analyses'. //
22 // //
23 // This library is free software; you can redistribute //
24 // it and/or modify it under the terms of the GNU Lesser //
25 // General Public License as published by the Free //
26 // Software Foundation, either version 2.1 of the //
27 // License, or (at your option) any later version. //
28 // //
29 // This library is distributed in the hope that it will //
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32 // PARTICULAR PURPOSE. See the GNU Lesser General Public //
33 // License for more details. //
34 // //
35 // You should have received a copy of the GNU Lesser //
36 // General Public License along with this program; if //
37 // not, see <http://www.gnu.org/licenses/>. //
38 // //
39 //-------------------------------------------------------//
40 // //
41 // contact: Olaf Conrad //
42 // Institute of Geography //
43 // University of Goettingen //
44 // Goldschmidtstr. 5 //
45 // 37077 Goettingen //
46 // Germany //
47 // //
48 // e-mail: oconrad@saga-gis.org //
49 // //
51 
52 //---------------------------------------------------------
53 #include "mat_tools.h"
54 #include "table.h"
55 
56 
58 // //
59 // //
60 // //
62 
63 //---------------------------------------------------------
64 enum ESG_Multiple_Regression_Info_Model
65 {
66  MLR_MODEL_R2 = 0,
67  MLR_MODEL_R2_ADJ,
68  MLR_MODEL_SE,
69  MLR_MODEL_SSR,
70  MLR_MODEL_SSE,
71  MLR_MODEL_SST,
72  MLR_MODEL_MSR,
73  MLR_MODEL_MSE,
74  MLR_MODEL_F,
75  MLR_MODEL_SIG,
76  MLR_MODEL_NPREDICT,
77  MLR_MODEL_NSAMPLES,
78  MLR_MODEL_CV_MSE,
79  MLR_MODEL_CV_RMSE,
80  MLR_MODEL_CV_NRMSE,
81  MLR_MODEL_CV_R2,
82  MLR_MODEL_CV_NSAMPLES
83 };
84 
85 //---------------------------------------------------------
86 enum ESG_Multiple_Regression_Info_Steps
87 {
88  MLR_STEP_NR = 0,
89  MLR_STEP_R,
90  MLR_STEP_R2,
91  MLR_STEP_R2_ADJ,
92  MLR_STEP_SE,
93  MLR_STEP_SSR,
94  MLR_STEP_SSE,
95  MLR_STEP_MSR,
96  MLR_STEP_MSE,
97  MLR_STEP_DF,
98  MLR_STEP_F,
99  MLR_STEP_SIG,
100  MLR_STEP_VAR_F,
101  MLR_STEP_VAR_SIG,
102  MLR_STEP_DIR,
103  MLR_STEP_VAR
104 };
105 
106 
108 // //
109 // //
110 // //
112 
113 //---------------------------------------------------------
114 CSG_Regression_Multiple::CSG_Regression_Multiple(bool bIntercept)
115 {
116  m_pRegression = new CSG_Table;
117 
118  m_pRegression ->Add_Field("VAR_ID" , SG_DATATYPE_Int); // MLR_VAR_ID
119  m_pRegression ->Add_Field("VAR_NAME" , SG_DATATYPE_String); // MLR_VAR_NAME
120  m_pRegression ->Add_Field("REGCOEFF" , SG_DATATYPE_Double); // MLR_VAR_RCOEFF
121  m_pRegression ->Add_Field("R" , SG_DATATYPE_Double); // MLR_VAR_R
122  m_pRegression ->Add_Field("R2" , SG_DATATYPE_Double); // MLR_VAR_R2
123  m_pRegression ->Add_Field("R2_ADJ" , SG_DATATYPE_Double); // MLR_VAR_R2_ADJ
124  m_pRegression ->Add_Field("STD_ERROR" , SG_DATATYPE_Double); // MLR_VAR_SE
125  m_pRegression ->Add_Field("T" , SG_DATATYPE_Double); // MLR_VAR_T
126  m_pRegression ->Add_Field("SIG" , SG_DATATYPE_Double); // MLR_VAR_SIG
127  m_pRegression ->Add_Field("P" , SG_DATATYPE_Double); // MLR_VAR_P
128 
129  //-----------------------------------------------------
130  m_pSteps = new CSG_Table;
131 
132  m_pSteps ->Add_Field("MODEL" , SG_DATATYPE_Int); // MLR_STEP_NR
133  m_pSteps ->Add_Field("R" , SG_DATATYPE_Double); // MLR_STEP_R
134  m_pSteps ->Add_Field("R2" , SG_DATATYPE_Double); // MLR_STEP_R2
135  m_pSteps ->Add_Field("R2_ADJ" , SG_DATATYPE_Double); // MLR_STEP_R2_ADJ
136  m_pSteps ->Add_Field("STD_ERROR" , SG_DATATYPE_Double); // MLR_STEP_SE
137  m_pSteps ->Add_Field("SSR" , SG_DATATYPE_Double); // MLR_STEP_SSR
138  m_pSteps ->Add_Field("SSE" , SG_DATATYPE_Double); // MLR_STEP_SSE
139  m_pSteps ->Add_Field("MSR" , SG_DATATYPE_Double); // MLR_STEP_MSR
140  m_pSteps ->Add_Field("MSE" , SG_DATATYPE_Double); // MLR_STEP_MSE
141  m_pSteps ->Add_Field("DF" , SG_DATATYPE_Double); // MLR_STEP_DF
142  m_pSteps ->Add_Field("F" , SG_DATATYPE_Double); // MLR_STEP_F
143  m_pSteps ->Add_Field("SIG" , SG_DATATYPE_Double); // MLR_STEP_SIG
144  m_pSteps ->Add_Field("VAR_F" , SG_DATATYPE_Double); // MLR_STEP_VAR_F
145  m_pSteps ->Add_Field("VAR_SIG" , SG_DATATYPE_Double); // MLR_STEP_VAR_SIG
146  m_pSteps ->Add_Field("DIR" , SG_DATATYPE_String); // MLR_STEP_DIR
147  m_pSteps ->Add_Field("VARIABLE" , SG_DATATYPE_String); // MLR_STEP_VAR
148 
149  //-----------------------------------------------------
150  m_pModel = new CSG_Table;
151 
152  m_pModel ->Add_Field("PARAMETER" , SG_DATATYPE_String);
153  m_pModel ->Add_Field("VALUE" , SG_DATATYPE_Double);
154 
155  m_pModel ->Add_Record()->Set_Value(0, SG_T("R2" )); // MLR_MODEL_R2
156  m_pModel ->Add_Record()->Set_Value(0, SG_T("R2_ADJ" )); // MLR_MODEL_R2_ADJ
157  m_pModel ->Add_Record()->Set_Value(0, SG_T("STD_ERROR" )); // MLR_MODEL_SE
158  m_pModel ->Add_Record()->Set_Value(0, SG_T("SSR" )); // MLR_MODEL_SSR
159  m_pModel ->Add_Record()->Set_Value(0, SG_T("SSE" )); // MLR_MODEL_SSE
160  m_pModel ->Add_Record()->Set_Value(0, SG_T("SST" )); // MLR_MODEL_SST
161  m_pModel ->Add_Record()->Set_Value(0, SG_T("MSR" )); // MLR_MODEL_MSR
162  m_pModel ->Add_Record()->Set_Value(0, SG_T("MSE" )); // MLR_MODEL_MSE
163  m_pModel ->Add_Record()->Set_Value(0, SG_T("F" )); // MLR_MODEL_F
164  m_pModel ->Add_Record()->Set_Value(0, SG_T("SIG" )); // MLR_MODEL_SIG
165  m_pModel ->Add_Record()->Set_Value(0, SG_T("PREDICTORS" )); // MLR_MODEL_NPREDICT
166  m_pModel ->Add_Record()->Set_Value(0, SG_T("SAMPLES" )); // MLR_MODEL_NSAMPLES
167  m_pModel ->Add_Record()->Set_Value(0, SG_T("CV_MSE" )); // MLR_MODEL_CV_MSE
168  m_pModel ->Add_Record()->Set_Value(0, SG_T("CV_RMSE" )); // MLR_MODEL_CV_RMSE
169  m_pModel ->Add_Record()->Set_Value(0, SG_T("CV_NRMSE" )); // MLR_MODEL_CV_RMSE
170  m_pModel ->Add_Record()->Set_Value(0, SG_T("CV_R2" )); // MLR_MODEL_CV_R2
171  m_pModel ->Add_Record()->Set_Value(0, SG_T("CV_SAMPLES" )); // MLR_MODEL_CV_NSAMPLES
172 
173  //-----------------------------------------------------
174  m_Predictor = NULL;
175  m_nPredictors = 0;
176 
177  m_bIntercept = bIntercept;
178 }
179 
180 //---------------------------------------------------------
181 CSG_Regression_Multiple::~CSG_Regression_Multiple(void)
182 {
183  Destroy();
184 
185  delete(m_pRegression);
186  delete(m_pModel);
187  delete(m_pSteps);
188 }
189 
190 
192 // //
194 
195 //---------------------------------------------------------
196 void CSG_Regression_Multiple::Destroy(void)
197 {
198  m_Names .Clear ();
199  m_Samples .Destroy();
200  m_Samples_Model.Destroy();
201 
202  m_pRegression->Del_Records();
203  m_pSteps ->Del_Records();
204 
205  for(int i=0; i<m_pModel->Get_Count(); i++)
206  {
207  m_pModel->Get_Record(i)->Set_NoData(1);
208  }
209 
210  if( m_Predictor )
211  {
212  delete[](m_bIncluded);
213  delete[](m_Predictor);
214 
215  m_Predictor = NULL;
216  m_nPredictors = 0;
217  }
218 }
219 
220 
222 // //
224 
225 //---------------------------------------------------------
226 bool CSG_Regression_Multiple::Set_Data(const CSG_Matrix &Samples, CSG_Strings *pNames)
227 {
228  Destroy();
229 
230  int nPredictors = Samples.Get_NX() - 1;
231 
232  if( nPredictors < 1 || Samples.Get_NY() <= nPredictors )
233  {
234  return( false );
235  }
236 
237  //-------------------------------------------------
238  for(int i=0; i<=nPredictors; i++)
239  {
240  m_Names += pNames && pNames->Get_Count() == Samples.Get_NCols() ? pNames->Get_String(i) : i == 0
241  ? CSG_String::Format( "%s", _TL("Dependent"))
242  : CSG_String::Format("%d. %s", i + 1, _TL("Predictor"));
243  }
244 
245  m_Samples = Samples;
246 
247  m_bIncluded = new int[nPredictors];
248  m_Predictor = new int[nPredictors];
249 
250  //-------------------------------------------------
251  return( true );
252 }
253 
254 //---------------------------------------------------------
255 bool CSG_Regression_Multiple::_Initialize(bool bInclude)
256 {
257  int nPredictors = m_Samples.Get_NX() - 1;
258 
259  if( nPredictors < 1 || m_Samples.Get_NY() <= nPredictors )
260  {
261  return( false );
262  }
263 
264  //-------------------------------------------------
265  if( bInclude )
266  {
267  m_nPredictors = nPredictors;
268  m_Samples_Model.Create(m_Samples);
269  }
270  else
271  {
272  m_nPredictors = 0;
273  m_Samples_Model.Set_Col(m_Samples.Get_Col(0));
274  }
275 
276  for(int i=0; i<nPredictors; i++)
277  {
278  m_Predictor[i] = i;
279  m_bIncluded[i] = bInclude;
280  }
281 
282  for(int i=0; i<m_pModel->Get_Count(); i++)
283  {
284  m_pModel->Get_Record(i)->Set_NoData(1);
285  }
286 
287  //-------------------------------------------------
288  return( true );
289 }
290 
291 
293 // //
295 
296 //---------------------------------------------------------
297 bool CSG_Regression_Multiple::Get_Model(const CSG_Matrix &Samples, CSG_Strings *pNames)
298 {
299  return( Set_Data(Samples, pNames) && Get_Model() );
300 }
301 
302 bool CSG_Regression_Multiple::Get_Model_Forward(const CSG_Matrix &Samples, double P_in, CSG_Strings *pNames)
303 {
304  return( Set_Data(Samples, pNames) && Get_Model_Forward(P_in) );
305 }
306 
307 bool CSG_Regression_Multiple::Get_Model_Backward(const CSG_Matrix &Samples, double P_out, CSG_Strings *pNames)
308 {
309  return( Set_Data(Samples, pNames) && Get_Model_Backward(P_out) );
310 }
311 
312 bool CSG_Regression_Multiple::Get_Model_Stepwise(const CSG_Matrix &Samples, double P_in, double P_out, CSG_Strings *pNames)
313 {
314  return( Set_Data(Samples, pNames) && Get_Model_Stepwise(P_in, P_out) );
315 }
316 
317 //---------------------------------------------------------
318 bool CSG_Regression_Multiple::Get_Model(void)
319 {
320  return( _Initialize(true) && _Get_Regression(m_Samples) );
321 }
322 
323 //---------------------------------------------------------
324 bool CSG_Regression_Multiple::Get_Model_Forward(double P_in)
325 {
326  if( _Initialize(false) )
327  {
328  double R2 = 0.;
329 
330  while( _Get_Step_In(m_Samples_Model, P_in, R2, m_Samples) >= 0 );
331 
332  return( _Set_Step_Info(m_Samples_Model) );
333  }
334 
335  return( false );
336 }
337 
338 //---------------------------------------------------------
339 bool CSG_Regression_Multiple::Get_Model_Backward(double P_out)
340 {
341  if( _Initialize(true) )
342  {
343  double R2 = 0.;
344 
345  while( _Get_Step_Out(m_Samples_Model, P_out, R2) >= 0 );
346 
347  return( _Set_Step_Info(m_Samples_Model) );
348  }
349 
350  return( false );
351 }
352 
353 //---------------------------------------------------------
354 bool CSG_Regression_Multiple::Get_Model_Stepwise(double P_in, double P_out)
355 {
356  if( _Initialize(false) )
357  {
358  double R2 = 0.;
359 
360  if( P_out <= P_in )
361  {
362  P_out = P_in + 0.001;
363  }
364 
365  while( _Get_Step_In(m_Samples_Model, P_in, R2, m_Samples) >= 0 && SG_UI_Process_Get_Okay() )
366  {
367  if( m_nPredictors > 1 )
368  {
369  _Get_Step_Out(m_Samples_Model, P_out, R2);
370  }
371  }
372 
373  return( _Set_Step_Info(m_Samples_Model) );
374  }
375 
376  return( false );
377 }
378 
379 
381 // //
383 
384 //---------------------------------------------------------
385 bool CSG_Regression_Multiple::Get_CrossValidation(int nSubSamples)
386 {
387  if( m_Samples_Model.Get_NCols() <= 1 )
388  {
389  return( false );
390  }
391 
392  //-----------------------------------------------------
393  CSG_Regression_Multiple Model(m_bIntercept);
394  CSG_Simple_Statistics Stats, SR, SE;
395 
396  int i, nModels = 0;
397 
398  for(i=0; i<m_Samples_Model.Get_NRows(); i++)
399  {
400  Stats += m_Samples_Model[i][0];
401  }
402 
403  //-----------------------------------------------------
404  // leave-one-out cross validation (LOOCV)
405  if( nSubSamples <= 1 || nSubSamples > m_Samples_Model.Get_NRows() / 2 )
406  {
407  for(i=0; i<m_Samples_Model.Get_NRows() && SG_UI_Process_Get_Okay(); i++)
408  {
409  CSG_Matrix Samples(m_Samples_Model);
410  Samples.Del_Row(i);
411 
412  if( Model.Get_Model(Samples) )
413  {
414  nModels++;
415 
416  double dObsrv = m_Samples_Model[i][0];
417  double dModel = Model.Get_Value(CSG_Vector(m_nPredictors, m_Samples_Model[i] + 1));
418 
419  SE += SG_Get_Square(dModel - dObsrv);
420  SR += SG_Get_Square(dModel - (Stats.Get_Sum() - dObsrv) / Samples.Get_NRows());
421  }
422  }
423  }
424 
425  //-----------------------------------------------------
426  // k-fold cross validation
427  else
428  {
429  int *SubSet = new int[m_Samples_Model.Get_NRows()];
430 
431  for(i=0; i<m_Samples_Model.Get_NRows(); i++)
432  {
433  SubSet[i] = i % nSubSamples;
434  }
435 
436  //-------------------------------------------------
437  for(int iSubSet=0; iSubSet<nSubSamples && SG_UI_Process_Get_Okay(); iSubSet++)
438  {
439  CSG_Simple_Statistics Samples_Stats;
440  CSG_Matrix Samples(m_Samples_Model), Validation;
441 
442  for(i=Samples.Get_NY()-1; i>=0; i--)
443  {
444  if( SubSet[i] == iSubSet )
445  {
446  Validation.Add_Row(Samples.Get_Row(i));
447  Samples .Del_Row(i);
448  }
449  else
450  {
451  Samples_Stats += Samples[i][0];
452  }
453  }
454 
455  //---------------------------------------------
456  if( Model.Get_Model(Samples) )
457  {
458  nModels++;
459 
460  for(i=0; i<Validation.Get_NRows(); i++)
461  {
462  double dObsrv = Validation[i][0];
463  double dModel = Model.Get_Value(CSG_Vector(m_nPredictors, Validation[i] + 1));
464 
465  SE += SG_Get_Square(dModel - dObsrv);
466  SR += SG_Get_Square(dModel - Samples_Stats.Get_Mean());
467  }
468  }
469  }
470 
471  delete[](SubSet);
472  }
473 
474  //-----------------------------------------------------
475  m_pModel->Get_Record(MLR_MODEL_CV_MSE )->Set_Value(1, SE.Get_Mean());
476  m_pModel->Get_Record(MLR_MODEL_CV_RMSE )->Set_Value(1, sqrt(SE.Get_Mean()));
477  m_pModel->Get_Record(MLR_MODEL_CV_NRMSE )->Set_Value(1, sqrt(SE.Get_Mean()) / Stats.Get_Range());
478  m_pModel->Get_Record(MLR_MODEL_CV_R2 )->Set_Value(1, SR.Get_Sum() / (SR.Get_Sum() + SE.Get_Sum()));
479  m_pModel->Get_Record(MLR_MODEL_CV_NSAMPLES)->Set_Value(1, nModels);
480 
481  //-----------------------------------------------------
482  return( true );
483 }
484 
485 
487 // //
488 // //
489 // //
491 
492 //---------------------------------------------------------
493 double CSG_Regression_Multiple::Get_Value(const CSG_Vector &Predictors) const
494 {
495  double Value; Get_Value(Predictors, Value); return( Value );
496 }
497 
498 bool CSG_Regression_Multiple::Get_Value(const CSG_Vector &Predictors, double &Value) const
499 {
500  if( m_nPredictors == Predictors.Get_N() )
501  {
502  Value = Get_RConst();
503 
504  for(int i=0; i<m_nPredictors; i++)
505  {
506  Value += Get_RCoeff(i) * Predictors(i);
507  }
508 
509  return( true );
510  }
511 
512  Value = 0.;
513 
514  return( false );
515 }
516 
517 //---------------------------------------------------------
518 double CSG_Regression_Multiple::Get_Residual(int iSample) const
519 {
520  double Value; Get_Residual(iSample, Value); return( Value );
521 }
522 
523 bool CSG_Regression_Multiple::Get_Residual(int iSample, double &Residual) const
524 {
525  if( iSample >= 0 && iSample < m_Samples_Model.Get_NRows() )
526  {
527  Residual = Get_RConst();
528 
529  for(int i=0; i<m_nPredictors; i++)
530  {
531  Residual += Get_RCoeff(i) * m_Samples_Model[iSample][1 + i];
532  }
533 
534  Residual -= m_Samples_Model[iSample][0];
535 
536  return( true );
537  }
538 
539  Residual = 0.;
540 
541  return( false );
542 }
543 
544 //---------------------------------------------------------
545 bool CSG_Regression_Multiple::Get_Residuals(CSG_Vector &Residuals) const
546 {
547  Residuals.Create(m_Samples_Model.Get_NRows());
548 
549  for(int i=0; i<Residuals.Get_N(); i++)
550  {
551  Get_Residual(i, Residuals[i]);
552  }
553 
554  return( Residuals.Get_N() > 0 );
555 }
556 
557 
559 // //
561 
562 //---------------------------------------------------------
563 inline double CSG_Regression_Multiple::_Get_F(int nPredictors, int nSamples, double r2_full, double r2_reduced)
564 {
565  return( (nSamples - nPredictors - 1) * (r2_full - r2_reduced) / (1. - r2_full) );
566 }
567 
568 //---------------------------------------------------------
569 inline double CSG_Regression_Multiple::_Get_P(int nPredictors, int nSamples, double r2_full, double r2_reduced)
570 {
571  double f = _Get_F(nPredictors, nSamples, r2_full, r2_reduced);
572 
573  return( CSG_Test_Distribution::Get_F_Tail(f, nPredictors, nSamples - nPredictors - 1, TESTDIST_TYPE_Right) );
574 }
575 
576 
578 // //
580 
581 //---------------------------------------------------------
582 bool CSG_Regression_Multiple::_Get_Regression(const CSG_Matrix &Samples)
583 {
584  int nPredictors = Samples.Get_NX() - 1;
585  int nSamples = Samples.Get_NY();
586 
587  //-----------------------------------------------------
588  int i, j;
589  double Ym, SSR, SSE, SST, MSR, MSE, SE, R2, F;
590  CSG_Vector Y, Yr, B;
591  CSG_Matrix X, Xt, C;
592 
593  Y.Create(nSamples);
594  X.Create(nPredictors + (m_bIntercept ? 1 : 0), nSamples);
595 
596  //-----------------------------------------------------
597  for(i=0, Ym=0.; i<nSamples; i++)
598  {
599  Ym += Y[i] = Samples[i][0];
600 
601  if( m_bIntercept )
602  {
603  X [i][0] = 1.;
604 
605  for(j=1; j<=nPredictors; j++)
606  {
607  X[i][j] = Samples[i][j];
608  }
609  }
610  else
611  {
612  for(j=0; j<nPredictors; j++)
613  {
614  X[i][j] = Samples[i][j + 1];
615  }
616  }
617  }
618 
619  Ym /= nSamples;
620 
621  //-----------------------------------------------------
622  Xt = X.Get_Transpose();
623 
624  C = (Xt * X).Get_Inverse();
625 
626  B = C * (Xt * Y);
627 
628  //-----------------------------------------------------
629  Yr = X * B;
630 
631  for(i=0, SSE=0., SSR=0., SST=0.; i<nSamples; i++)
632  {
633  SSE += SG_Get_Square(Yr[i] - Y[i]);
634  SSR += SG_Get_Square(Yr[i] - Ym);
635  // SST += SG_Get_Square(Y [i] - Ym);
636  }
637 
638 // SSE = SST - SSR;
639  SST = SSR + SSE;
640  MSR = SSR / nPredictors;
641  MSE = SSE / (nSamples - nPredictors - 1);
642  SE = sqrt(SSE / (nSamples - nPredictors));
643  R2 = SSR / SST;
644  F = MSR / MSE; // = (nSamples - nPredictors - 1) * (R2 / nPredictors) / (1. - R2);
645 
646  //-----------------------------------------------------
647  m_pModel->Get_Record(MLR_MODEL_R2 )->Set_Value(1, R2);
648  m_pModel->Get_Record(MLR_MODEL_R2_ADJ )->Set_Value(1, SG_Regression_Get_Adjusted_R2(R2, nSamples, nPredictors));
649  m_pModel->Get_Record(MLR_MODEL_SE )->Set_Value(1, SE);
650  m_pModel->Get_Record(MLR_MODEL_SSR )->Set_Value(1, SSR);
651  m_pModel->Get_Record(MLR_MODEL_SSE )->Set_Value(1, SSE);
652  m_pModel->Get_Record(MLR_MODEL_SST )->Set_Value(1, SST);
653  m_pModel->Get_Record(MLR_MODEL_MSR )->Set_Value(1, MSR);
654  m_pModel->Get_Record(MLR_MODEL_MSE )->Set_Value(1, MSE);
655  m_pModel->Get_Record(MLR_MODEL_F )->Set_Value(1, F);
656  m_pModel->Get_Record(MLR_MODEL_SIG )->Set_Value(1, CSG_Test_Distribution::Get_F_Tail_from_R2(R2, nPredictors, nSamples));
657  m_pModel->Get_Record(MLR_MODEL_NPREDICT)->Set_Value(1, nPredictors);
658  m_pModel->Get_Record(MLR_MODEL_NSAMPLES)->Set_Value(1, nSamples);
659 
660  //-----------------------------------------------------
661  CSG_Matrix P = SG_Get_Correlation_Matrix(Samples, true).Get_Inverse(); // get partial correlation
662 
663  if( !m_bIntercept )
664  {
665  m_pRegression->Add_Record()->Set_Value(MLR_VAR_NAME, m_Names[0]);
666  }
667 
668  for(j=0; j<B.Get_N(); j++)
669  {
670  double se = SE * sqrt(fabs(C[j][j]));
671  double b = B[j];
672  double t = b / se;
673  int k = (m_bIntercept ? j : j + 1);
674  double r = -P[k][0] / sqrt(P[k][k] * P[0][0]);
675 
676  CSG_Table_Record *pRecord = m_pRegression->Add_Record();
677 
678  pRecord->Set_Value(MLR_VAR_ID , m_bIntercept ? j - 1 : j);
679  pRecord->Set_Value(MLR_VAR_NAME , m_Names[k]);
680  pRecord->Set_Value(MLR_VAR_RCOEFF , b);
681  pRecord->Set_Value(MLR_VAR_R , r);
682  pRecord->Set_Value(MLR_VAR_R2 , r*r);
683  pRecord->Set_Value(MLR_VAR_R2_ADJ , SG_Regression_Get_Adjusted_R2(r*r, nSamples, nPredictors));
684  pRecord->Set_Value(MLR_VAR_SE , se);
685  pRecord->Set_Value(MLR_VAR_T , t);
686  pRecord->Set_Value(MLR_VAR_SIG , CSG_Test_Distribution::Get_T_Tail(t, nSamples - nPredictors, TESTDIST_TYPE_TwoTail));
687  }
688 
689  //-----------------------------------------------------
690  return( true );
691 }
692 
693 
695 // //
696 // //
697 // //
699 
700 //---------------------------------------------------------
701 int CSG_Regression_Multiple::_Get_Step_In(CSG_Matrix &X, double P_in, double &R2, const CSG_Matrix &Samples)
702 {
703  int iBest, iPredictor; double rBest;
704 
705  CSG_Regression_Multiple R(m_bIntercept);
706 
707  X.Add_Cols(1);
708 
709  //-----------------------------------------------------
710  for(iPredictor=0, iBest=-1, rBest=0.; iPredictor<Samples.Get_NX()-1; iPredictor++)
711  {
712  if( !m_bIncluded[iPredictor] )
713  {
714  X.Set_Col(1 + m_nPredictors, Samples.Get_Col(1 + iPredictor));
715 
716  if( R.Get_Model(X) && (iBest < 0 || rBest < R.Get_R2()) )
717  {
718  iBest = iPredictor;
719  rBest = R.Get_R2();
720  }
721  }
722  }
723 
724  //-----------------------------------------------------
725  if( iBest >= 0 && _Get_P(1, Samples.Get_NY() - m_nPredictors, rBest, R2) <= P_in )
726  {
727  m_bIncluded[iBest] = true;
728  m_Predictor[m_nPredictors] = iBest;
729 
730  m_nPredictors++;
731 
732  X.Set_Col(m_nPredictors, Samples.Get_Col(1 + iBest));
733  _Set_Step_Info(X, R2, iBest, true);
734  R2 = rBest;
735 
736  return( iBest );
737  }
738 
739  X.Del_Col(X.Get_NX() - 1);
740 
741  return( -1 );
742 }
743 
744 //---------------------------------------------------------
745 int CSG_Regression_Multiple::_Get_Step_Out(CSG_Matrix &X, double P_out, double &R2)
746 {
747  int iBest, iPredictor; double rBest;
748 
749  CSG_Regression_Multiple R(m_bIntercept);
750 
751  if( R2 <= 0. )
752  {
753  R.Get_Model(X);
754 
755  R2 = R.Get_R2();
756  }
757 
758  //-----------------------------------------------------
759  for(iPredictor=0, iBest=-1, rBest=0.; iPredictor<m_nPredictors; iPredictor++)
760  {
761  CSG_Matrix X_reduced(X);
762 
763  X_reduced.Del_Col(1 + iPredictor);
764 
765  if( R.Get_Model(X_reduced) && (iBest < 0 || rBest < R.Get_R2()) )
766  {
767  iBest = iPredictor;
768  rBest = R.Get_R2();
769  }
770  }
771 
772  //-----------------------------------------------------
773  if( iBest >= 0 && _Get_P(1, X.Get_NY() - (m_nPredictors - 1), R2, rBest) > P_out )
774  {
775  m_nPredictors--;
776 
777  X.Del_Col(1 + iBest);
778  _Set_Step_Info(X, R2, m_Predictor[iBest], false);
779  R2 = rBest;
780 
781  m_bIncluded[m_Predictor[iBest]] = false;
782 
783  for(iPredictor=iBest; iPredictor<m_nPredictors; iPredictor++)
784  {
785  m_Predictor[iPredictor] = m_Predictor[iPredictor + 1];
786  }
787 
788  return( iBest );
789  }
790 
791  return( -1 );
792 }
793 
794 
796 // //
797 // //
798 // //
800 
801 //---------------------------------------------------------
802 bool CSG_Regression_Multiple::_Set_Step_Info(const CSG_Matrix &X)
803 {
804  CSG_Regression_Multiple R(m_bIntercept);
805 
806  if( m_nPredictors > 0 && R.Get_Model(X) )
807  {
808  m_pModel ->Assign(R.m_pModel);
809  m_pRegression ->Assign(R.m_pRegression);
810 
811  m_pRegression->Get_Record(0)->Set_Value(MLR_VAR_NAME, m_Names[0]);
812 
813  for(int i=0; i<m_nPredictors; i++)
814  {
815  CSG_Table_Record *pRecord = m_pRegression->Get_Record(1 + i);
816 
817  pRecord->Set_Value(MLR_VAR_ID , m_Predictor[i]);
818  pRecord->Set_Value(MLR_VAR_NAME, m_Names[1 + m_Predictor[i]]);
819  }
820 
821  return( true );
822  }
823 
824  return( false );
825 }
826 
827 //---------------------------------------------------------
828 bool CSG_Regression_Multiple::_Set_Step_Info(const CSG_Matrix &X, double R2_prev, int iVariable, bool bIn)
829 {
830  CSG_Regression_Multiple R(m_bIntercept);
831 
832  R.Get_Model(X);
833 
834  CSG_Table_Record *pRecord = m_pSteps->Add_Record();
835 
836  pRecord->Set_Value(MLR_STEP_NR , (int)m_pSteps->Get_Count());
837  pRecord->Set_Value(MLR_STEP_R , sqrt(R.Get_R2()));
838  pRecord->Set_Value(MLR_STEP_R2 , R.Get_R2());
839  pRecord->Set_Value(MLR_STEP_R2_ADJ , R.Get_R2_Adj());
840  pRecord->Set_Value(MLR_STEP_SE , R.Get_StdError());
841  pRecord->Set_Value(MLR_STEP_SSR , R.m_pModel->Get_Record(MLR_MODEL_SSR)->asDouble(1));
842  pRecord->Set_Value(MLR_STEP_SSE , R.m_pModel->Get_Record(MLR_MODEL_SSE)->asDouble(1));
843  pRecord->Set_Value(MLR_STEP_MSR , R.m_pModel->Get_Record(MLR_MODEL_MSR)->asDouble(1));
844  pRecord->Set_Value(MLR_STEP_MSE , R.m_pModel->Get_Record(MLR_MODEL_MSE)->asDouble(1));
845  pRecord->Set_Value(MLR_STEP_DF , X.Get_NRows() - m_nPredictors - 1);
846  pRecord->Set_Value(MLR_STEP_F , R.m_pModel->Get_Record(MLR_MODEL_F )->asDouble(1));
847  pRecord->Set_Value(MLR_STEP_SIG , R.m_pModel->Get_Record(MLR_MODEL_SIG)->asDouble(1));
848  pRecord->Set_Value(MLR_STEP_VAR_F , _Get_F(1, X.Get_NY() - (m_nPredictors - 1), bIn ? R.Get_R2() : R2_prev, bIn ? R2_prev : R.Get_R2()));
849  pRecord->Set_Value(MLR_STEP_VAR_SIG , _Get_P(1, X.Get_NY() - (m_nPredictors - 1), bIn ? R.Get_R2() : R2_prev, bIn ? R2_prev : R.Get_R2()));
850  pRecord->Set_Value(MLR_STEP_DIR , bIn ? SG_T(">>") : SG_T("<<"));
851  pRecord->Set_Value(MLR_STEP_VAR , m_Names[1 + iVariable]);
852 
853  return( true );
854 }
855 
856 
858 // //
859 // //
860 // //
862 
863 //---------------------------------------------------------
864 double CSG_Regression_Multiple::Get_R2 (void) const { return( m_pModel->Get_Record(MLR_MODEL_R2 )->asDouble(1) ); }
865 double CSG_Regression_Multiple::Get_R2_Adj (void) const { return( m_pModel->Get_Record(MLR_MODEL_R2_ADJ )->asDouble(1) ); }
866 double CSG_Regression_Multiple::Get_StdError (void) const { return( m_pModel->Get_Record(MLR_MODEL_SE )->asDouble(1) ); }
867 double CSG_Regression_Multiple::Get_F (void) const { return( m_pModel->Get_Record(MLR_MODEL_F )->asDouble(1) ); }
868 double CSG_Regression_Multiple::Get_P (void) const { return( m_pModel->Get_Record(MLR_MODEL_SIG )->asDouble(1) ); }
869 double CSG_Regression_Multiple::Get_CV_RMSE (void) const { return( m_pModel->Get_Record(MLR_MODEL_CV_RMSE )->asDouble(1) ); }
870 double CSG_Regression_Multiple::Get_CV_NRMSE (void) const { return( m_pModel->Get_Record(MLR_MODEL_CV_NRMSE )->asDouble(1) ); }
871 double CSG_Regression_Multiple::Get_CV_R2 (void) const { return( m_pModel->Get_Record(MLR_MODEL_CV_R2 )->asDouble(1) ); }
872 int CSG_Regression_Multiple::Get_CV_nSamples (void) const { return( m_pModel->Get_Record(MLR_MODEL_CV_NSAMPLES)->asInt (1) ); }
873 int CSG_Regression_Multiple::Get_nPredictors (void) const { return( m_pModel->Get_Record(MLR_MODEL_NPREDICT )->asInt (1) ); }
874 int CSG_Regression_Multiple::Get_nSamples (void) const { return( m_pModel->Get_Record(MLR_MODEL_NSAMPLES )->asInt (1) ); }
875 int CSG_Regression_Multiple::Get_DegFreedom (void) const { return( Get_nSamples() - Get_nPredictors() - 1 ); }
876 
877 //---------------------------------------------------------
878 const SG_Char * CSG_Regression_Multiple::Get_Name(int iVariable) const
879 {
880  if( iVariable >= 0 && iVariable < m_pRegression->Get_Count() - 1 )
881  {
882  return( m_pRegression->Get_Record(1 + iVariable)->asString(MLR_VAR_NAME) );
883  }
884 
885  return( SG_T("") );
886 }
887 
888 //---------------------------------------------------------
889 double CSG_Regression_Multiple::Get_RConst(void) const
890 {
891  if( m_pRegression->Get_Count() > 0 )
892  {
893  return( m_pRegression->Get_Record(0)->asDouble(MLR_VAR_RCOEFF) );
894  }
895 
896  return( 0. );
897 }
898 
899 //---------------------------------------------------------
900 double CSG_Regression_Multiple::Get_Parameter(int iVariable, int Parameter) const
901 {
902  if( iVariable >= 0 && iVariable < m_pRegression->Get_Count() - 1 && Parameter >= 0 && Parameter <= MLR_VAR_P )
903  {
904  return( m_pRegression->Get_Record(1 + iVariable)->asDouble(Parameter) );
905  }
906 
907  return( 0. );
908 }
909 
910 
912 // //
914 
915 //---------------------------------------------------------
916 CSG_String CSG_Regression_Multiple::Get_Info(void) const
917 {
918  CSG_String s;
919 
920  if( Get_nPredictors() < 1 )
921  {
922  return( s );
923  }
924 
925  //-----------------------------------------------------
926  if( m_pSteps->Get_Count() > 0 )
927  {
928  s += CSG_String::Format("\n%s:\n\n", _TL("Steps"));
929  s += CSG_String::Format("No. \tR \tR2 \tR2 adj\tStdErr\tF \tP \tF step\tP step\tVariable\n");
930  s += CSG_String::Format("------\t------\t------\t------\t------\t------\t------\t------\t------\t------\n");
931 
932  for(int i=0; i<m_pSteps->Get_Count(); i++)
933  {
934  CSG_Table_Record *pRecord = m_pSteps->Get_Record(i);
935 
936  s += CSG_String::Format("%d.\t%.2f\t%.2f\t%.2f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%s %s\n",
937  pRecord->asInt (MLR_STEP_NR ),
938  pRecord->asDouble(MLR_STEP_R ),
939  pRecord->asDouble(MLR_STEP_R2 ) * 100.,
940  pRecord->asDouble(MLR_STEP_R2_ADJ ) * 100.,
941  pRecord->asDouble(MLR_STEP_SE ),
942  pRecord->asDouble(MLR_STEP_F ),
943  pRecord->asDouble(MLR_STEP_SIG ) * 100.,
944  pRecord->asDouble(MLR_STEP_VAR_F ),
945  pRecord->asDouble(MLR_STEP_VAR_SIG) * 100.,
946  pRecord->asString(MLR_STEP_DIR ),
947  pRecord->asString(MLR_STEP_VAR )
948  );
949  }
950  }
951 
952  //-----------------------------------------------------
953  s += CSG_String::Format("\n%s:\n\n", _TL("Correlation"));
954  s += CSG_String::Format("No. \tR \tR2 \tR2 adj\tStdErr\tt \tSig. \tb \t\tVariable\n");
955  s += CSG_String::Format("------\t------\t------\t------\t------\t------\t---------\t---------\t\t---------\n");
956 
957  for(int i=0; i<m_pRegression->Get_Count(); i++)
958  {
959  CSG_Table_Record *pRecord = m_pRegression->Get_Record(i);
960 
961  s += CSG_String::Format("%d.\t%.2f\t%.2f\t%.2f\t%.3f\t%.3f\t%.6f\t%.6f\t%s\n",
962  i,
963  pRecord->asDouble(MLR_VAR_R ),
964  pRecord->asDouble(MLR_VAR_R2 ) * 100.,
965  pRecord->asDouble(MLR_VAR_R2_ADJ) * 100.,
966  pRecord->asDouble(MLR_VAR_SE ),
967  pRecord->asDouble(MLR_VAR_T ),
968  pRecord->asDouble(MLR_VAR_SIG ) * 100.,
969  pRecord->asDouble(MLR_VAR_RCOEFF),
970  pRecord->asString(MLR_VAR_NAME )
971  );
972  }
973 
974  //-----------------------------------------------------
975  s += CSG_String::Format("\n%s: %g", _TL("Formula"), Get_RConst());
976 
977  for(int i=0; i<Get_nPredictors(); i++)
978  {
979  double b = Get_RCoeff(i);
980 
981  s += CSG_String::Format(" %c %g * X%d", b < 0. ? '-' : '+', fabs(b), i + 1);
982  }
983 
984  //-----------------------------------------------------
985  s += "\n\n";
986 
987  s += CSG_String::Format("%s: %f (%s: %d)\n", _TL("Residual standard error"), Get_StdError(), _TL("degrees of freedom"), Get_DegFreedom());
988  s += CSG_String::Format("%s: %f (%s: %f)\n", _TL("Multiple R-squared"), 100. * Get_R2(), _TL("adjusted"), 100. * Get_R2_Adj());
989  s += CSG_String::Format("%s: %f (%d/%d DF), %s: %g\n", _TL("F-statistic"), Get_F(), Get_nPredictors(), Get_DegFreedom(), _TL("p-value"), Get_P());
990 
991  //-----------------------------------------------------
992  return( s );
993 }
994 
995 
997 // //
998 // //
999 // //
1001 
1002 //---------------------------------------------------------
CSG_Regression_Multiple::Destroy
void Destroy(void)
Definition: mat_regression_multiple.cpp:196
MLR_STEP_NR
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Definition: mat_regression_multiple.cpp:88
MLR_STEP_R2
@ MLR_STEP_R2
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MLR_MODEL_SIG
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SG_T
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SG_DATATYPE_String
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_TL
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C
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const SG_Char * Get_Name(int iVariable) const
Definition: mat_regression_multiple.cpp:878
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bool Create(const CSG_Vector &Vector)
Definition: mat_matrix.cpp:87
MLR_VAR_NAME
@ MLR_VAR_NAME
Definition: mat_tools.h:1680
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Definition: mat_tools.h:1761
MLR_STEP_SSR
@ MLR_STEP_SSR
Definition: mat_regression_multiple.cpp:93
MLR_MODEL_SSR
@ MLR_MODEL_SSR
Definition: mat_regression_multiple.cpp:69
MLR_MODEL_NSAMPLES
@ MLR_MODEL_NSAMPLES
Definition: mat_regression_multiple.cpp:77
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bool m_bIntercept
Definition: mat_tools.h:1759
MLR_MODEL_R2
@ MLR_MODEL_R2
Definition: mat_regression_multiple.cpp:66
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Definition: table.h:392
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double SG_Get_Square(double Value)
Definition: mat_tools.cpp:70
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Definition: mat_tools.h:382
CSG_Regression_Multiple::_Get_P
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Definition: mat_regression_multiple.cpp:569
MLR_MODEL_F
@ MLR_MODEL_F
Definition: mat_regression_multiple.cpp:74
ESG_Multiple_Regression_Info_Steps
ESG_Multiple_Regression_Info_Steps
Definition: mat_regression_multiple.cpp:87
CSG_Regression_Multiple::_Get_Step_Out
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Definition: mat_regression_multiple.cpp:745
CSG_Regression_Multiple::CSG_Regression_Multiple
CSG_Regression_Multiple(bool bIntercept=true)
Definition: mat_regression_multiple.cpp:114
MLR_MODEL_SSE
@ MLR_MODEL_SSE
Definition: mat_regression_multiple.cpp:70
CSG_Regression_Multiple::Get_Parameter
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Definition: mat_regression_multiple.cpp:900
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CSG_Strings
Definition: api_core.h:699
CSG_Regression_Multiple::Get_CV_nSamples
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Definition: mat_regression_multiple.cpp:872
CSG_Matrix::Set_Col
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Definition: mat_matrix.cpp:1194
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static CSG_String Format(const char *Format,...)
Definition: api_string.cpp:270
CSG_Strings::Get_String
CSG_String & Get_String(int Index) const
Definition: api_core.h:722
MLR_MODEL_CV_NRMSE
@ MLR_MODEL_CV_NRMSE
Definition: mat_regression_multiple.cpp:80
MLR_STEP_VAR_SIG
@ MLR_STEP_VAR_SIG
Definition: mat_regression_multiple.cpp:101
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Definition: mat_matrix.cpp:1829
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virtual bool Add_Field(const CSG_String &Name, TSG_Data_Type Type, int Position=-1)
Definition: table.cpp:481
CSG_Table
Definition: table.h:283
CSG_Regression_Multiple::Get_P
double Get_P(void) const
Definition: mat_regression_multiple.cpp:868
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int asInt(int Field) const
Definition: table_record.cpp:494
TESTDIST_TYPE_TwoTail
@ TESTDIST_TYPE_TwoTail
Definition: mat_tools.h:1513
SG_Char
#define SG_Char
Definition: api_core.h:536
CSG_Regression_Multiple::Get_CV_RMSE
double Get_CV_RMSE(void) const
Definition: mat_regression_multiple.cpp:869
MLR_MODEL_CV_MSE
@ MLR_MODEL_CV_MSE
Definition: mat_regression_multiple.cpp:78
B
#define B
CSG_String
Definition: api_core.h:563
MLR_MODEL_R2_ADJ
@ MLR_MODEL_R2_ADJ
Definition: mat_regression_multiple.cpp:67
CSG_Regression_Multiple::m_pSteps
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Definition: mat_tools.h:1767
CSG_Regression_Multiple::Get_Model
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Definition: mat_regression_multiple.cpp:297
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Definition: mat_tools.h:748
MLR_STEP_R2_ADJ
@ MLR_STEP_R2_ADJ
Definition: mat_regression_multiple.cpp:91
MLR_VAR_P
@ MLR_VAR_P
Definition: mat_tools.h:1688
CSG_Regression_Multiple::m_Names
CSG_Strings m_Names
Definition: mat_tools.h:1763
CSG_Table_Record::Set_Value
bool Set_Value(int Field, const CSG_String &Value)
Definition: table_record.cpp:270
CSG_Regression_Multiple::m_bIncluded
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Definition: mat_tools.h:1761
CSG_Matrix::Destroy
bool Destroy(void)
Definition: mat_matrix.cpp:923
MLR_MODEL_MSR
@ MLR_MODEL_MSR
Definition: mat_regression_multiple.cpp:72
CSG_Regression_Multiple::Get_RConst
double Get_RConst(void) const
Definition: mat_regression_multiple.cpp:889
ESG_Multiple_Regression_Info_Model
ESG_Multiple_Regression_Info_Model
Definition: mat_regression_multiple.cpp:65
MLR_STEP_SE
@ MLR_STEP_SE
Definition: mat_regression_multiple.cpp:92
MLR_STEP_MSR
@ MLR_STEP_MSR
Definition: mat_regression_multiple.cpp:95
MLR_MODEL_CV_NSAMPLES
@ MLR_MODEL_CV_NSAMPLES
Definition: mat_regression_multiple.cpp:82
MLR_VAR_ID
@ MLR_VAR_ID
Definition: mat_tools.h:1679
MLR_MODEL_MSE
@ MLR_MODEL_MSE
Definition: mat_regression_multiple.cpp:73
CSG_Regression_Multiple::m_pRegression
class CSG_Table * m_pRegression
Definition: mat_tools.h:1767
CSG_Matrix::Add_Row
bool Add_Row(const double *Data=NULL)
Definition: mat_matrix.cpp:1100
CSG_Regression_Multiple::_Get_Step_In
int _Get_Step_In(CSG_Matrix &X, double P_in, double &R2, const CSG_Matrix &Samples)
Definition: mat_regression_multiple.cpp:701
MLR_VAR_SE
@ MLR_VAR_SE
Definition: mat_tools.h:1685
MLR_MODEL_CV_R2
@ MLR_MODEL_CV_R2
Definition: mat_regression_multiple.cpp:81
CSG_Regression_Multiple::Get_R2_Adj
double Get_R2_Adj(void) const
Definition: mat_regression_multiple.cpp:865
MLR_MODEL_NPREDICT
@ MLR_MODEL_NPREDICT
Definition: mat_regression_multiple.cpp:76
CSG_Test_Distribution::Get_F_Tail_from_R2
static double Get_F_Tail_from_R2(double R2, int nPredictors, int nSamples, TSG_Test_Distribution_Type Type=TESTDIST_TYPE_Right)
Definition: mat_tools.cpp:3271
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int Get_Count(void) const
Definition: api_core.h:712
CSG_Regression_Multiple::Get_Model
bool Get_Model(void)
Definition: mat_regression_multiple.cpp:318
CSG_Regression_Multiple::Get_CV_NRMSE
double Get_CV_NRMSE(void) const
Definition: mat_regression_multiple.cpp:870
CSG_Regression_Multiple::_Get_Regression
bool _Get_Regression(const class CSG_Matrix &Samples)
Definition: mat_regression_multiple.cpp:582
MLR_VAR_SIG
@ MLR_VAR_SIG
Definition: mat_tools.h:1687
CSG_Table::Add_Record
virtual CSG_Table_Record * Add_Record(CSG_Table_Record *pCopy=NULL)
Definition: table.cpp:795
SG_Regression_Get_Adjusted_R2
double SG_Regression_Get_Adjusted_R2(double r2, int n, int p, TSG_Regression_Correction Correction)
Definition: mat_regression.cpp:63
CSG_Matrix
Definition: mat_tools.h:478
CSG_Test_Distribution::Get_T_Tail
static double Get_T_Tail(double T, int df, TSG_Test_Distribution_Type Type=TESTDIST_TYPE_Right)
Definition: mat_tools.cpp:3073
CSG_Simple_Statistics
Definition: mat_tools.h:723
table.h
CSG_Regression_Multiple::Get_CrossValidation
bool Get_CrossValidation(int nSubSamples=0)
Definition: mat_regression_multiple.cpp:385
CSG_Table_Record::Set_NoData
bool Set_NoData(int Field)
Definition: table_record.cpp:366
CSG_Matrix::Get_NY
int Get_NY(void) const
Definition: mat_tools.h:521
MLR_STEP_F
@ MLR_STEP_F
Definition: mat_regression_multiple.cpp:98
MLR_STEP_VAR_F
@ MLR_STEP_VAR_F
Definition: mat_regression_multiple.cpp:100
CSG_Matrix::Get_NX
int Get_NX(void) const
Definition: mat_tools.h:520
CSG_Regression_Multiple
Definition: mat_tools.h:1693
SG_DATATYPE_Double
@ SG_DATATYPE_Double
Definition: api_core.h:1004