inmost_dense.h 29.6 KB
Newer Older
1
2
3
4
5
6
#ifndef INMOST_DENSE_INCLUDED
#define INMOST_DENSE_INCLUDED
#include "inmost_common.h"
#if defined(USE_AUTODIFF)
#include "inmost_expression.h"
#endif
Kirill Terekhov's avatar
Kirill Terekhov committed
7
#include <iomanip>
8
9
10
11
12
13
14
15
16
17
18

// Matrix with n columns and m rows
//   __m__
//  |     |
// n|     |
//  |_____|
//
// todo: 
// 1. expression templates for operations
//    (???) how to for multiplication?
// 2. (ok) template matrix type for AD variables
Kirill Terekhov's avatar
Kirill Terekhov committed
19
20
21
// 3. template container type for data storage.
// 4. option for wrapper container around provided data storage. (to perform matrix operations with existing data)
// 5. class Subset for fortran-like access to matrix.
22
23
24
25
26
27
28
29
30
31
32
33

namespace INMOST
{
  

  template<class A, class B> struct Promote;
  template<> struct Promote<INMOST_DATA_REAL_TYPE, INMOST_DATA_REAL_TYPE> {typedef INMOST_DATA_REAL_TYPE type;};
#if defined(USE_AUTODIFF)
  template<> struct Promote<INMOST_DATA_REAL_TYPE, variable>  {typedef variable type;};
  template<> struct Promote<variable, INMOST_DATA_REAL_TYPE>  {typedef variable type;};
  template<> struct Promote<variable, variable> {typedef variable type;};
#else
34
  __INLINE INMOST_DATA_REAL_TYPE get_value(INMOST_DATA_REAL_TYPE x) {return x;}
35
36
37
38
39
40
41
42
43
44
45
46
#endif

  template<typename Var>
  class Matrix
  {
  public:
    typedef unsigned enumerator;
  protected:
    array<Var> space;
    enumerator n, m;
  

Kirill Terekhov's avatar
Kirill Terekhov committed
47
48
    static Var sign_func(const Var & a, const Var & b) {return (b >= 0.0 ? fabs(a) : -fabs(a));}
	  static INMOST_DATA_REAL_TYPE max_func(INMOST_DATA_REAL_TYPE x, INMOST_DATA_REAL_TYPE y) { return x > y ? x : y; }
49
50
51
	  static Var pythag(const Var & a, const Var & b)
	  {
		  Var at = fabs(a), bt = fabs(b), ct, result;
Kirill Terekhov's avatar
Kirill Terekhov committed
52
53
		  if (at > bt)       { ct = bt / at; result = at * sqrt(1.0 + ct * ct); }
		  else if (bt > 0.0) { ct = at / bt; result = bt * sqrt(1.0 + ct * ct); }
54
55
56
57
		  else result = 0.0;
		  return result;
	  }
  public:
Kirill Terekhov's avatar
Kirill Terekhov committed
58
59
60
61
62
63
64
65
66
67
    void RemoveRow(enumerator row)
    {
      for(enumerator k = row+1; k < n; ++k)
      {
        for(enumerator l = 0; l < m; ++l)
          (*this)(k-1,l) = (*this)(k,l);
      }
      space.resize((n-1)*m);
      --n;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
68
69
70
71
72
73
74
75
76
77
78
    void RemoveRows(enumerator first, enumerator last)
    {
      enumerator shift = last-first;
      for(enumerator k = last+1; k < n; ++k)
      {
        for(enumerator l = 0; l < m; ++l)
        (*this)(k-shift-1,l) = (*this)(k,l);
      }
      space.resize((n-shift)*m);
      n-=shift;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
79
80
    void RemoveColumn(enumerator col)
    {
Kirill Terekhov's avatar
Kirill Terekhov committed
81
      Matrix<Var> tmp(n,m-1);
Kirill Terekhov's avatar
Kirill Terekhov committed
82
83
      for(enumerator k = 0; k < n; ++k)
      {
Kirill Terekhov's avatar
Kirill Terekhov committed
84
85
        for(enumerator l = 0; l < col; ++l)
            tmp(k,l) = (*this)(k,l);
Kirill Terekhov's avatar
Kirill Terekhov committed
86
        for(enumerator l = col+1; l < m; ++l)
Kirill Terekhov's avatar
Kirill Terekhov committed
87
          tmp(k,l-1) = (*this)(k,l);
Kirill Terekhov's avatar
Kirill Terekhov committed
88
      }
Kirill Terekhov's avatar
Kirill Terekhov committed
89
      this->Swap(tmp);
Kirill Terekhov's avatar
Kirill Terekhov committed
90
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
      void RemoveColumns(enumerator first, enumerator last)
      {
          enumerator shift = last-first;
          Matrix<Var> tmp(n,m-shift);
          for(enumerator k = 0; k < n; ++k)
          {
              for(enumerator l = 0; l < first; ++l)
                  tmp(k,l) = (*this)(k,l);
              for(enumerator l = last+1; l < m; ++l)
                  tmp(k,l-shift-1) = (*this)(k,l);
          }
          this->Swap(tmp);
      }
      void RemoveSubset(enumerator firstrow, enumerator lastrow, enumerator firstcol, enumerator lastcol)
      {
          enumerator shiftrow = lastrow-firstrow;
          enumerator shiftcol = lastcol-firstcol;
          Matrix<Var> tmp(n-shiftrow, m-shiftcol);
          for(enumerator k = 0; k < firstrow; ++k)
          {
              for(enumerator l = 0; l < firstcol; ++l)
                  tmp(k,l) = (*this)(k,l);
              for(enumerator l = lastcol+1; l < m; ++l)
                  tmp(k,l-shiftcol-1) = (*this)(k,l);
          }
          for(enumerator k = lastrow+1; k < n; ++k)
          {
              for(enumerator l = 0; l < firstcol; ++l)
                  tmp(k-shiftrow-1,l) = (*this)(k,l);
              for(enumerator l = lastcol+1; l < m; ++l)
                  tmp(k-shiftrow-1,l-shiftcol-1) = (*this)(k,l);
          }
          this->Swap(tmp);
      }
125
126
127
128
129
130
    void Swap(Matrix & b)
    {
      space.swap(b.space);
      std::swap(n,b.n);
      std::swap(m,b.m);
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
131
132
133
134
135
136
137
    /// Singular value decomposition.
    /// Reconstruct matrix: A = U*Sigma*V.Transpose().
    /// @param U Left unitary matrix, U^T U = I.
    /// @param Sigma Diagonal matrix with singular values.
    /// @param V Right unitary matrix, not transposed.
    /// @param order_singular_values
    bool SVD(Matrix & U, Matrix & Sigma, Matrix & V, bool order_singular_values = true)
138
139
140
    {
      int flag, i, its, j, jj, k, l, nm;
      Var c, f, h, s, x, y, z;
Kirill Terekhov's avatar
Kirill Terekhov committed
141
142
      Var g = 0.0, scale = 0.0;
      INMOST_DATA_REAL_TYPE anorm = 0.0;
143
144
      if (n < m) 
      {
Kirill Terekhov's avatar
Kirill Terekhov committed
145
        bool success = Transpose().SVD(U,Sigma,V);
146
147
        if( success )
        {
Kirill Terekhov's avatar
Kirill Terekhov committed
148
          U.Swap(V);
149
          U = U.Transpose();
Kirill Terekhov's avatar
Kirill Terekhov committed
150
          V = V.Transpose();
151
152
153
154
155
156
157
158
159
          return true;
        }
        else return false;
      } //m <= n
      array<Var> _rv1(m);
      shell<Var> rv1(_rv1);
      U = (*this);
      Sigma.Resize(m,m);
      Sigma.Zero();
Kirill Terekhov's avatar
Kirill Terekhov committed
160
      V.Resize(m,m);
161
162
163
  
      std::swap(n,m); //this how original algorithm takes it
      // Householder reduction to bidiagonal form
Kirill Terekhov's avatar
Kirill Terekhov committed
164
      for (i = 0; i < (int)n; i++) 
165
166
167
168
169
      {
        // left-hand reduction
        l = i + 1;
        rv1[i] = scale * g;
        g = s = scale = 0.0;
Kirill Terekhov's avatar
Kirill Terekhov committed
170
        if (i < (int)m) 
171
        {
Kirill Terekhov's avatar
Kirill Terekhov committed
172
          for (k = i; k < (int)m; k++) scale += fabs(U(k,i));
173
174
          if (get_value(scale)) 
          {
Kirill Terekhov's avatar
Kirill Terekhov committed
175
            for (k = i; k < (int)m; k++) 
176
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
177
178
              U(k,i) /= scale;
              s += U(k,i) * U(k,i);
179
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
180
            f = U(i,i);
181
182
            g = -sign_func(sqrt(s), f);
            h = f * g - s;
Kirill Terekhov's avatar
Kirill Terekhov committed
183
            U(i,i) = f - g;
184
185
            if (i != n - 1) 
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
186
              for (j = l; j < (int)n; j++) 
187
              {
Kirill Terekhov's avatar
Kirill Terekhov committed
188
                for (s = 0.0, k = i; k < (int)m; k++) s += U(k,i) * U(k,j);
189
                f = s / h;
Kirill Terekhov's avatar
Kirill Terekhov committed
190
                for (k = i; k < (int)m; k++) U(k,j) += f * U(k,i);
191
192
              }
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
193
            for (k = i; k < (int)m; k++) U(k,i) *= scale;
194
195
          }
        }
Kirill Terekhov's avatar
Kirill Terekhov committed
196
        Sigma(i,i) = scale * g;
197
198
        // right-hand reduction
        g = s = scale = 0.0;
Kirill Terekhov's avatar
Kirill Terekhov committed
199
        if (i < (int)m && i != n - 1) 
200
        {
Kirill Terekhov's avatar
Kirill Terekhov committed
201
          for (k = l; k < (int)n; k++) scale += fabs(U(i,k));
202
203
          if (get_value(scale)) 
          {
Kirill Terekhov's avatar
Kirill Terekhov committed
204
            for (k = l; k < (int)n; k++) 
205
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
206
207
              U(i,k) = U(i,k)/scale;
              s += U(i,k) * U(i,k);
208
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
209
            f = U(i,l);
210
211
            g = -sign_func(sqrt(s), f);
            h = f * g - s;
Kirill Terekhov's avatar
Kirill Terekhov committed
212
213
            U(i,l) = f - g;
            for (k = l; k < (int)n; k++) rv1[k] = U(i,k) / h;
214
215
            if (i != m - 1) 
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
216
              for (j = l; j < (int)m; j++) 
217
              {
Kirill Terekhov's avatar
Kirill Terekhov committed
218
219
                for (s = 0.0, k = l; k < (int)n; k++) s += U(j,k) * U(i,k);
                for (k = l; k < (int)n; k++) U(j,k) += s * rv1[k];
220
221
              }
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
222
            for (k = l; k < (int)n; k++) U(i,k) *= scale;
223
224
          }
        }
Kirill Terekhov's avatar
Kirill Terekhov committed
225
        anorm = max_func(anorm,fabs(get_value(Sigma(i,i))) + fabs(get_value(rv1[i])));
226
227
228
229
230
      }

      // accumulate the right-hand transformation
      for (i = n - 1; i >= 0; i--) 
      {
Kirill Terekhov's avatar
Kirill Terekhov committed
231
        if (i < (int)(n - 1)) 
232
233
234
        {
          if (get_value(g)) 
          {
Kirill Terekhov's avatar
Kirill Terekhov committed
235
            for (j = l; j < (int)n; j++) V(j,i) = ((U(i,j) / U(i,l)) / g);
236
            // double division to avoid underflow
Kirill Terekhov's avatar
Kirill Terekhov committed
237
            for (j = l; j < (int)n; j++) 
238
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
239
240
              for (s = 0.0, k = l; k < (int)n; k++) s += U(i,k) * V(k,j);
              for (k = l; k < (int)n; k++) V(k,j) += s * V(k,i);
241
242
            }
          }
Kirill Terekhov's avatar
Kirill Terekhov committed
243
          for (j = l; j < (int)n; j++) V(i,j) = V(j,i) = 0.0;
244
        }
Kirill Terekhov's avatar
Kirill Terekhov committed
245
        V(i,i) = 1.0;
246
247
248
249
250
251
252
253
        g = rv1[i];
        l = i;
      }

      // accumulate the left-hand transformation
      for (i = n - 1; i >= 0; i--) 
      {
        l = i + 1;
Kirill Terekhov's avatar
Kirill Terekhov committed
254
255
256
257
        g = Sigma(i,i);
        if (i < (int)(n - 1)) 
          for (j = l; j < (int)n; j++) 
            U(i,j) = 0.0;
258
259
260
261
262
        if (get_value(g)) 
        {
          g = 1.0 / g;
          if (i != n - 1) 
          {
Kirill Terekhov's avatar
Kirill Terekhov committed
263
            for (j = l; j < (int)n; j++) 
264
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
265
266
267
              for (s = 0.0, k = l; k < (int)m; k++) s += (U(k,i) * U(k,j));
              f = (s / U(i,i)) * g;
              for (k = i; k < (int)m; k++) U(k,j) += f * U(k,i);
268
269
            }
          }
Kirill Terekhov's avatar
Kirill Terekhov committed
270
          for (j = i; j < (int)m; j++) U(j,i) = U(j,i)*g;
271
        }
Kirill Terekhov's avatar
Kirill Terekhov committed
272
273
        else for (j = i; j < (int)m; j++) U(j,i) = 0.0;
        U(i,i) += 1;
274
275
276
277
278
279
280
281
282
283
284
      }

      // diagonalize the bidiagonal form
      for (k = n - 1; k >= 0; k--) 
      {// loop over singular values
        for (its = 0; its < 30; its++) 
        {// loop over allowed iterations
          flag = 1;
          for (l = k; l >= 0; l--) 
          {// test for splitting
            nm = l - 1;
Kirill Terekhov's avatar
Kirill Terekhov committed
285
            if (fabs(get_value(rv1[l])) + anorm == anorm) 
286
287
288
289
            {
              flag = 0;
              break;
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
290
            if (fabs(get_value(Sigma(nm,nm))) + anorm == anorm) 
291
292
293
294
295
296
297
298
299
              break;
          }
          if (flag) 
          {
            c = 0.0;
            s = 1.0;
            for (i = l; i <= k; i++) 
            {
              f = s * rv1[i];
Kirill Terekhov's avatar
Kirill Terekhov committed
300
              if (fabs(get_value(f)) + anorm != anorm) 
301
              {
Kirill Terekhov's avatar
Kirill Terekhov committed
302
                g = Sigma(i,i);
303
                h = pythag(f, g);
Kirill Terekhov's avatar
Kirill Terekhov committed
304
                Sigma(i,i) = h; 
305
306
307
                h = 1.0 / h;
                c = g * h;
                s = (- f * h);
Kirill Terekhov's avatar
Kirill Terekhov committed
308
                for (j = 0; j < (int)m; j++) 
309
                {
Kirill Terekhov's avatar
Kirill Terekhov committed
310
311
312
313
                  y = U(j,nm);
                  z = U(j,i);
                  U(j,nm) = (y * c + z * s);
                  U(j,i) = (z * c - y * s);
314
315
316
317
                }
              }
            }
          }
Kirill Terekhov's avatar
Kirill Terekhov committed
318
          z = Sigma(k,k);
319
320
321
322
          if (l == k) 
          {// convergence
            if (z < 0.0) 
            {// make singular value nonnegative
Kirill Terekhov's avatar
Kirill Terekhov committed
323
324
              Sigma(k,k) = -z;
              for (j = 0; j < (int)n; j++) V(j,k) = -V(j,k);
325
326
327
328
329
330
331
332
333
334
            }
            break;
          }
          if (its >= 30) 
          {
            std::cout << "No convergence after " << its << " iterations" << std::endl;
            std::swap(n,m);
            return false;
          }
          // shift from bottom 2 x 2 minor
Kirill Terekhov's avatar
Kirill Terekhov committed
335
          x = Sigma(l,l);
336
          nm = k - 1;
Kirill Terekhov's avatar
Kirill Terekhov committed
337
          y = Sigma(nm,nm);
338
339
340
341
342
343
344
345
346
347
348
          g = rv1[nm];
          h = rv1[k];
          f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
          g = pythag(f, 1.0);
          f = ((x - z) * (x + z) + h * ((y / (f + sign_func(g, f))) - h)) / x;
          // next QR transformation
          c = s = 1.0;
          for (j = l; j <= nm; j++) 
          {
            i = j + 1;
            g = rv1[i];
Kirill Terekhov's avatar
Kirill Terekhov committed
349
            y = Sigma(i,i);
350
351
352
353
354
355
356
357
358
359
            h = s * g;
            g = c * g;
            z = pythag(f, h);
            rv1[j] = z;
            c = f / z;
            s = h / z;
            f = x * c + g * s;
            g = g * c - x * s;
            h = y * s;
            y = y * c;
Kirill Terekhov's avatar
Kirill Terekhov committed
360
            for (jj = 0; jj < (int)n; jj++) 
361
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
362
363
364
365
              x = V(jj,j);
              z = V(jj,i);
              V(jj,j) = (x * c + z * s);
              V(jj,i) = (z * c - x * s);
366
367
            }
            z = pythag(f, h);
Kirill Terekhov's avatar
Kirill Terekhov committed
368
            Sigma(j,j) = z;
369
370
371
372
373
374
375
376
            if (z) 
            {
              z = 1.0 / z;
              c = f * z;
              s = h * z;
            }
            f = (c * g) + (s * y);
            x = (c * y) - (s * g);
Kirill Terekhov's avatar
Kirill Terekhov committed
377
            for (jj = 0; jj < (int)m; jj++) 
378
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
379
380
381
382
              y = U(jj,j);
              z = U(jj,i);
              U(jj,j) = (y * c + z * s);
              U(jj,i) = (z * c - y * s);
383
384
385
386
            }
          }
          rv1[l] = 0.0;
          rv1[k] = f;
Kirill Terekhov's avatar
Kirill Terekhov committed
387
          Sigma(k,k) = x;
388
389
        }
      }
Kirill Terekhov's avatar
Kirill Terekhov committed
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
      //CHECK THIS!
      if( order_singular_values )
      {
        for(i = 0; i < (int)n; i++)
		    {
			    k = i;
			    for(j = i+1; j < (int)n; ++j)
				    if( Sigma(k,k) < Sigma(j,j) ) k = j;
			    Var temp;
			    if( Sigma(k,k) > Sigma(i,i) )
			    {
				    temp       = Sigma(k,k);
				    Sigma(k,k) = Sigma(i,i);
				    Sigma(i,i) = temp;
            // U is m by n
            for(int j = 0; j < (int)m; ++j)
				    {
					    temp   = U(j,k);
					    U(j,k) = U(j,i);
					    U(j,i) = temp;
            }
            // V is n by n
            for(int j = 0; j < (int)n; ++j)
            {
					    temp   = V(j,k);
					    V(j,k) = V(j,i);
					    V(j,i) = temp;
				    }
			    }
		    }
      }
      
422
423
424
      std::swap(n,m);
      return true;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
425
    Matrix() : space(0),n(0),m(0) {}
426
427
428
429
430
431
432
    Matrix(Var * pspace, enumerator pn, enumerator pm) : space(pspace,pspace+pn*pm), n(pn), m(pm) {}
    Matrix(enumerator pn, enumerator pm) : space(pn*pm), n(pn), m(pm) {}
    Matrix(const Matrix & other) : space(other.n*other.m), n(other.n), m(other.m) 
    {
      for(enumerator i = 0; i < n*m; ++i)
        space[i] = other.space[i];
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
433
434
435
436
437
438
439
      template<typename typeB>
      Matrix(const Matrix<typeB> & other) : space(other.Cols()*other.Rows()), n(other.Rows()), m(other.Cols())
      {
          for(enumerator i = 0; i < n; ++i)
              for(enumerator j = 0; j < m; ++j)
                  (*this)(i,j) = get_value(other(i,j));
      }
440
441
442
443
444
445
446
447
448
449
    ~Matrix() {}
    void Resize(enumerator nrows, enumerator mcols)
    {
      if( space.size() != mcols*nrows )
        space.resize(mcols*nrows);
      n = nrows;
      m = mcols;
    }
    Matrix & operator =(Matrix const & other)
    {
Kirill Terekhov's avatar
Kirill Terekhov committed
450
      if( n*m != other.n*other.m ) space.resize(other.n*other.m);
451
452
453
454
455
456
      for(enumerator i = 0; i < other.n*other.m; ++i)
        space[i] = other.space[i];
      n = other.n;
      m = other.m;
      return *this;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
457
458
459
460
461
462
463
464
465
466
      template<typename typeB>
      Matrix & operator =(Matrix<typeB> const & other)
      {
          if( n*m != other.n*other.m ) space.resize(other.n*other.m);
          for(enumerator i = 0; i < other.n*other.m; ++i)
              space[i] = get_value(other.space[i]);
          n = other.n;
          m = other.m;
          return *this;
      }
467
468
469
470
471
472
473
474
475
    // i is in [0,n] - row index
    // j is in [0,m] - column index
    Var & operator()(enumerator i, enumerator j)
    {
      assert(i >= 0 && i < n);
      assert(j >= 0 && j < m);
      assert(i*m+j < n*m); //overflow check?
      return space[i*m+j];
    }
476
    const Var & operator()(enumerator i, enumerator j) const
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
    {
      assert(i >= 0 && i < n);
      assert(j >= 0 && j < m);
      assert(i*m+j < n*m); //overflow check?
      return space[i*m+j];
    }
    Matrix operator-() const
    {
      Matrix ret(n,m);
      for(enumerator k = 0; k < n*m; ++k) ret.space[k] = -space[k];
      return ret;
    }
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator-(const Matrix<typeB> & other) const
    {
      assert(Rows() == other.Rows());
      assert(Cols() == other.Cols());
      Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
Kirill Terekhov's avatar
Kirill Terekhov committed
495
496
497
        for(enumerator i = 0; i < Rows(); ++i)
            for(enumerator j = 0; j < Cols(); ++j)
                ret(i,j) = (*this)(i,j)-other(i,j);
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
      return ret;
    }
    Matrix & operator-=(const Matrix & other)
    {
      assert(n == other.n);
      assert(m == other.m);
      for(enumerator k = 0; k < n*m; ++k) space[k] -= other.space[k];
      return *this;
    }
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator+(const Matrix<typeB> & other) const
    {
      assert(Rows() == other.Rows());
      assert(Cols() == other.Cols());
      Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
Kirill Terekhov's avatar
Kirill Terekhov committed
513
514
515
      for(enumerator i = 0; i < Rows(); ++i)
          for(enumerator j = 0; j < Cols(); ++j)
              ret(i,j) = (*this)(i,j)+other(i,j);
516
517
518
519
520
521
522
523
524
525
526
527
528
      return ret;
    }
    Matrix & operator+=(const Matrix & other)
    {
      assert(n == other.n);
      assert(m == other.m);
      for(enumerator k = 0; k < n*m; ++k) space[k] += other.space[k];
      return *this;
    }
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator*(typeB coef) const
    {
      Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
Kirill Terekhov's avatar
Kirill Terekhov committed
529
530
      for(enumerator i = 0; i < Rows(); ++i)
        for(enumerator j = 0; j < Cols(); ++j) ret(i,j) = (*this)(i,j)*coef;
531
532
533
534
535
536
537
538
539
540
541
      return ret;
    }
    Matrix & operator*=(Var coef)
    {
      for(enumerator k = 0; k < n*m; ++k) space[k] *= coef;
      return *this;
    }
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator/(typeB coef) const
    {
      Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
Kirill Terekhov's avatar
Kirill Terekhov committed
542
543
        for(enumerator i = 0; i < Rows(); ++i)
            for(enumerator j = 0; j < Cols(); ++j) ret(i,j) = (*this)(i,j)/coef;
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
      return ret;
    }
    Matrix & operator/=(Var coef)
    {
      for(enumerator k = 0; k < n*m; ++k) space[k] /= coef;
      return *this;
    }
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator*(const Matrix<typeB> & other) const
    {
      assert(Cols() == other.Rows());
      Matrix<typename Promote<Var,typeB>::type> ret(Rows(),other.Cols()); //check RVO
      for(enumerator i = 0; i < Rows(); ++i) //loop rows
      {
        for(enumerator j = 0; j < other.Cols(); ++j) //loop columns
        {
          typename Promote<Var,typeB>::type tmp = 0.0;
          for(enumerator k = 0; k < Cols(); ++k)
            tmp += (*this)(i,k)*other(k,j);
          ret(i,j) = tmp;
        }
      }
      return ret;
    }
    /// performs A*B^{-1}
    /// checks existence of B^{-1} only in debug mode.
    template<typename typeB>
    Matrix<typename Promote<Var,typeB>::type> operator/(const Matrix<typeB> & other) const
    {
      std::pair<Matrix<typeB>,bool> other_inv = other.Invert();
      assert(other_inv.second);
      assert(Cols() == other_inv.Rows());
      Matrix<typename Promote<Var,typeB>::type> ret(n,other.m); //check RVO
      for(enumerator i = 0; i < Rows(); ++i) //loop rows
      {
        for(enumerator j = 0; j < other_inv.Cols(); ++j) //loop columns
        {
          typename Promote<Var,typeB>::type tmp = 0.0;
          for(enumerator k = 0; k < Cols(); ++k)
            tmp += (*this)(i,k)*other_inv.first(k,j);
          ret(i,j) = tmp;
        }
      }
      return ret;
    }
    Matrix Transpose() const
    {
      Matrix ret(m,n);
      for(enumerator i = 0; i < n; ++i)
      {
        for(enumerator j = 0; j < m; ++j)
        {
          ret(j,i) = (*this)(i,j);
        }
      }
      return ret;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
601
    std::pair<Matrix,bool> Invert(bool print_fail = false) const
602
603
604
    {
      std::pair<Matrix,bool> ret = std::make_pair(Matrix(m,n),true);
      Matrix At = Transpose(); //m by n matrix
Kirill Terekhov's avatar
Kirill Terekhov committed
605
      Matrix AtB = At; //m by n matrix
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
      Matrix AtA = At*(*this); //m by m matrix
      enumerator * order = new enumerator [m];
      for(enumerator i = 0; i < m; ++i) order[i] = i;
      for(enumerator i = 0; i < m; i++)
	    {
		    enumerator maxk = i, maxq = i, temp2;
        Var max, temp;
		    max = fabs(AtA(maxk,maxq));
		    //Find best pivot
        for(enumerator k = i; k < m; k++) // over rows
		    {
			    for(enumerator q = i; q < m; q++) // over columns
			    {
				    if( fabs(AtA(k,q)) > max )
				    {
					    max = fabs(AtA(k,q));
					    maxk = k;
					    maxq = q;
				    }
			    }
		    }
		    //Exchange rows
		    if( maxk != i ) 
		    {
			    for(enumerator q = 0; q < m; q++) // over columns of A
			    {
				    temp = AtA(maxk,q);
				    AtA(maxk,q) = AtA(i,q);
				    AtA(i,q) = temp;
			    }
			    //exchange rhs
			    for(enumerator q = 0; q < n; q++) // over columns of B
			    {
				    temp = AtB(maxk,q);
				    AtB(maxk,q) = AtB(i,q);
				    AtB(i,q) = temp;
			    }
		    }
		    //Exchange columns
		    if( maxq != i ) 
		    {
			    for(enumerator k = 0; k < m; k++) //over rows
			    {
				    temp = AtA(k,maxq);
				    AtA(k,maxq) = AtA(k,i);
				    AtA(k,i) = temp;
			    }
			    //remember order in sol
			    {
				    temp2 = order[maxq];
				    order[maxq] = order[i];
				    order[i] = temp2;
			    }
		    }

		    if( fabs(AtA(i,i)) < 1.0e-54 )
		    {
			    bool ok = true;
			    for(enumerator k = 0; k < n; k++) // over columns of B
			    {
				    if( fabs(AtB(i,k)/1.0e-54) > 1 )
				    {
					    ok = false;
					    break;
				    }
			    }
			    if( ok ) AtA(i,i) = AtA(i,i) < 0.0 ? - 1.0e-12 : 1.0e-12;
			    else
Kirill Terekhov's avatar
Kirill Terekhov committed
674
675
676
677
678
679
				{
					if( print_fail ) std::cout << "Failed to invert matrix" << std::endl;
					ret.second = false;
					delete [] order;
					return ret;
				}
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
		    }
		    for(enumerator k = i+1; k < m; k++)
		    {
			    AtA(i,k) /= AtA(i,i);
			    AtA(k,i) /= AtA(i,i);
		    }
		    for(enumerator k = i+1; k < m; k++)
		    for(enumerator q = i+1; q < m; q++)
		    {
			    AtA(k,q) -= AtA(k,i) * AtA(i,i) * AtA(i,q);
		    }
		    for(enumerator k = 0; k < n; k++)
		    {
			    for(enumerator j = i+1; j < m; j++) //iterate over columns of L
			    {
				    AtB(j,k) -= AtB(i,k) * AtA(j,i);
			    }
			    AtB(i,k) /= AtA(i,i);
		    }
	    }

	    for(enumerator k = 0; k < n; k++)
	    {
		    for(enumerator i = m; i-- > 0; ) //iterate over rows of U
			    for(enumerator j = i+1; j < m; j++) 
			    {
				    AtB(i,k) -= AtB(j,k) * AtA(i,j);
			    }
		    for(enumerator i = 0; i < m; i++)
			    ret.first(order[i],k) = AtB(i,k);
	    }
      delete [] order;
      return ret;
    }
    void Zero()
    {
      for(enumerator i = 0; i < n*m; ++i) space[i] = 0.0;
    }
    Var Trace() const
    {
      assert(n == m);
      Var ret = 0.0;
      for(enumerator i = 0; i < n; ++i) ret += (*this)(i,i);
      return ret;
    }
    Var * data() {return space.data();}
    const Var * data() const {return space.data();}
    enumerator Rows() const {return n;}
    enumerator Cols() const {return m;}
    void Print(INMOST_DATA_REAL_TYPE threshold = 1.0e-10) const
    {
      for(enumerator k = 0; k < n; ++k)
      {
        for(enumerator l = 0; l < m; ++l) 
        {
          if( fabs(get_value((*this)(k,l))) > threshold )
Kirill Terekhov's avatar
Kirill Terekhov committed
736
#if defined(USE_AUTODIFF)
Kirill Terekhov's avatar
Kirill Terekhov committed
737
            std::cout << std::setw(10) << get_value((*this)(k,l));
Kirill Terekhov's avatar
Kirill Terekhov committed
738
739
740
741
#else
            std::cout << std::setw(10) << (*this)(k,l);
#endif
          else
Kirill Terekhov's avatar
Kirill Terekhov committed
742
            std::cout << std::setw(10) << 0;
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
          std::cout << " ";
        }
        std::cout << std::endl;
      }
    }
    bool isSymmetric() const
    {
      if( n != m ) return false;
      for(enumerator k = 0; k < n; ++k)
      {
        for(enumerator l = k+1; l < n; ++l)
          if( fabs((*this)(k,l)-(*this)(l,k)) > 1.0e-7 )
            return false;
      }
      return true;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
759
760
    template<typename typeB>
    typename Promote<Var,typeB>::type DotProduct(const Matrix<typeB> & other) const
761
762
763
    {
      assert(n == other.n);
      assert(m == other.m);
Kirill Terekhov's avatar
Kirill Terekhov committed
764
765
766
767
      typename Promote<Var,typeB>::type ret = 0.0;
      for(enumerator i = 0; i < n; ++i)
        for(enumerator j = 0; j < m; ++j)
          ret += ((*this)(i,j))*other(i,j);
768
769
      return ret;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
770
771
772
773
774
      template<typename typeB>
      typename Promote<Var,typeB>::type operator ^(const Matrix<typeB> & other) const
      {
          return DotProduct(other);
      }
775
776
777
778
779
780
781
782
783
784
785
786
787
788
    Var FrobeniusNorm()
    {
      Var ret = 0;
      for(enumerator i = 0; i < n*m; ++i) ret += space[i]*space[i];
      return sqrt(ret);
    }
    static Matrix<Var> FromTensor(Var * K, enumerator size)
    {
      Matrix<Var> Kc(3,3);
      switch(size)
      {
      case 1: //scalar permeability tensor
        Kc.Zero();
        Kc(0,0) = Kc(1,1) = Kc(2,2) = K[0];
Kirill Terekhov's avatar
Kirill Terekhov committed
789
		break;
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
      case 3:
        Kc.Zero(); //diagonal permeability tensor 
        Kc(0,0) = K[0]; //KXX
        Kc(1,1) = K[1]; //KYY
        Kc(2,2) = K[2]; //KZZ
        break;
      case 6: //symmetric permeability tensor
        Kc(0,0) = K[0]; //KXX
        Kc(0,1) = Kc(1,0) = K[1]; //KXY
        Kc(0,2) = Kc(2,0) = K[2]; //KXZ
        Kc(1,1) = K[3]; //KYY
        Kc(1,2) = Kc(2,1) = K[4]; //KYZ
        Kc(2,2) = K[5]; //KZZ
        break;
      case 9: //full permeability tensor
        Kc(0,0) = K[0]; //KXX
        Kc(0,1) = K[1]; //KXY
        Kc(0,2) = K[2]; //KXZ
        Kc(1,0) = K[3]; //KYX
        Kc(1,1) = K[4]; //KYY
        Kc(1,2) = K[5]; //KYZ
        Kc(2,0) = K[6]; //KZX
        Kc(2,1) = K[7]; //KZY
        Kc(2,2) = K[8]; //KZZ
        break;
      }
      return Kc;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
818
    ///Retrive vector in matrix form from array
819
820
821
822
    static Matrix<Var> FromVector(Var * n, enumerator size)
    {
      return Matrix(n,size,1);
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
823
    ///Create diagonal matrix from array
824
825
826
827
828
829
830
    static Matrix<Var> FromDiagonal(Var * r, enumerator size)
    {
      Matrix ret(size,size);
      ret.Zero();
      for(enumerator k = 0; k < size; ++k) ret(k,k) = r[k];
      return ret;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
831
    ///Create diagonal matrix from array of inversed values
832
833
834
835
836
837
838
    static Matrix<Var> FromDiagonalInverse(Var * r, enumerator size)
    {
      Matrix ret(size,size);
      ret.Zero();
      for(enumerator k = 0; k < size; ++k) ret(k,k) = 1.0/r[k];
      return ret;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
	static Matrix CrossProduct(Var vec[3])
	{
		// |  0  -z   y |
		// |  z   0  -x |
		// | -y   x   0 |
		Matrix ret(3,3);
		ret(0,0) = 0.0;
		ret(0,1) = -vec[2]; //-z
		ret(0,2) = vec[1]; //y
		ret(1,0) = vec[2]; //z
		ret(1,1) = 0;
		ret(1,2) = -vec[0]; //-x
		ret(2,0) = -vec[1]; //-y
		ret(2,1) = vec[0]; //x
		ret(2,2) = 0;
		return ret;
	}
Kirill Terekhov's avatar
Kirill Terekhov committed
856
    ///Unit matrix
857
858
859
860
861
862
863
    static Matrix Unit(enumerator pn)
    {
      Matrix ret(pn,pn);
      ret.Zero();
      for(enumerator i = 0; i < pn; ++i) ret(i,i) = 1.0;
      return ret;
    }
Kirill Terekhov's avatar
Kirill Terekhov committed
864
865
866
    /// Concatenate B matrix as columns of current matrix.
    /// Assumes that number of rows of current matrix is
    /// equal to number of rows of B matrix.
Kirill Terekhov's avatar
Kirill Terekhov committed
867
    Matrix ConcatCols(const Matrix & B)
Kirill Terekhov's avatar
Kirill Terekhov committed
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
    {
        assert(Rows() == B.Rows());
        Matrix ret(Rows(),Cols()+B.Cols());
        Matrix & A = *this;
        for(enumerator i = 0; i < Rows(); ++i)
        {
            for(enumerator j = 0; j < Cols(); ++j)
                ret(i,j) = A(i,j);
            for(enumerator j = 0; j < B.Cols(); ++j)
                ret(i,j+Cols()) = B(i,j);
        }
        return ret;
    }
    /// Concatenate B matrix as rows of current matrix.
    /// Assumes that number of colums of current matrix is
    /// equal to number of columns of B matrix.
Kirill Terekhov's avatar
Kirill Terekhov committed
884
    Matrix ConcatRows(const Matrix & B)
Kirill Terekhov's avatar
Kirill Terekhov committed
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
    {
        assert(Cols() == B.Cols());
        Matrix ret(Rows()+B.Rows(),Cols());
        Matrix & A = *this;
        for(enumerator i = 0; i < Rows(); ++i)
        {
            for(enumerator j = 0; j < Cols(); ++j)
                ret(i,j) = A(i,j);
        }
        for(enumerator i = 0; i < B.Rows(); ++i)
        {
            for(enumerator j = 0; j < Cols(); ++j)
                ret(i+Rows(),j) = B(i,j);
        }
        return ret;
    }

    /// Joint diagonalization algorithm by Cardoso
    /// http://perso.telecom-paristech.fr/~cardoso/Algo/Joint_Diag/joint_diag_r.m
    /// Current matrix should have size n by n*m
    /// And represent concatination of m n by n matrices
Kirill Terekhov's avatar
Kirill Terekhov committed
906
    Matrix JointDiagonalization(INMOST_DATA_REAL_TYPE threshold = 1.0e-7)
Kirill Terekhov's avatar
Kirill Terekhov committed
907
    {
Kirill Terekhov's avatar
Kirill Terekhov committed
908
909
        enumerator N = Rows();
        enumerator M = Cols() / Rows();
Kirill Terekhov's avatar
Kirill Terekhov committed
910
        Matrix V = Matrix::Unit(m);
Kirill Terekhov's avatar
Kirill Terekhov committed
911
        Matrix R(2,M);
Kirill Terekhov's avatar
Kirill Terekhov committed
912
913
914
915
916
917
918
        Matrix G(2,2);
        Matrix & A = *this;
        Var ton, toff, theta, c, s, Ap, Aq, Vp, Vq;
        bool repeat;
        do
        {
            repeat = false;
Kirill Terekhov's avatar
Kirill Terekhov committed
919
            for(enumerator p = 0; p < N-1; ++p)
Kirill Terekhov's avatar
Kirill Terekhov committed
920
            {
Kirill Terekhov's avatar
Kirill Terekhov committed
921
                for(enumerator q = p+1; q < N; ++q)
Kirill Terekhov's avatar
Kirill Terekhov committed
922
                {
Kirill Terekhov's avatar
Kirill Terekhov committed
923
                    for(enumerator k = 0; k < M; ++k)
Kirill Terekhov's avatar
Kirill Terekhov committed
924
                    {
Kirill Terekhov's avatar
Kirill Terekhov committed
925
926
                        R(0,k) = A(p,p + k*N) - A(q,q + k*N);
                        R(1,k) = A(p,q + k*N) + A(q,p + k*N);
Kirill Terekhov's avatar
Kirill Terekhov committed
927
928
929
930
931
932
933
934
935
                    }
                    G = R*R.Transpose();
                    Var ton  = G(0,0) - G(1,1);
                    Var toff = G(0,1) + G(1,0);
                    Var theta = 0.5 * atan2( toff, ton + sqrt(ton*ton + toff*toff) );
                    Var c = cos(theta);
                    Var s = sin(theta);
                    if( fabs(s) > threshold )
                    {
Kirill Terekhov's avatar
Kirill Terekhov committed
936
937
938
                        //std::cout << "p,q: " << p << "," << q << " c,s: " << c << "," << s << std::endl;
                        repeat = true;
                        for(enumerator k = 0; k < M; ++k)
Kirill Terekhov's avatar
Kirill Terekhov committed
939
                        {
Kirill Terekhov's avatar
Kirill Terekhov committed
940
                            for(enumerator i = 0; i < N; ++i)
Kirill Terekhov's avatar
Kirill Terekhov committed
941
                            {
Kirill Terekhov's avatar
Kirill Terekhov committed
942
943
944
945
                                Ap = A(i,p + k*N);
                                Aq = A(i,q + k*N);
                                A(i,p + k*N) = Ap*c + Aq*s;
                                A(i,q + k*N) = Aq*c - Ap*s;
Kirill Terekhov's avatar
Kirill Terekhov committed
946
947
                            }
                        }
Kirill Terekhov's avatar
Kirill Terekhov committed
948
                        for(enumerator k = 0; k < M; ++k)
Kirill Terekhov's avatar
Kirill Terekhov committed
949
                        {
Kirill Terekhov's avatar
Kirill Terekhov committed
950
                            for(enumerator j = 0; j < N; ++j)
Kirill Terekhov's avatar
Kirill Terekhov committed
951
                            {
Kirill Terekhov's avatar
Kirill Terekhov committed
952
953
954
955
                                Ap = A(p,j + k*N);
                                Aq = A(q,j + k*N);
                                A(p,j + k*N) = Ap*c + Aq*s;
                                A(q,j + k*N) = Aq*c - Ap*s;
Kirill Terekhov's avatar
Kirill Terekhov committed
956
957
                            }
                        }
Kirill Terekhov's avatar
Kirill Terekhov committed
958
                        for(enumerator i = 0; i < N; ++i)
Kirill Terekhov's avatar
Kirill Terekhov committed
959
960
961
962
                        {
                            Vp = V(i,p);
                            Vq = V(i,q);
                            V(i,p) = Vp*c + Vq*s;
Kirill Terekhov's avatar
Kirill Terekhov committed
963
                            V(i,q) = Vq*c - Vp*s;
Kirill Terekhov's avatar
Kirill Terekhov committed
964
965
966
967
                        }
                    }
                }
            }
Kirill Terekhov's avatar
Kirill Terekhov committed
968
            //Print();
Kirill Terekhov's avatar
Kirill Terekhov committed
969
970
971
972
        } while( repeat );
        return V;
    }

973
  };
Kirill Terekhov's avatar
Kirill Terekhov committed
974
    
Kirill Terekhov's avatar
Kirill Terekhov committed
975
	typedef Matrix<INMOST_DATA_REAL_TYPE> rMatrix; //shortcut for real matrix
Kirill Terekhov's avatar
Kirill Terekhov committed
976
#if defined(USE_AUTODIFF)
Kirill Terekhov's avatar
Kirill Terekhov committed
977
	typedef Matrix<variable> vMatrix; //shortcut for matrix with variations
Kirill Terekhov's avatar
Kirill Terekhov committed
978
#endif
Kirill Terekhov's avatar
Kirill Terekhov committed
979
980
    
}
981

Kirill Terekhov's avatar
Kirill Terekhov committed
982
983
984
985
template<typename typeB>
INMOST::Matrix<typename INMOST::Promote<INMOST_DATA_REAL_TYPE,typeB>::type> operator *(INMOST_DATA_REAL_TYPE coef, const INMOST::Matrix<typeB> & other)
{return other*coef;}
	
986
#if defined(USE_AUTODIFF)
Kirill Terekhov's avatar
Kirill Terekhov committed
987
988
989
template<typename typeB>
INMOST::Matrix<typename INMOST::Promote<INMOST::variable,typeB>::type> operator *(const INMOST::variable & coef, const INMOST::Matrix<typeB> & other)
{return other*coef;}
990
991
992
993
#endif


#endif //INMOST_DENSE_INCLUDED