src/math/jama_lu.hpp

#ifndef JAMA_LU_H
#define JAMA_LU_H

#include "tnt_array1d.hpp"
#include "tnt_array1d_utils.hpp"
#include "tnt_array2d.hpp"
#include "tnt_array2d_utils.hpp"
#include "tnt_math_utils.hpp"

#include <algorithm>
//for min(), max() below

using namespace TNT;
using namespace std;

namespace JAMA
{

   /** LU Decomposition.
   <P>
   For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
   unit lower triangular matrix L, an n-by-n upper triangular matrix U,
   and a permutation vector piv of length m so that A(piv,:) = L*U.
   If m < n, then L is m-by-m and U is m-by-n.
   <P>
   The LU decompostion with pivoting always exists, even if the matrix is
   singular, so the constructor will never fail.  The primary use of the
   LU decomposition is in the solution of square systems of simultaneous
   linear equations.  This will fail if isNonsingular() returns false.
   */
template <class Real>
class LU
{


   /* Array for internal storage of decomposition.  */
   Array2D<Real>  LU_;
   int m, n, pivsign; 
   Array1D<int> piv;


   Array2D<Real> permute_copy(const Array2D<Real> &A, 
                        const Array1D<int> &piv, int j0, int j1)
        {
                int piv_length = piv.dim();

                Array2D<Real> X(piv_length, j1-j0+1);


         for (int i = 0; i < piv_length; i++) 
            for (int j = j0; j <= j1; j++) 
               X[i][j-j0] = A[piv[i]][j];

                return X;
        }

   Array1D<Real> permute_copy(const Array1D<Real> &A, 
                const Array1D<int> &piv)
        {
                int piv_length = piv.dim();
                if (piv_length != A.dim())
                        return Array1D<Real>();

                Array1D<Real> x(piv_length);


         for (int i = 0; i < piv_length; i++) 
               x[i] = A[piv[i]];

                return x;
        }


        public :

   /** LU Decomposition
   @param  A   Rectangular matrix
   @return     LU Decomposition object to access L, U and piv.
   */

    LU (const Array2D<Real> &A) : LU_(A.copy()), m(A.dim1()), n(A.dim2()), 
                piv(A.dim1())
        
        {

   // Use a "left-looking", dot-product, Crout/Doolittle algorithm.


      for (int i = 0; i < m; i++) {
         piv[i] = i;
      }
      pivsign = 1;
      Real *LUrowi = 0;;
      Array1D<Real> LUcolj(m);

      // Outer loop.

      for (int j = 0; j < n; j++) {

         // Make a copy of the j-th column to localize references.

         for (int i = 0; i < m; i++) {
            LUcolj[i] = LU_[i][j];
         }

         // Apply previous transformations.

         for (int i = 0; i < m; i++) {
            LUrowi = LU_[i];

            // Most of the time is spent in the following dot product.

            int kmax = min(i,j);
            double s = 0.0;
            for (int k = 0; k < kmax; k++) {
               s += LUrowi[k]*LUcolj[k];
            }

            LUrowi[j] = LUcolj[i] -= s;
         }
   
         // Find pivot and exchange if necessary.

         int p = j;
         for (int i = j+1; i < m; i++) {
            if (abs(LUcolj[i]) > abs(LUcolj[p])) {
               p = i;
            }
         }
         if (p != j) {
                    int k=0;
            for (k = 0; k < n; k++) {
               double t = LU_[p][k]; 
                           LU_[p][k] = LU_[j][k]; 
                           LU_[j][k] = t;
            }
            k = piv[p]; 
                        piv[p] = piv[j]; 
                        piv[j] = k;
            pivsign = -pivsign;
         }

         // Compute multipliers.
         
         if ((j < m) && (LU_[j][j] != 0.0)) {
            for (int i = j+1; i < m; i++) {
               LU_[i][j] /= LU_[j][j];
            }
         }
      }
   }


   /** Is the matrix nonsingular?
   @return     1 (true)  if upper triangular factor U (and hence A) 
                                is nonsingular, 0 otherwise.
   */

   int isNonsingular () {
      for (int j = 0; j < n; j++) {
         if (LU_[j][j] == 0)
            return 0;
      }
      return 1;
   }

   /** Return lower triangular factor
   @return     L
   */

   Array2D<Real> getL () {
      Array2D<Real> L_(m,n);
      for (int i = 0; i < m; i++) {
         for (int j = 0; j < n; j++) {
            if (i > j) {
               L_[i][j] = LU_[i][j];
            } else if (i == j) {
               L_[i][j] = 1.0;
            } else {
               L_[i][j] = 0.0;
            }
         }
      }
      return L_;
   }

   /** Return upper triangular factor
   @return     U portion of LU factorization.
   */

   Array2D<Real> getU () {
          Array2D<Real> U_(n,n);
      for (int i = 0; i < n; i++) {
         for (int j = 0; j < n; j++) {
            if (i <= j) {
               U_[i][j] = LU_[i][j];
            } else {
               U_[i][j] = 0.0;
            }
         }
      }
      return U_;
   }

   /** Return pivot permutation vector
   @return     piv
   */

   Array1D<int> getPivot () {
      return piv;
   }


   /** Compute determinant using LU factors.
   @return     determinant of A, or 0 if A is not square.
   */

   Real det () {
      if (m != n) {
         return Real(0);
      }
      Real d = Real(pivsign);
      for (int j = 0; j < n; j++) {
         d *= LU_[j][j];
      }
      return d;
   }

   /** Solve A*X = B
   @param  B   A Matrix with as many rows as A and any number of columns.
   @return     X so that L*U*X = B(piv,:), if B is nonconformant, returns
                                        0x0 (null) array.
   */

   Array2D<Real> solve (const Array2D<Real> &B) 
   {

          /* Dimensions: A is mxn, X is nxk, B is mxk */
      
      if (B.dim1() != m) {
                return Array2D<Real>(0,0);
      }
      if (!isNonsingular()) {
        return Array2D<Real>(0,0);
      }

      // Copy right hand side with pivoting
      int nx = B.dim2();


          Array2D<Real> X = permute_copy(B, piv, 0, nx-1);

      // Solve L*Y = B(piv,:)
      for (int k = 0; k < n; k++) {
         for (int i = k+1; i < n; i++) {
            for (int j = 0; j < nx; j++) {
               X[i][j] -= X[k][j]*LU_[i][k];
            }
         }
      }
      // Solve U*X = Y;
      for (int k = n-1; k >= 0; k--) {
         for (int j = 0; j < nx; j++) {
            X[k][j] /= LU_[k][k];
         }
         for (int i = 0; i < k; i++) {
            for (int j = 0; j < nx; j++) {
               X[i][j] -= X[k][j]*LU_[i][k];
            }
         }
      }
      return X;
   }


   /** Solve A*x = b, where x and b are vectors of length equal 
                to the number of rows in A.

   @param  b   a vector (Array1D> of length equal to the first dimension
                                                of A.
   @return x a vector (Array1D> so that L*U*x = b(piv), if B is nonconformant,
                                        returns 0x0 (null) array.
   */

   Array1D<Real> solve (const Array1D<Real> &b) 
   {

          /* Dimensions: A is mxn, X is nxk, B is mxk */
      
      if (b.dim1() != m) {
                return Array1D<Real>();
      }
      if (!isNonsingular()) {
        return Array1D<Real>();
      }


          Array1D<Real> x = permute_copy(b, piv);

      // Solve L*Y = B(piv)
      for (int k = 0; k < n; k++) {
         for (int i = k+1; i < n; i++) {
               x[i] -= x[k]*LU_[i][k];
            }
         }
      
          // Solve U*X = Y;
      for (int k = n-1; k >= 0; k--) {
            x[k] /= LU_[k][k];
                for (int i = 0; i < k; i++) 
                x[i] -= x[k]*LU_[i][k];
      }
     

      return x;
   }

}; /* class LU */

} /* namespace JAMA */

#endif
/* JAMA_LU_H */
Revision:	3495
Committed:	Tue Apr 7 20:16:26 2009 UTC (15 years, 2 months ago) by gezelter
File size:	7165 byte(s)
Log Message:	adding jama and tnt libraries for various linear algebra routines
#	Content
1	#ifndef JAMA_LU_H
2	#define JAMA_LU_H
3
4	#include "tnt_array1d.hpp"
5	#include "tnt_array1d_utils.hpp"
6	#include "tnt_array2d.hpp"
7	#include "tnt_array2d_utils.hpp"
8	#include "tnt_math_utils.hpp"
9
10	#include <algorithm>
11	//for min(), max() below
12
13	using namespace TNT;
14	using namespace std;
15
16	namespace JAMA
17	{
18
19	/** LU Decomposition.
20	<P>
21	For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
22	unit lower triangular matrix L, an n-by-n upper triangular matrix U,
23	and a permutation vector piv of length m so that A(piv,:) = L*U.
24	If m < n, then L is m-by-m and U is m-by-n.
25	<P>
26	The LU decompostion with pivoting always exists, even if the matrix is
27	singular, so the constructor will never fail. The primary use of the
28	LU decomposition is in the solution of square systems of simultaneous
29	linear equations. This will fail if isNonsingular() returns false.
30	*/
31	template <class Real>
32	class LU
33	{
34
35
36
37	/* Array for internal storage of decomposition. */
38	Array2D<Real> LU_;
39	int m, n, pivsign;
40	Array1D<int> piv;
41
42
43	Array2D<Real> permute_copy(const Array2D<Real> &A,
44	const Array1D<int> &piv, int j0, int j1)
45	{
46	int piv_length = piv.dim();
47
48	Array2D<Real> X(piv_length, j1-j0+1);
49
50
51	for (int i = 0; i < piv_length; i++)
52	for (int j = j0; j <= j1; j++)
53	X[i][j-j0] = A[piv[i]][j];
54
55	return X;
56	}
57
58	Array1D<Real> permute_copy(const Array1D<Real> &A,
59	const Array1D<int> &piv)
60	{
61	int piv_length = piv.dim();
62	if (piv_length != A.dim())
63	return Array1D<Real>();
64
65	Array1D<Real> x(piv_length);
66
67
68	for (int i = 0; i < piv_length; i++)
69	x[i] = A[piv[i]];
70
71	return x;
72	}
73
74
75	public :
76
77	/** LU Decomposition
78	@param A Rectangular matrix
79	@return LU Decomposition object to access L, U and piv.
80	*/
81
82	LU (const Array2D<Real> &A) : LU_(A.copy()), m(A.dim1()), n(A.dim2()),
83	piv(A.dim1())
84
85	{
86
87	// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
88
89
90	for (int i = 0; i < m; i++) {
91	piv[i] = i;
92	}
93	pivsign = 1;
94	Real *LUrowi = 0;;
95	Array1D<Real> LUcolj(m);
96
97	// Outer loop.
98
99	for (int j = 0; j < n; j++) {
100
101	// Make a copy of the j-th column to localize references.
102
103	for (int i = 0; i < m; i++) {
104	LUcolj[i] = LU_[i][j];
105	}
106
107	// Apply previous transformations.
108
109	for (int i = 0; i < m; i++) {
110	LUrowi = LU_[i];
111
112	// Most of the time is spent in the following dot product.
113
114	int kmax = min(i,j);
115	double s = 0.0;
116	for (int k = 0; k < kmax; k++) {
117	s += LUrowi[k]*LUcolj[k];
118	}
119
120	LUrowi[j] = LUcolj[i] -= s;
121	}
122
123	// Find pivot and exchange if necessary.
124
125	int p = j;
126	for (int i = j+1; i < m; i++) {
127	if (abs(LUcolj[i]) > abs(LUcolj[p])) {
128	p = i;
129	}
130	}
131	if (p != j) {
132	int k=0;
133	for (k = 0; k < n; k++) {
134	double t = LU_[p][k];
135	LU_[p][k] = LU_[j][k];
136	LU_[j][k] = t;
137	}
138	k = piv[p];
139	piv[p] = piv[j];
140	piv[j] = k;
141	pivsign = -pivsign;
142	}
143
144	// Compute multipliers.
145
146	if ((j < m) && (LU_[j][j] != 0.0)) {
147	for (int i = j+1; i < m; i++) {
148	LU_[i][j] /= LU_[j][j];
149	}
150	}
151	}
152	}
153
154
155	/** Is the matrix nonsingular?
156	@return 1 (true) if upper triangular factor U (and hence A)
157	is nonsingular, 0 otherwise.
158	*/
159
160	int isNonsingular () {
161	for (int j = 0; j < n; j++) {
162	if (LU_[j][j] == 0)
163	return 0;
164	}
165	return 1;
166	}
167
168	/** Return lower triangular factor
169	@return L
170	*/
171
172	Array2D<Real> getL () {
173	Array2D<Real> L_(m,n);
174	for (int i = 0; i < m; i++) {
175	for (int j = 0; j < n; j++) {
176	if (i > j) {
177	L_[i][j] = LU_[i][j];
178	} else if (i == j) {
179	L_[i][j] = 1.0;
180	} else {
181	L_[i][j] = 0.0;
182	}
183	}
184	}
185	return L_;
186	}
187
188	/** Return upper triangular factor
189	@return U portion of LU factorization.
190	*/
191
192	Array2D<Real> getU () {
193	Array2D<Real> U_(n,n);
194	for (int i = 0; i < n; i++) {
195	for (int j = 0; j < n; j++) {
196	if (i <= j) {
197	U_[i][j] = LU_[i][j];
198	} else {
199	U_[i][j] = 0.0;
200	}
201	}
202	}
203	return U_;
204	}
205
206	/** Return pivot permutation vector
207	@return piv
208	*/
209
210	Array1D<int> getPivot () {
211	return piv;
212	}
213
214
215	/** Compute determinant using LU factors.
216	@return determinant of A, or 0 if A is not square.
217	*/
218
219	Real det () {
220	if (m != n) {
221	return Real(0);
222	}
223	Real d = Real(pivsign);
224	for (int j = 0; j < n; j++) {
225	d *= LU_[j][j];
226	}
227	return d;
228	}
229
230	/** Solve A*X = B
231	@param B A Matrix with as many rows as A and any number of columns.
232	@return X so that LUX = B(piv,:), if B is nonconformant, returns
233	0x0 (null) array.
234	*/
235
236	Array2D<Real> solve (const Array2D<Real> &B)
237	{
238
239	/* Dimensions: A is mxn, X is nxk, B is mxk */
240
241	if (B.dim1() != m) {
242	return Array2D<Real>(0,0);
243	}
244	if (!isNonsingular()) {
245	return Array2D<Real>(0,0);
246	}
247
248	// Copy right hand side with pivoting
249	int nx = B.dim2();
250
251
252	Array2D<Real> X = permute_copy(B, piv, 0, nx-1);
253
254	// Solve L*Y = B(piv,:)
255	for (int k = 0; k < n; k++) {
256	for (int i = k+1; i < n; i++) {
257	for (int j = 0; j < nx; j++) {
258	X[i][j] -= X[k][j]*LU_[i][k];
259	}
260	}
261	}
262	// Solve U*X = Y;
263	for (int k = n-1; k >= 0; k--) {
264	for (int j = 0; j < nx; j++) {
265	X[k][j] /= LU_[k][k];
266	}
267	for (int i = 0; i < k; i++) {
268	for (int j = 0; j < nx; j++) {
269	X[i][j] -= X[k][j]*LU_[i][k];
270	}
271	}
272	}
273	return X;
274	}
275
276
277	/** Solve A*x = b, where x and b are vectors of length equal
278	to the number of rows in A.
279
280	@param b a vector (Array1D> of length equal to the first dimension
281	of A.
282	@return x a vector (Array1D> so that LUx = b(piv), if B is nonconformant,
283	returns 0x0 (null) array.
284	*/
285
286	Array1D<Real> solve (const Array1D<Real> &b)
287	{
288
289	/* Dimensions: A is mxn, X is nxk, B is mxk */
290
291	if (b.dim1() != m) {
292	return Array1D<Real>();
293	}
294	if (!isNonsingular()) {
295	return Array1D<Real>();
296	}
297
298
299	Array1D<Real> x = permute_copy(b, piv);
300
301	// Solve L*Y = B(piv)
302	for (int k = 0; k < n; k++) {
303	for (int i = k+1; i < n; i++) {
304	x[i] -= x[k]*LU_[i][k];
305	}
306	}
307
308	// Solve U*X = Y;
309	for (int k = n-1; k >= 0; k--) {
310	x[k] /= LU_[k][k];
311	for (int i = 0; i < k; i++)
312	x[i] -= x[k]*LU_[i][k];
313	}
314
315
316	return x;
317	}
318
319	}; /* class LU */
320
321	} /* namespace JAMA */
322
323	#endif
324	/* JAMA_LU_H */