src/math/jama_cholesky.hpp

#ifndef JAMA_CHOLESKY_H
#define JAMA_CHOLESKY_H

#include <cmath>
        /* needed for sqrt() below. */


namespace JAMA
{

using namespace TNT;

/** 
   <P>
   For a symmetric, positive definite matrix A, this function
   computes the Cholesky factorization, i.e. it computes a lower 
   triangular matrix L such that A = L*L'.
   If the matrix is not symmetric or positive definite, the function
   computes only a partial decomposition.  This can be tested with
   the is_spd() flag.

   <p>Typical usage looks like:
   <pre>
        Array2D<double> A(n,n);
        Array2D<double> L;

         ... 

        Cholesky<double> chol(A);

        if (chol.is_spd())
                L = chol.getL();
                
        else
                cout << "factorization was not complete.\n";

        </pre>


   <p>
        (Adapted from JAMA, a Java Matrix Library, developed by jointly 
        by the Mathworks and NIST; see  http://math.nist.gov/javanumerics/jama).

   */

template <class Real>
class Cholesky
{
        Array2D<Real> L_;               // lower triangular factor
        int isspd;                              // 1 if matrix to be factored was SPD

public:

        Cholesky();
        Cholesky(const Array2D<Real> &A);
        Array2D<Real> getL() const;
        Array1D<Real> solve(const Array1D<Real> &B);
        Array2D<Real> solve(const Array2D<Real> &B);
        int is_spd() const;

};

template <class Real>
Cholesky<Real>::Cholesky() : L_(0,0), isspd(0) {}

/**
        @return 1, if original matrix to be factored was symmetric 
                positive-definite (SPD).
*/
template <class Real>
int Cholesky<Real>::is_spd() const
{
        return isspd;
}

/**
        @return the lower triangular factor, L, such that L*L'=A.
*/
template <class Real>
Array2D<Real> Cholesky<Real>::getL() const
{
        return L_;
}

/**
        Constructs a lower triangular matrix L, such that L*L'= A.
        If A is not symmetric positive-definite (SPD), only a
        partial factorization is performed.  If is_spd()
        evalutate true (1) then the factorizaiton was successful.
*/
template <class Real>
Cholesky<Real>::Cholesky(const Array2D<Real> &A)
{


        int m = A.dim1();
        int n = A.dim2();
        
        isspd = (m == n);

        if (m != n)
        {
                L_ = Array2D<Real>(0,0);
                return;
        }

        L_ = Array2D<Real>(n,n);


      // Main loop.
     for (int j = 0; j < n; j++) 
         {
        Real d(0.0);
        for (int k = 0; k < j; k++) 
                {
            Real s(0.0);
            for (int i = 0; i < k; i++) 
                        {
               s += L_[k][i]*L_[j][i];
            }
            L_[j][k] = s = (A[j][k] - s)/L_[k][k];
            d = d + s*s;
            isspd = isspd && (A[k][j] == A[j][k]); 
         }
         d = A[j][j] - d;
         isspd = isspd && (d > 0.0);
         L_[j][j] = sqrt(d > 0.0 ? d : 0.0);
         for (int k = j+1; k < n; k++) 
                 {
            L_[j][k] = 0.0;
         }
        }
}

/**

        Solve a linear system A*x = b, using the previously computed
        cholesky factorization of A: L*L'.

   @param  B   A Matrix with as many rows as A and any number of columns.
   @return     x so that L*L'*x = b.  If b is nonconformat, or if A
                                was not symmetric posidtive definite, a null (0x0)
                                                array is returned.
*/
template <class Real>
Array1D<Real> Cholesky<Real>::solve(const Array1D<Real> &b)
{
        int n = L_.dim1();
        if (b.dim1() != n)
                return Array1D<Real>();


        Array1D<Real> x = b.copy();


      // Solve L*y = b;
      for (int k = 0; k < n; k++) 
          {
         for (int i = 0; i < k; i++) 
               x[k] -= x[i]*L_[k][i];
                 x[k] /= L_[k][k];
                
      }

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

        return x;
}


/**

        Solve a linear system A*X = B, using the previously computed
        cholesky factorization of A: L*L'.

   @param  B   A Matrix with as many rows as A and any number of columns.
   @return     X so that L*L'*X = B.  If B is nonconformat, or if A
                                was not symmetric posidtive definite, a null (0x0)
                                                array is returned.
*/
template <class Real>
Array2D<Real> Cholesky<Real>::solve(const Array2D<Real> &B)
{
        int n = L_.dim1();
        if (B.dim1() != n)
                return Array2D<Real>();


        Array2D<Real> X = B.copy();
        int nx = B.dim2();

// Cleve's original code
#if 0
      // Solve L*Y = B;
      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]*L_[k][i];
            }
         }
         for (int j = 0; j < nx; j++) {
            X[k][j] /= L_[k][k];
         }
      }

      // Solve L'*X = Y;
      for (int k = n-1; k >= 0; k--) {
         for (int j = 0; j < nx; j++) {
            X[k][j] /= L_[k][k];
         }
         for (int i = 0; i < k; i++) {
            for (int j = 0; j < nx; j++) {
               X[i][j] -= X[k][j]*L_[k][i];
            }
         }
      }
#endif


      // Solve L*y = b;
          for (int j=0; j< nx; j++)
          {
        for (int k = 0; k < n; k++) 
                {
                        for (int i = 0; i < k; i++) 
               X[k][j] -= X[i][j]*L_[k][i];
                    X[k][j] /= L_[k][k];
                 }
      }

      // Solve L'*X = Y;
     for (int j=0; j<nx; j++)
         {
        for (int k = n-1; k >= 0; k--) 
                {
                for (int i = k+1; i < n; i++) 
               X[k][j] -= X[i][j]*L_[i][k];
                X[k][j] /= L_[k][k];
                }
      }


        return X;
}


}
// namespace JAMA

#endif
// JAMA_CHOLESKY_H
Revision:	3495
Committed:	Tue Apr 7 20:16:26 2009 UTC (15 years, 2 months ago) by gezelter
File size:	5232 byte(s)
Log Message:	adding jama and tnt libraries for various linear algebra routines
#	Content
1	#ifndef JAMA_CHOLESKY_H
2	#define JAMA_CHOLESKY_H
3
4	#include <cmath>
5	/* needed for sqrt() below. */
6
7
8	namespace JAMA
9	{
10
11	using namespace TNT;
12
13	/**
14	<P>
15	For a symmetric, positive definite matrix A, this function
16	computes the Cholesky factorization, i.e. it computes a lower
17	triangular matrix L such that A = L*L'.
18	If the matrix is not symmetric or positive definite, the function
19	computes only a partial decomposition. This can be tested with
20	the is_spd() flag.
21
22	<p>Typical usage looks like:
23	<pre>
24	Array2D<double> A(n,n);
25	Array2D<double> L;
26
27	...
28
29	Cholesky<double> chol(A);
30
31	if (chol.is_spd())
32	L = chol.getL();
33
34	else
35	cout << "factorization was not complete.\n";
36
37	</pre>
38
39
40	<p>
41	(Adapted from JAMA, a Java Matrix Library, developed by jointly
42	by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).
43
44	*/
45
46	template <class Real>
47	class Cholesky
48	{
49	Array2D<Real> L_; // lower triangular factor
50	int isspd; // 1 if matrix to be factored was SPD
51
52	public:
53
54	Cholesky();
55	Cholesky(const Array2D<Real> &A);
56	Array2D<Real> getL() const;
57	Array1D<Real> solve(const Array1D<Real> &B);
58	Array2D<Real> solve(const Array2D<Real> &B);
59	int is_spd() const;
60
61	};
62
63	template <class Real>
64	Cholesky<Real>::Cholesky() : L_(0,0), isspd(0) {}
65
66	/**
67	@return 1, if original matrix to be factored was symmetric
68	positive-definite (SPD).
69	*/
70	template <class Real>
71	int Cholesky<Real>::is_spd() const
72	{
73	return isspd;
74	}
75
76	/**
77	@return the lower triangular factor, L, such that L*L'=A.
78	*/
79	template <class Real>
80	Array2D<Real> Cholesky<Real>::getL() const
81	{
82	return L_;
83	}
84
85	/**
86	Constructs a lower triangular matrix L, such that L*L'= A.
87	If A is not symmetric positive-definite (SPD), only a
88	partial factorization is performed. If is_spd()
89	evalutate true (1) then the factorizaiton was successful.
90	*/
91	template <class Real>
92	Cholesky<Real>::Cholesky(const Array2D<Real> &A)
93	{
94
95
96	int m = A.dim1();
97	int n = A.dim2();
98
99	isspd = (m == n);
100
101	if (m != n)
102	{
103	L_ = Array2D<Real>(0,0);
104	return;
105	}
106
107	L_ = Array2D<Real>(n,n);
108
109
110	// Main loop.
111	for (int j = 0; j < n; j++)
112	{
113	Real d(0.0);
114	for (int k = 0; k < j; k++)
115	{
116	Real s(0.0);
117	for (int i = 0; i < k; i++)
118	{
119	s += L_[k][i]*L_[j][i];
120	}
121	L_[j][k] = s = (A[j][k] - s)/L_[k][k];
122	d = d + s*s;
123	isspd = isspd && (A[k][j] == A[j][k]);
124	}
125	d = A[j][j] - d;
126	isspd = isspd && (d > 0.0);
127	L_[j][j] = sqrt(d > 0.0 ? d : 0.0);
128	for (int k = j+1; k < n; k++)
129	{
130	L_[j][k] = 0.0;
131	}
132	}
133	}
134
135	/**
136
137	Solve a linear system A*x = b, using the previously computed
138	cholesky factorization of A: L*L'.
139
140	@param B A Matrix with as many rows as A and any number of columns.
141	@return x so that LL'x = b. If b is nonconformat, or if A
142	was not symmetric posidtive definite, a null (0x0)
143	array is returned.
144	*/
145	template <class Real>
146	Array1D<Real> Cholesky<Real>::solve(const Array1D<Real> &b)
147	{
148	int n = L_.dim1();
149	if (b.dim1() != n)
150	return Array1D<Real>();
151
152
153	Array1D<Real> x = b.copy();
154
155
156	// Solve L*y = b;
157	for (int k = 0; k < n; k++)
158	{
159	for (int i = 0; i < k; i++)
160	x[k] -= x[i]*L_[k][i];
161	x[k] /= L_[k][k];
162
163	}
164
165	// Solve L'*X = Y;
166	for (int k = n-1; k >= 0; k--)
167	{
168	for (int i = k+1; i < n; i++)
169	x[k] -= x[i]*L_[i][k];
170	x[k] /= L_[k][k];
171	}
172
173	return x;
174	}
175
176
177	/**
178
179	Solve a linear system A*X = B, using the previously computed
180	cholesky factorization of A: L*L'.
181
182	@param B A Matrix with as many rows as A and any number of columns.
183	@return X so that LL'X = B. If B is nonconformat, or if A
184	was not symmetric posidtive definite, a null (0x0)
185	array is returned.
186	*/
187	template <class Real>
188	Array2D<Real> Cholesky<Real>::solve(const Array2D<Real> &B)
189	{
190	int n = L_.dim1();
191	if (B.dim1() != n)
192	return Array2D<Real>();
193
194
195	Array2D<Real> X = B.copy();
196	int nx = B.dim2();
197
198	// Cleve's original code
199	#if 0
200	// Solve L*Y = B;
201	for (int k = 0; k < n; k++) {
202	for (int i = k+1; i < n; i++) {
203	for (int j = 0; j < nx; j++) {
204	X[i][j] -= X[k][j]*L_[k][i];
205	}
206	}
207	for (int j = 0; j < nx; j++) {
208	X[k][j] /= L_[k][k];
209	}
210	}
211
212	// Solve L'*X = Y;
213	for (int k = n-1; k >= 0; k--) {
214	for (int j = 0; j < nx; j++) {
215	X[k][j] /= L_[k][k];
216	}
217	for (int i = 0; i < k; i++) {
218	for (int j = 0; j < nx; j++) {
219	X[i][j] -= X[k][j]*L_[k][i];
220	}
221	}
222	}
223	#endif
224
225
226	// Solve L*y = b;
227	for (int j=0; j< nx; j++)
228	{
229	for (int k = 0; k < n; k++)
230	{
231	for (int i = 0; i < k; i++)
232	X[k][j] -= X[i][j]*L_[k][i];
233	X[k][j] /= L_[k][k];
234	}
235	}
236
237	// Solve L'*X = Y;
238	for (int j=0; j<nx; j++)
239	{
240	for (int k = n-1; k >= 0; k--)
241	{
242	for (int i = k+1; i < n; i++)
243	X[k][j] -= X[i][j]*L_[i][k];
244	X[k][j] /= L_[k][k];
245	}
246	}
247
248
249
250	return X;
251	}
252
253
254	}
255	// namespace JAMA
256
257	#endif
258	// JAMA_CHOLESKY_H