1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
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
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
|
/*
* BSD Licence:
* Copyright (c) 2001, 2002 Ben Houston [ ben@exocortex.org ]
* Exocortex Technologies [ www.exocortex.org ]
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the <ORGANIZATION> nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.
*/
using System;
using System.Diagnostics;
namespace Exocortex.DSP
{
// Comments? Questions? Bugs? Tell Ben Houston at ben@exocortex.org
// Version: May 4, 2002
/// <summary>
/// <p>A set of statistical utilities for complex number arrays</p>
/// </summary>
public class ComplexStats
{
//---------------------------------------------------------------------------------------------
private ComplexStats() {
}
//---------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------------------
/// <summary>
/// Calculate the sum
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public ComplexF Sum( ComplexF[] data ) {
Debug.Assert( data != null );
return SumRecursion( data, 0, data.Length );
}
static private ComplexF SumRecursion( ComplexF[] data, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= data.Length, "end = " + end + " and data.Length = " + data.Length );
if( ( end - start ) <= 1000 ) {
ComplexF sum = ComplexF.Zero;
for( int i = start; i < end; i ++ ) {
sum += data[ i ];
}
return sum;
}
else {
int middle = ( start + end ) >> 1;
return SumRecursion( data, start, middle ) + SumRecursion( data, middle, end );
}
}
/// <summary>
/// Calculate the sum
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public Complex Sum( Complex[] data ) {
Debug.Assert( data != null );
return SumRecursion( data, 0, data.Length );
}
static private Complex SumRecursion( Complex[] data, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= data.Length, "end = " + end + " and data.Length = " + data.Length );
if( ( end - start ) <= 1000 ) {
Complex sum = Complex.Zero;
for( int i = start; i < end; i ++ ) {
sum += data[ i ];
}
return sum;
}
else {
int middle = ( start + end ) >> 1;
return SumRecursion( data, start, middle ) + SumRecursion( data, middle, end );
}
}
//--------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------------------
/// <summary>
/// Calculate the sum of squares
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public ComplexF SumOfSquares( ComplexF[] data ) {
Debug.Assert( data != null );
return SumOfSquaresRecursion( data, 0, data.Length );
}
static private ComplexF SumOfSquaresRecursion( ComplexF[] data, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= data.Length, "end = " + end + " and data.Length = " + data.Length );
if( ( end - start ) <= 1000 ) {
ComplexF sumOfSquares = ComplexF.Zero;
for( int i = start; i < end; i ++ ) {
sumOfSquares += data[ i ] * data[ i ];
}
return sumOfSquares;
}
else {
int middle = ( start + end ) >> 1;
return SumOfSquaresRecursion( data, start, middle ) + SumOfSquaresRecursion( data, middle, end );
}
}
/// <summary>
/// Calculate the sum of squares
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public Complex SumOfSquares( Complex[] data ) {
Debug.Assert( data != null );
return SumOfSquaresRecursion( data, 0, data.Length );
}
static private Complex SumOfSquaresRecursion( Complex[] data, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= data.Length, "end = " + end + " and data.Length = " + data.Length );
if( ( end - start ) <= 1000 ) {
Complex sumOfSquares = Complex.Zero;
for( int i = start; i < end; i ++ ) {
sumOfSquares += data[ i ] * data[ i ];
}
return sumOfSquares;
}
else {
int middle = ( start + end ) >> 1;
return SumOfSquaresRecursion( data, start, middle ) + SumOfSquaresRecursion( data, middle, end );
}
}
//--------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------------------
/// <summary>
/// Calculate the mean (average)
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public ComplexF Mean( ComplexF[] data ) {
return ComplexStats.Sum( data ) / data.Length;
}
/// <summary>
/// Calculate the mean (average)
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public Complex Mean( Complex[] data ) {
return ComplexStats.Sum( data ) / data.Length;
}
/// <summary>
/// Calculate the variance
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public ComplexF Variance( ComplexF[] data ) {
Debug.Assert( data != null );
if( data.Length == 0 ) {
throw new DivideByZeroException( "length of data is zero" );
}
return ComplexStats.SumOfSquares( data ) / data.Length - ComplexStats.Sum( data );
}
/// <summary>
/// Calculate the variance
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public Complex Variance( Complex[] data ) {
Debug.Assert( data != null );
if( data.Length == 0 ) {
throw new DivideByZeroException( "length of data is zero" );
}
return ComplexStats.SumOfSquares( data ) / data.Length - ComplexStats.Sum( data );
}
/// <summary>
/// Calculate the standard deviation
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public ComplexF StdDev( ComplexF[] data ) {
Debug.Assert( data != null );
if( data.Length == 0 ) {
throw new DivideByZeroException( "length of data is zero" );
}
return ComplexMath.Sqrt( ComplexStats.Variance( data ) );
}
/// <summary>
/// Calculate the standard deviation
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
static public Complex StdDev( Complex[] data ) {
Debug.Assert( data != null );
if( data.Length == 0 ) {
throw new DivideByZeroException( "length of data is zero" );
}
return ComplexMath.Sqrt( ComplexStats.Variance( data ) );
}
//--------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------------------
/// <summary>
/// Calculate the root mean squared (RMS) error between two sets of data.
/// </summary>
/// <param name="alpha"></param>
/// <param name="beta"></param>
/// <returns></returns>
static public float RMSError( ComplexF[] alpha, ComplexF[] beta ) {
Debug.Assert( alpha != null );
Debug.Assert( beta != null );
Debug.Assert( beta.Length == alpha.Length );
return (float) Math.Sqrt( SumOfSquaredErrorRecursion( alpha, beta, 0, alpha.Length ) );
}
static private float SumOfSquaredErrorRecursion( ComplexF[] alpha, ComplexF[] beta, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= alpha.Length, "end = " + end + " and alpha.Length = " + alpha.Length );
Debug.Assert( beta.Length == alpha.Length );
if( ( end - start ) <= 1000 ) {
float sumOfSquaredError = 0;
for( int i = start; i < end; i ++ ) {
ComplexF delta = beta[ i ] - alpha[ i ];
sumOfSquaredError += ( delta.Re * delta.Re ) + ( delta.Im * delta.Im );
}
return sumOfSquaredError;
}
else {
int middle = ( start + end ) >> 1;
return SumOfSquaredErrorRecursion( alpha, beta, start, middle ) + SumOfSquaredErrorRecursion( alpha, beta, middle, end );
}
}
/// <summary>
/// Calculate the root mean squared (RMS) error between two sets of data.
/// </summary>
/// <param name="alpha"></param>
/// <param name="beta"></param>
/// <returns></returns>
static public double RMSError( Complex[] alpha, Complex[] beta ) {
Debug.Assert( alpha != null );
Debug.Assert( beta != null );
Debug.Assert( beta.Length == alpha.Length );
return Math.Sqrt( SumOfSquaredErrorRecursion( alpha, beta, 0, alpha.Length ) );
}
static private double SumOfSquaredErrorRecursion( Complex[] alpha, Complex[] beta, int start, int end ) {
Debug.Assert( 0 <= start, "start = " + start );
Debug.Assert( start < end, "start = " + start + " and end = " + end );
Debug.Assert( end <= alpha.Length, "end = " + end + " and alpha.Length = " + alpha.Length );
Debug.Assert( beta.Length == alpha.Length );
if( ( end - start ) <= 1000 ) {
double sumOfSquaredError = 0;
for( int i = start; i < end; i ++ ) {
Complex delta = beta[ i ] - alpha[ i ];
sumOfSquaredError += ( delta.Re * delta.Re ) + ( delta.Im * delta.Im );
}
return sumOfSquaredError;
}
else {
int middle = ( start + end ) >> 1;
return SumOfSquaredErrorRecursion( alpha, beta, start, middle ) + SumOfSquaredErrorRecursion( alpha, beta, middle, end );
}
}
}
}
|