-
Notifications
You must be signed in to change notification settings - Fork 0
/
poly1.cxx
418 lines (343 loc) · 13.6 KB
/
poly1.cxx
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
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
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
// Sean Shelton, Patrick Vidican
// Feb 7 2016
// poly1.cxx
// Duplicated our original solution with the purpose of trying to figure out each part slowly, one at a time.
// Currently working on: test 2, the derivative
// Need to overload assignment operator
// Destructor is causing certain problems, not implemented for now.
#include <iostream>
#include <cassert>
#include "poly1.h"
#include <cmath>
#include <climits>
#include <algorithm>
using namespace std;
//test 2 (derivative) FAIL
//test 11 (assignment operator) FAIL (incorrect degree)
//test 5 (operator +) ERROR
//test 6 (operator -) ERROR
//test 7 (operator *) malloc corruption
//test 9 (find_root) FAIL not implemented
//test 8 (operator <<) PASS
//test 1 (basics) PASS
//test 10 (copy constructor) PASS
//test 4 (next and prev) PASS
//test 3 (eval and operator() ) PASS
namespace main_savitch_4 {
bool near(double a, double b);
bool near(double a, double b) {
const double small = 0.0001;
return (fabs(a-b) < small) || (fabs(1-a/b) < small);
}
//constructor
polynomial::polynomial(double c, unsigned int exponent) {
// assert(exponent <= DEFAULT_CAPACITY);
if (near(c, 0))
current_degree = 0;
//size = 1; //might change to 0 if needed
else
current_degree = exponent;
//size = exponent + 1;
/*for (int i=DEFAULT_CAPACITY; i>current_degree; i--)
*(coef + i) = 0;*/
//if (current_degree < DEFAULT_CAPACITY)
if (exponent == 0)
size = DEFAULT_CAPACITY;
else
size = exponent + 1;
//coef = new double [current_degree + 1];
coef = new double[size];
for (int j=0; j < size; j++)
*(coef + j) = 0;
*(coef + exponent) = c;
}
// copy constructor
polynomial::polynomial(const polynomial &source) {
/*if (source.current_degree < DEFAULT_CAPACITY)
size = DEFAULT_CAPACITY;
//coef = new double[DEFAULT_CAPACITY];
else
size = source.size;
//coef = new double[source.current_degree + 1];*/
size = source.size;
coef = new double[size];
current_degree = source.current_degree;
//copy(source.coef, source.coef + size, coef);
copy(source.coef, source.coef + size, coef);
}
polynomial::~polynomial( ) {
//cout << "delete!\n";
//if (coef)
delete [] coef;
}
// not tested yet
polynomial& polynomial::operator =(const polynomial& source){
//polynomial p;
double *new_coef;
// Check for possible self-assignment:
if (this == &source)
return *this;
// If needed, allocate an array with a different size:
if (this->size != source.size) {
new_coef = new double[ source.size ];
delete [ ] this->coef;
this->coef = new_coef;
this->size = source.size;
}
// Copy the data from the source array:
this->current_degree = source.current_degree;
copy(source.coef, source.coef + source.size, this->coef);
return *this;
}
//modification members
void polynomial::add_to_coef(double amount, unsigned int exponent) {
// assert(exponent <= DEFAULT_CAPACITY);
if ((current_degree < exponent) && (amount != 0))
current_degree = exponent;
if ((exponent >= size) && (amount != 0)) {
reserve(exponent+1);
size = exponent + 1;
}
*(coef + exponent) += amount;
//if (*(coef + current_degree) == 0)
if (near(0, coef[current_degree])) {
current_degree = previous_term(current_degree);
if (current_degree == UINT_MAX)
current_degree = 0;
//coef[current_degree] = 0;
}
/* for (int i = 0; i <= DEFAULT_CAPACITY; i++) {
if ( coef[i] != 0){
current_degree = i;
}
}*/
}
void polynomial::assign_coef(double coefficient, unsigned int exponent) {
// assert(exponent <= DEFAULT_CAPACITY);
//coef[exponent] = coefficient;
if (exponent >= size) {
size = exponent + 1;
//reserve(exponent+1);
reserve(size);
}
*(coef + exponent) = coefficient;
/*for (int i = 0; i <= DEFAULT_CAPACITY; i++) {
if ( coef[i] != 0){
current_degree = i;
}
}*/
if (current_degree < exponent)
current_degree = exponent;
if (*(coef + current_degree) == 0) {
current_degree = previous_term(current_degree);
if (current_degree == UINT_MAX)
current_degree = 0;
}
}
void polynomial::clear(){
for (int i=0; i<=degree(); i++)
*(coef + i) = 0;
//coef[i] = 0;
current_degree = 0;
}
void polynomial::reserve(unsigned int number) {
/*if (number == size)
return;*/
if (number < size)
number = degree()+1;
//return;
//number = size;
number += 5;
double *largerCoef = new double[number];
for (int i = 0; i < number; i++)
largerCoef[i] = 0;
//copy(coef, coef + size, largerCoef);
copy(coef, coef + size+1, largerCoef);
delete [ ] coef;
coef = largerCoef;
size = number;
}
double polynomial::coefficient(unsigned int exponent) const{
//if (exponent > DEFAULT_CAPACITY)
if (exponent > size)
return 0;
else
return( *(coef + exponent) );
}
// FROM HERE ON OUT DONT USE PRIVATE VARIABLES as per directions
polynomial polynomial::derivative() const{
polynomial d(0,0);
if ( degree() == 0 ){
return d;
}
//polynomial d( degree()*coefficient( degree() ), degree()-1 );
for (int i = degree(); i != UINT_MAX; i = previous_term(i)){
if (i == 0)
return d;
//d.assign_coef(0, 0);
else
d.assign_coef(i*coefficient(i), i-1);
}
/*for (int j = 0; j <= degree(); j++)
d.assign_coef( coefficient(j+1)*(j+1), j );*/
return d;
}
double polynomial::eval(double x) const{
double result = coefficient(0); // i changed this to use the function rather than accessing the private array directly
for (int i=1; i<=degree(); i++){
result += coefficient(i) * pow( x, i);
}
return( result );
}
void polynomial::find_root(
double& answer,
bool& success,
unsigned int& iterations,
double guess,
unsigned int maximum_iterations,
double epsilon
)
const {
assert( epsilon > 0 ); //assert precondition that epsilon must be greater than zero
polynomial d( derivative() ); // calculate derivative of the polynomial
answer = guess; // set answer to starting guess
double f = eval( answer ); // initialize a variable f by evaluating polynomial at answer
double fprime = d.eval( answer ); // initialize a variable fprime by evaluating derivative at answer
// set iterations to 0 // loop until maximum iterations or until either |f| or |fprime| is less than or equal to epsilon: // increment iterations
/*for (iterations = 0; iterations <= maximum_iterations|| ((fabs(fprime) > epsilon)||(fabs(f) > epsilon)); iterations++){
answer -= (f/fprime); // calculate new answer as prior answer - f / fprime
f = eval( answer ); // reset f by evaluating polynomial at new answer
fprime = d.eval( answer ); // reset fprime by evaluating derivative at new answer
}
if ( fabs(f) < epsilon ) // set success true if |f| is less than epsilon, or false otherwise
success = true;
else
success = false;*/
for (iterations = 0; iterations < maximum_iterations; iterations++){
if (fabs(f) < epsilon)
success = true;
else
success = false;
if ((fabs(fprime) <= epsilon)||(fabs(f) <= epsilon)) {
//success = true;
return;
}
answer -= (f/fprime); // calculate new answer as prior answer - f / fprime
f = eval( answer ); // reset f by evaluating polynomial at new answer
fprime = d.eval( answer ); // reset fprime by evaluating derivative at new answer
}
//success = false;
}
unsigned int polynomial::next_term(unsigned int e) const{
for (int i = (e+1); i < size /*DEFAULT_CAPACITY*/; i++){
if (coefficient(i) != 0)
return i;
}
return 0;
}
unsigned int polynomial::previous_term(unsigned int e) const{
//int prev = UINT_MAX;
/*for (int i = 0; i < e; i++){
if (coefficient(i) != 0)
prev = i;
}*/
for (int i = e-1; i >= 0; i--) {
//if (coefficient(i) != 0) {
if (fabs(coefficient(i))-0 >= 0.0001)
return i;
}
//return prev;
return UINT_MAX;
}
//constant operator is inline so nothing to do here
//nonmember binary operators
polynomial operator +(const polynomial& p1, const polynomial& p2){
//double sum;
unsigned int largest_degree = 0;
if (p1.degree() > p2.degree())
largest_degree = p1.degree();
else
largest_degree = p2.degree();
polynomial polySum(0, largest_degree);
//polySum.reserve(largest_degree + 1);
/*for (int i = 0; i <= largest_degree; i++) {
//sum = (p1.coefficient(i) + p2.coefficient(i));
//polySum.assign_coef
polySum.add_to_coef(p1.coefficient(i), i);
polySum.add_to_coef(p2.coefficient(i), i);
}*/
//polynomial polySum;
for (int i = p1.degree(); i != UINT_MAX; i = p1.previous_term(i))
polySum.add_to_coef(p1.coefficient(i), i);
for (int j = p2.degree(); j != UINT_MAX; j = p2.previous_term(j))
polySum.add_to_coef(p2.coefficient(j), j);
return polySum;
}
polynomial operator -(const polynomial& p1, const polynomial& p2){
unsigned int largest_degree = 0;
if (p1.degree() >= p2.degree())
largest_degree = p1.degree();
else
largest_degree = p2.degree();
polynomial polySum(0, largest_degree);
/*for (int i = 0; i <= largest_degree; i++) {
//sum = (p1.coefficient(i) + p2.coefficient(i));
//polySum.assign_coef
polySum.add_to_coef(p1.coefficient(i), i);
polySum.add_to_coef((p2.coefficient(i) * -1), i);
}*/
//polynomial polySum;
for (int i = p1.degree(); i != UINT_MAX; i = p1.previous_term(i))
polySum.add_to_coef(p1.coefficient(i), i);
for (int j = p2.degree(); j != UINT_MAX; j = p2.previous_term(j))
polySum.add_to_coef((p2.coefficient(j) * -1), j);
return polySum;
}
polynomial operator *(const polynomial& p1, const polynomial& p2){
unsigned int largest_degree = 0;
if (p1.degree() >= p2.degree())
largest_degree = p1.degree();
else
largest_degree = p2.degree();
polynomial product(0, largest_degree);
/*for (int i = 0; i <= p1.degree(); i++) {
if (p1.coefficient(i) != 0) {
for (int j = 0; j <= p2.degree(); j++) {
if (p2.coefficient(j) != 0)
product.add_to_coef((p1.coefficient(i) * p2.coefficient(j)), (i+j));
}
}
}*/
for (int i = p1.degree(); i != UINT_MAX; i = p1.previous_term(i)) {
for (int j = p2.degree(); j != UINT_MAX; j = p2.previous_term(j))
product.add_to_coef((p1.coefficient(i) * p2.coefficient(j)), (i+j));
}
return product;
}
//nonmember output function
std::ostream& operator << (std::ostream& out, const polynomial& p){
for (int i = p.degree(); i >= 0; i--) {
// this part is just dealing with the coefficients
if (i == p.degree())
out << p.coefficient( p.degree() );
if (p.coefficient(i) < 0 && i != p.degree())
out << p.coefficient(i) * -1;
if (p.coefficient(i) > 0 && i != p.degree() && !(near(0, p.coefficient(i))))
out << p.coefficient(i);
// below is dealing with the x and degrees
if (p.coefficient(i) != 0 && i == 1 && !(near(0, p.coefficient(i))))
out << "x";
if (p.coefficient(i) != 0 && i > 1 && !(near(0, p.coefficient(i))))
out << "x^" << i;
// below deals with + or -
if (p.previous_term(i) != UINT_MAX) {
if (p.coefficient(p.previous_term(i)) < 0 && p.coefficient(i-1) != 0 && !(near(0, p.coefficient(i-1))))
out << " - ";
if (p.coefficient(p.previous_term(i)) > 0 && p.coefficient(i-1) != 0 && !(near(0, p.coefficient(p.previous_term(i)))) && !(near(0, p.coefficient(i-1))))
out << " + ";
}
}
out << "\n";
return out;
}
}