load lecture4.mat
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempLinearNPlot,'b',timePlot,TempSplineNPlot,'r')
polyfit(timeMeasuredN,TempMeasuredN,1)
ans =
-6.3385 12.4480
coefLinFit=polyfit(timeMeasuredN,TempMeasuredN,1)
coefLinFit =
-6.3385 12.4480
TempLinFitPlot=polyval(coefLinFit,timePlot)
TempLinFitPlot =
Columns 1 through 5
12.4480 12.4057 12.3635 12.3212 12.2790
Columns 6 through 10
12.2367 12.1945 12.1522 12.1100 12.0677
Columns 11 through 15
12.0254 11.9832 11.9409 11.8987 11.8564
Columns 16 through 20
11.8142 11.7719 11.7296 11.6874 11.6451
Columns 21 through 25
11.6029 11.5606 11.5184 11.4761 11.4338
Columns 26 through 30
11.3916 11.3493 11.3071 11.2648 11.2226
Columns 31 through 35
11.1803 11.1381 11.0958 11.0535 11.0113
Columns 36 through 40
10.9690 10.9268 10.8845 10.8423 10.8000
Columns 41 through 45
10.7577 10.7155 10.6732 10.6310 10.5887
Columns 46 through 50
10.5465 10.5042 10.4620 10.4197 10.3774
Columns 51 through 55
10.3352 10.2929 10.2507 10.2084 10.1662
Columns 56 through 60
10.1239 10.0816 10.0394 9.9971 9.9549
Columns 61 through 65
9.9126 9.8704 9.8281 9.7858 9.7436
Columns 66 through 70
9.7013 9.6591 9.6168 9.5746 9.5323
Columns 71 through 75
9.4901 9.4478 9.4055 9.3633 9.3210
Columns 76 through 80
9.2788 9.2365 9.1943 9.1520 9.1097
Columns 81 through 85
9.0675 9.0252 8.9830 8.9407 8.8985
Columns 86 through 90
8.8562 8.8140 8.7717 8.7294 8.6872
Columns 91 through 95
8.6449 8.6027 8.5604 8.5182 8.4759
Columns 96 through 100
8.4336 8.3914 8.3491 8.3069 8.2646
Columns 101 through 105
8.2224 8.1801 8.1378 8.0956 8.0533
Columns 106 through 110
8.0111 7.9688 7.9266 7.8843 7.8421
Columns 111 through 115
7.7998 7.7575 7.7153 7.6730 7.6308
Columns 116 through 120
7.5885 7.5463 7.5040 7.4617 7.4195
Columns 121 through 125
7.3772 7.3350 7.2927 7.2505 7.2082
Columns 126 through 130
7.1660 7.1237 7.0814 7.0392 6.9969
Columns 131 through 135
6.9547 6.9124 6.8702 6.8279 6.7856
Columns 136 through 140
6.7434 6.7011 6.6589 6.6166 6.5744
Columns 141 through 145
6.5321 6.4898 6.4476 6.4053 6.3631
Columns 146 through 150
6.3208 6.2786 6.2363 6.1941 6.1518
Columns 151 through 155
6.1095 6.0673 6.0250 5.9828 5.9405
Columns 156 through 160
5.8983 5.8560 5.8137 5.7715 5.7292
Columns 161 through 165
5.6870 5.6447 5.6025 5.5602 5.5180
Columns 166 through 170
5.4757 5.4334 5.3912 5.3489 5.3067
Columns 171 through 175
5.2644 5.2222 5.1799 5.1376 5.0954
Columns 176 through 180
5.0531 5.0109 4.9686 4.9264 4.8841
Columns 181 through 185
4.8418 4.7996 4.7573 4.7151 4.6728
Columns 186 through 190
4.6306 4.5883 4.5461 4.5038 4.4615
Columns 191 through 195
4.4193 4.3770 4.3348 4.2925 4.2503
Columns 196 through 200
4.2080 4.1657 4.1235 4.0812 4.0390
Columns 201 through 205
3.9967 3.9545 3.9122 3.8700 3.8277
Columns 206 through 210
3.7854 3.7432 3.7009 3.6587 3.6164
Columns 211 through 215
3.5742 3.5319 3.4896 3.4474 3.4051
Columns 216 through 220
3.3629 3.3206 3.2784 3.2361 3.1939
Columns 221 through 225
3.1516 3.1093 3.0671 3.0248 2.9826
Columns 226 through 230
2.9403 2.8981 2.8558 2.8135 2.7713
Columns 231 through 235
2.7290 2.6868 2.6445 2.6023 2.5600
Columns 236 through 240
2.5177 2.4755 2.4332 2.3910 2.3487
Columns 241 through 245
2.3065 2.2642 2.2220 2.1797 2.1374
Columns 246 through 250
2.0952 2.0529 2.0107 1.9684 1.9262
Columns 251 through 255
1.8839 1.8416 1.7994 1.7571 1.7149
Columns 256 through 260
1.6726 1.6304 1.5881 1.5459 1.5036
Columns 261 through 265
1.4613 1.4191 1.3768 1.3346 1.2923
Columns 266 through 270
1.2501 1.2078 1.1655 1.1233 1.0810
Columns 271 through 275
1.0388 0.9965 0.9543 0.9120 0.8697
Columns 276 through 280
0.8275 0.7852 0.7430 0.7007 0.6585
Columns 281 through 285
0.6162 0.5740 0.5317 0.4894 0.4472
Columns 286 through 290
0.4049 0.3627 0.3204 0.2782 0.2359
Columns 291 through 295
0.1936 0.1514 0.1091 0.0669 0.0246
Columns 296 through 300
-0.0176 -0.0599 -0.1021 -0.1444 -0.1867
Column 301
-0.2289
TempLinFitPlot=polyval(coefLinFit,timePlot);
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempLinFitPlot,'y')
coefQuadFit=polyfit(timeMeasuredN,TempMeasuredN,2)
coefQuadFit =
2.7259 -11.7902 14.2187
TempQuadFitPlot=polyval(coefQuadFit,timePlot);
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempQuadFitPlot,'c')
coefQuartFit=polyfit(timeMeasuredN,TempMeasuredN,4)
coefQuartFit =
1.1746 -5.3555 10.6889 -15.9337 14.6908
TempQuartFitPlot=polyval(coefQuartFit,timePlot);
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempQuartFitPlot,'c')
coefCubeFit=polyfit(timeMeasuredN,TempMeasuredN,3)
coefCubeFit =
-0.6573 4.6977 -13.3478 14.4617
TempCubeFitPlot=polyval(coefCubeFit,timePlot);
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempCubFitPlot,'m')
{Undefined function or variable 'TempCubFitPlot'.}
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempCubeFitPlot,'m')
errQuartFitMax=max(abs(TempQuartFitPlot-TempExactFunPlot))
{Undefined function or variable 'TempExactFunPlot'.}
errQuartFitMax=max(abs(TempQuartFitPlot-TempExactPlot))
errQuartFitMax =
0.4684
errLinearNMax
errLinearNMax =
1.7657
errSplineNMax
errSplineNMax =
2.0296
qExact=TempExactFun(2)/(-1.1)-TempExactFun(0)/(-1.1)
qExact =
11.8021
integral(TempExactFun,0,2)
ans =
11.8021
format long
integral(TempExactFun,0,2)
ans =
11.802067170827206
qExact
qExact =
11.802067170827204
integral(@(t) interp1(timeMeasured,TempMeasured,t),0,2)
ans =
12.095000369254418
integral(@(t) spline(timeMeasured,TempMeasured,t),0,2)
ans =
11.803333333333333
integral(@(t) polyval(coefLinFit,t),0,2)
ans =
12.219084009333578
integral(@(t) polyval(coefQuadFit,t),0,2)
ans =
12.125891672886226
integral(@(t) polyval(coefQuartFit,t),0,2)
ans =
12.113011014231544
integral(@(t) spline(timeMeasuredN,TempMeasuredN,t),0,2)
ans =
12.171005745875888
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempLinearNPlot,'b',timePlot,TempSplineNPlot,'r')
plot(timeMeasuredN,TempMeasuredN,'ok',timePlot,TempExactPlot,'--k',timePlot,TempLinearPlot,'b',timePlot,TempSplinePlot,'r')
plot(timeMeasured,TempMeasured,'ok',timePlot,TempExactPlot,'--k',timePlot,TempLinearPlot,'b',timePlot,TempSplinePlot,'r')
derCoefLinFit=polyder(CoefLinFit)
{Undefined function or variable 'CoefLinFit'.}
derCoefLinFit=polyder(coefLinFit)
derCoefLinFit =
-6.338460399026184
coefLinFit
coefLinFit =
-6.338460399026184 12.448002403692973
coefQuadFit
coefQuadFit =
Columns 1 through 2
2.725875841084907 -11.790212081196001
Column 3
14.218656796192571
derCoefQuadFit=polyder(coefQuadFit)
derCoefQuadFit =
5.451751682169815 -11.790212081196001
coefQuartFit
coefQuartFit =
Columns 1 through 2
1.174559586955105 -5.355528078839982
Columns 3 through 4
10.688914570008901 -15.933691226836668
Column 5
14.690776120030867
derCoefQuartFit=polyder(coefQuartFit)
derCoefQuartFit =
Columns 1 through 2
4.698238347820421 -16.066584236519947
Columns 3 through 4
21.377829140017802 -15.933691226836668
derExactPlot=-1.1*TempExactPlot;
derLinFitPlot=polyval(derCoefLinFit,timePlot)
derLinFitPlot =
Columns 1 through 2
-6.338460399026184 -6.338460399026184
Columns 3 through 4
-6.338460399026184 -6.338460399026184
Columns 5 through 6
-6.338460399026184 -6.338460399026184
Columns 7 through 8
-6.338460399026184 -6.338460399026184
Columns 9 through 10
-6.338460399026184 -6.338460399026184
Columns 11 through 12
-6.338460399026184 -6.338460399026184
Columns 13 through 14
-6.338460399026184 -6.338460399026184
Columns 15 through 16
-6.338460399026184 -6.338460399026184
Columns 17 through 18
-6.338460399026184 -6.338460399026184
Columns 19 through 20
-6.338460399026184 -6.338460399026184
Columns 21 through 22
-6.338460399026184 -6.338460399026184
Columns 23 through 24
-6.338460399026184 -6.338460399026184
Columns 25 through 26
-6.338460399026184 -6.338460399026184
Columns 27 through 28
-6.338460399026184 -6.338460399026184
Columns 29 through 30
-6.338460399026184 -6.338460399026184
Columns 31 through 32
-6.338460399026184 -6.338460399026184
Columns 33 through 34
-6.338460399026184 -6.338460399026184
Columns 35 through 36
-6.338460399026184 -6.338460399026184
Columns 37 through 38
-6.338460399026184 -6.338460399026184
Columns 39 through 40
-6.338460399026184 -6.338460399026184
Columns 41 through 42
-6.338460399026184 -6.338460399026184
Columns 43 through 44
-6.338460399026184 -6.338460399026184
Columns 45 through 46
-6.338460399026184 -6.338460399026184
Columns 47 through 48
-6.338460399026184 -6.338460399026184
Columns 49 through 50
-6.338460399026184 -6.338460399026184
Columns 51 through 52
-6.338460399026184 -6.338460399026184
Columns 53 through 54
-6.338460399026184 -6.338460399026184
Columns 55 through 56
-6.338460399026184 -6.338460399026184
Columns 57 through 58
-6.338460399026184 -6.338460399026184
Columns 59 through 60
-6.338460399026184 -6.338460399026184
Columns 61 through 62
-6.338460399026184 -6.338460399026184
Columns 63 through 64
-6.338460399026184 -6.338460399026184
Columns 65 through 66
-6.338460399026184 -6.338460399026184
Columns 67 through 68
-6.338460399026184 -6.338460399026184
Columns 69 through 70
-6.338460399026184 -6.338460399026184
Columns 71 through 72
-6.338460399026184 -6.338460399026184
Columns 73 through 74
-6.338460399026184 -6.338460399026184
Columns 75 through 76
-6.338460399026184 -6.338460399026184
Columns 77 through 78
-6.338460399026184 -6.338460399026184
Columns 79 through 80
-6.338460399026184 -6.338460399026184
Columns 81 through 82
-6.338460399026184 -6.338460399026184
Columns 83 through 84
-6.338460399026184 -6.338460399026184
Columns 85 through 86
-6.338460399026184 -6.338460399026184
Columns 87 through 88
-6.338460399026184 -6.338460399026184
Columns 89 through 90
-6.338460399026184 -6.338460399026184
Columns 91 through 92
-6.338460399026184 -6.338460399026184
Columns 93 through 94
-6.338460399026184 -6.338460399026184
Columns 95 through 96
-6.338460399026184 -6.338460399026184
Columns 97 through 98
-6.338460399026184 -6.338460399026184
Columns 99 through 100
-6.338460399026184 -6.338460399026184
Columns 101 through 102
-6.338460399026184 -6.338460399026184
Columns 103 through 104
-6.338460399026184 -6.338460399026184
Columns 105 through 106
-6.338460399026184 -6.338460399026184
Columns 107 through 108
-6.338460399026184 -6.338460399026184
Columns 109 through 110
-6.338460399026184 -6.338460399026184
Columns 111 through 112
-6.338460399026184 -6.338460399026184
Columns 113 through 114
-6.338460399026184 -6.338460399026184
Columns 115 through 116
-6.338460399026184 -6.338460399026184
Columns 117 through 118
-6.338460399026184 -6.338460399026184
Columns 119 through 120
-6.338460399026184 -6.338460399026184
Columns 121 through 122
-6.338460399026184 -6.338460399026184
Columns 123 through 124
-6.338460399026184 -6.338460399026184
Columns 125 through 126
-6.338460399026184 -6.338460399026184
Columns 127 through 128
-6.338460399026184 -6.338460399026184
Columns 129 through 130
-6.338460399026184 -6.338460399026184
Columns 131 through 132
-6.338460399026184 -6.338460399026184
Columns 133 through 134
-6.338460399026184 -6.338460399026184
Columns 135 through 136
-6.338460399026184 -6.338460399026184
Columns 137 through 138
-6.338460399026184 -6.338460399026184
Columns 139 through 140
-6.338460399026184 -6.338460399026184
Columns 141 through 142
-6.338460399026184 -6.338460399026184
Columns 143 through 144
-6.338460399026184 -6.338460399026184
Columns 145 through 146
-6.338460399026184 -6.338460399026184
Columns 147 through 148
-6.338460399026184 -6.338460399026184
Columns 149 through 150
-6.338460399026184 -6.338460399026184
Columns 151 through 152
-6.338460399026184 -6.338460399026184
Columns 153 through 154
-6.338460399026184 -6.338460399026184
Columns 155 through 156
-6.338460399026184 -6.338460399026184
Columns 157 through 158
-6.338460399026184 -6.338460399026184
Columns 159 through 160
-6.338460399026184 -6.338460399026184
Columns 161 through 162
-6.338460399026184 -6.338460399026184
Columns 163 through 164
-6.338460399026184 -6.338460399026184
Columns 165 through 166
-6.338460399026184 -6.338460399026184
Columns 167 through 168
-6.338460399026184 -6.338460399026184
Columns 169 through 170
-6.338460399026184 -6.338460399026184
Columns 171 through 172
-6.338460399026184 -6.338460399026184
Columns 173 through 174
-6.338460399026184 -6.338460399026184
Columns 175 through 176
-6.338460399026184 -6.338460399026184
Columns 177 through 178
-6.338460399026184 -6.338460399026184
Columns 179 through 180
-6.338460399026184 -6.338460399026184
Columns 181 through 182
-6.338460399026184 -6.338460399026184
Columns 183 through 184
-6.338460399026184 -6.338460399026184
Columns 185 through 186
-6.338460399026184 -6.338460399026184
Columns 187 through 188
-6.338460399026184 -6.338460399026184
Columns 189 through 190
-6.338460399026184 -6.338460399026184
Columns 191 through 192
-6.338460399026184 -6.338460399026184
Columns 193 through 194
-6.338460399026184 -6.338460399026184
Columns 195 through 196
-6.338460399026184 -6.338460399026184
Columns 197 through 198
-6.338460399026184 -6.338460399026184
Columns 199 through 200
-6.338460399026184 -6.338460399026184
Columns 201 through 202
-6.338460399026184 -6.338460399026184
Columns 203 through 204
-6.338460399026184 -6.338460399026184
Columns 205 through 206
-6.338460399026184 -6.338460399026184
Columns 207 through 208
-6.338460399026184 -6.338460399026184
Columns 209 through 210
-6.338460399026184 -6.338460399026184
Columns 211 through 212
-6.338460399026184 -6.338460399026184
Columns 213 through 214
-6.338460399026184 -6.338460399026184
Columns 215 through 216
-6.338460399026184 -6.338460399026184
Columns 217 through 218
-6.338460399026184 -6.338460399026184
Columns 219 through 220
-6.338460399026184 -6.338460399026184
Columns 221 through 222
-6.338460399026184 -6.338460399026184
Columns 223 through 224
-6.338460399026184 -6.338460399026184
Columns 225 through 226
-6.338460399026184 -6.338460399026184
Columns 227 through 228
-6.338460399026184 -6.338460399026184
Columns 229 through 230
-6.338460399026184 -6.338460399026184
Columns 231 through 232
-6.338460399026184 -6.338460399026184
Columns 233 through 234
-6.338460399026184 -6.338460399026184
Columns 235 through 236
-6.338460399026184 -6.338460399026184
Columns 237 through 238
-6.338460399026184 -6.338460399026184
Columns 239 through 240
-6.338460399026184 -6.338460399026184
Columns 241 through 242
-6.338460399026184 -6.338460399026184
Columns 243 through 244
-6.338460399026184 -6.338460399026184
Columns 245 through 246
-6.338460399026184 -6.338460399026184
Columns 247 through 248
-6.338460399026184 -6.338460399026184
Columns 249 through 250
-6.338460399026184 -6.338460399026184
Columns 251 through 252
-6.338460399026184 -6.338460399026184
Columns 253 through 254
-6.338460399026184 -6.338460399026184
Columns 255 through 256
-6.338460399026184 -6.338460399026184
Columns 257 through 258
-6.338460399026184 -6.338460399026184
Columns 259 through 260
-6.338460399026184 -6.338460399026184
Columns 261 through 262
-6.338460399026184 -6.338460399026184
Columns 263 through 264
-6.338460399026184 -6.338460399026184
Columns 265 through 266
-6.338460399026184 -6.338460399026184
Columns 267 through 268
-6.338460399026184 -6.338460399026184
Columns 269 through 270
-6.338460399026184 -6.338460399026184
Columns 271 through 272
-6.338460399026184 -6.338460399026184
Columns 273 through 274
-6.338460399026184 -6.338460399026184
Columns 275 through 276
-6.338460399026184 -6.338460399026184
Columns 277 through 278
-6.338460399026184 -6.338460399026184
Columns 279 through 280
-6.338460399026184 -6.338460399026184
Columns 281 through 282
-6.338460399026184 -6.338460399026184
Columns 283 through 284
-6.338460399026184 -6.338460399026184
Columns 285 through 286
-6.338460399026184 -6.338460399026184
Columns 287 through 288
-6.338460399026184 -6.338460399026184
Columns 289 through 290
-6.338460399026184 -6.338460399026184
Columns 291 through 292
-6.338460399026184 -6.338460399026184
Columns 293 through 294
-6.338460399026184 -6.338460399026184
Columns 295 through 296
-6.338460399026184 -6.338460399026184
Columns 297 through 298
-6.338460399026184 -6.338460399026184
Columns 299 through 300
-6.338460399026184 -6.338460399026184
Column 301
-6.338460399026184
derLinFitPlot=polyval(derCoefLinFit,timePlot);
derQuadFitPlot=polyval(derCoefQuadFit,timePlot);
derQuartFitPlot=polyval(derCoefQuartFit,timePlot);
plot(timePlot,derTempExact,'--k',timePlot,derLinFitPlot,'y',timeplot,derQuadFitPlot,'c',timeplot,derQuartFitPlot,'m')
{Undefined function or variable 'derTempExact'.}
plot(timePlot,derExactPlot,'--k',timePlot,derLinFitPlot,'y',timeplot,derQuadFitPlot,'c',timeplot,derQuartFitPlot,'m')
{Undefined function or variable 'timeplot'.}
plot(timePlot,derExactPlot,'--k',timePlot,derLinFitPlot,'y',timeplot,derQuadFitPlot,'c',timePlot,derQuartFitPlot,'m')
{Undefined function or variable 'timeplot'.}
plot(timePlot,derExactPlot,'--k',timePlot,derLinFitPlot,'y',timePlot,derQuadFitPlot,'c',timePlot,derQuartFitPlot,'m')
timeDesired=3
timeDesired =
3
TempLinear=interp1(timeMeasured,TempMeasured,timeDesired,'linear','extrap')
TempLinear =
-0.739999999999999
TempExact
TempExact =
0.538494244058104
TempSpline=spline(timeMeasuredN,TempMeasuredN,timeDesired)
TempSpline =
-8.348353902013725e+03
TempSpline=spline(timeMeasured,TempMeasured,timeDesired)
TempSpline =
-0.080000000000008
TempSplineN=spline(timeMeasuredN,TempMeasuredN,timeDesired)
TempSplineN =
-8.348353902013725e+03
TempLinearN=interp1(timeMeasuredN,TempMeasuredN,timeDesired,'linear','extrap')
TempLinearN =
-31.116374883265770
polyval(coefLinFit,3)
ans =
-6.567378793385581
polyval(coefQuadFit,3)
ans =
3.380903122368734
polyval(coefQuartFit,3)
ans =
13.630001984284986
save lecture5
help polyval
<strong>polyval</strong> Evaluate polynomial.
Y = <strong>polyval</strong>(P,X) returns the value of a polynomial P evaluated at X. P
is a vector of length N+1 whose elements are the coefficients of the
polynomial in descending powers.
Y = P(1)*X^N + P(2)*X^(N-1) + ... + P(N)*X + P(N+1)
If X is a matrix or vector, the polynomial is evaluated at all
points in X. See POLYVALM for evaluation in a matrix sense.
[Y,DELTA] = <strong>polyval</strong>(P,X,S) uses the optional output structure S created
by POLYFIT to generate prediction error estimates DELTA. DELTA is an
estimate of the standard deviation of the error in predicting a future
observation at X by P(X).
If the coefficients in P are least squares estimates computed by
POLYFIT, and the errors in the data input to POLYFIT are independent,
normal, with constant variance, then Y +/- DELTA will contain at least
50% of future observations at X.
Y = <strong>polyval</strong>(P,X,[],MU) or [Y,DELTA] = <strong>polyval</strong>(P,X,S,MU) uses XHAT =
(X-MU(1))/MU(2) in place of X. The centering and scaling parameters MU
are optional output computed by POLYFIT.
Example:
Evaluate the polynomial p(x) = 3x^2+2x+1 at x = 5,7, and 9:
p = [3 2 1];
polyval(p,[5 7 9])%
Class support for inputs P,X,S,MU:
float: double, single
See also <a href="matlab:help polyfit">polyfit</a>, <a href="matlab:help polyvalm">polyvalm</a>.
<a href="matlab:doc polyval">Reference page for polyval</a>
<a href="matlab:matlab.internal.language.introspective.overloads.displayOverloads('polyval')">Other functions named polyval</a>