doc plot
edit pol
left = 0; right = 4;
n=10;
x = linspace( left, right, n );
y = pol( x );
{Error using ^
Inputs must be a scalar and a square matrix.
To compute elementwise POWER, use POWER (.^) instead.
Error in pol (line 3)
y = .5*x^3 - x^2 + 3*x -.5;
}
y = pol( x );
plot( x, y )
close all; plot( x, y, 'g*-')
whitebg('black')
axis([0 3 -1 1])
hold on;
plot( x, y, 'ro-')
axis([0 3 -3 4])
y = pol( x );
plot( x, y, 'ro-')
axis([0 3 -10 10])
ezplot( sin )
{Error using sin
Not enough input arguments.
}
ezplot( @sin )
hold off
ezplot( @sin )
ezplot( @sin, [0 1] )
edit pol3
edit myplot3
myplot3
M = [ linspace( 2, 4, 4 ); linspace( 1, 5, 4 ); ]
M =
2.0000 2.6667 3.3333 4.0000
1.0000 2.3333 3.6667 5.0000
reshape( M, 4, 4 )
{Error using reshape
To RESHAPE the number of elements must not change.
}
reshape( M, 8, 1 )
ans =
2.0000
1.0000
2.6667
2.3333
3.3333
3.6667
4.0000
5.0000
M = [ linspace( 2, 4, 4 ); linspace( 5, 1, -4 ); ]
M =
2.0000 2.6667 3.3333 4.0000
M = [ 2:.5:4; 5:-1:1 ]
M =
2.0000 2.5000 3.0000 3.5000 4.0000
5.0000 4.0000 3.0000 2.0000 1.0000
M = [ 2:.5:4; 5.3:-1:1.3 ]
M =
2.0000 2.5000 3.0000 3.5000 4.0000
5.3000 4.3000 3.3000 2.3000 1.3000
reshape( M, 10, 1 )
ans =
2.0000
5.3000
2.5000
4.3000
3.0000
3.3000
3.5000
2.3000
4.0000
1.3000
x = reshape( M, 10, 1 )
x =
2.0000
5.3000
2.5000
4.3000
3.0000
3.3000
3.5000
2.3000
4.0000
1.3000
y = pol( x );
plot( x, y, 'b+-' )
x = sort(x);
y = pol( x );
close all;
plot( x, y, 'b+-' )
plot( x, y, 'w+-' )
myplot
{Undefined function or variable 'myplot'.
}
myplot3
myplot3
myplot3
myplot3
z =
-4
z =
-3.7895
z =
-3.5789
z =
-3.3684
z =
-3.1579
z =
-2.9474
z =
-2.7368
z =
-2.5263
z =
-2.3158
z =
-2.1053
z =
-1.8947
z =
-1.6842
z =
-1.4737
z =
-1.2632
z =
-1.0526
z =
-0.8421
z =
-0.6316
z =
-0.4211
z =
-0.2105
z =
0
z =
-5.2188
z =
-4.8404
z =
-4.4805
z =
-4.1394
z =
-3.8169
z =
-3.5130
z =
-3.2279
z =
-2.9614
z =
-2.7135
z =
-2.4843
z =
-2.2738
z =
-2.0819
z =
-1.9087
z =
-1.7542
z =
-1.6183
z =
-1.5011
z =
-1.4025
z =
-1.3226
z =
-1.2614
z =
-1.2188
z =
-6.3490
z =
-5.8026
z =
-5.2935
z =
-4.8217
z =
-4.3872
z =
-3.9901
z =
-3.6303
z =
-3.3078
z =
-3.0226
z =
-2.7747
z =
-2.5642
z =
-2.3910
z =
-2.2551
z =
-2.1566
z =
-2.0953
z =
-2.0714
z =
-2.0849
z =
-2.1356
z =
-2.2236
z =
-2.3490
z =
-7.3906
z =
-6.6762
z =
-6.0178
z =
-5.4154
z =
-4.8689
z =
-4.3785
z =
-3.9440
z =
-3.5655
z =
-3.2430
z =
-2.9765
z =
-2.7660
z =
-2.6115
z =
-2.5129
z =
-2.4703
z =
-2.4837
z =
-2.5531
z =
-2.6785
z =
-2.8599
z =
-3.0972
z =
-3.3906
z =
-8.3435
z =
-7.4611
z =
-6.6534
z =
-5.9204
z =
-5.2620
z =
-4.6782
z =
-4.1691
z =
-3.7347
z =
-3.3748
z =
-3.0897
z =
-2.8791
z =
-2.7433
z =
-2.6820
z =
-2.6954
z =
-2.7835
z =
-2.9462
z =
-3.1836
z =
-3.4956
z =
-3.8822
z =
-4.3435
z =
-9.2078
z =
-8.1575
z =
-7.2005
z =
-6.3368
z =
-5.5664
z =
-4.8893
z =
-4.3056
z =
-3.8151
z =
-3.4180
z =
-3.1142
z =
-2.9036
z =
-2.7864
z =
-2.7625
z =
-2.8319
z =
-2.9946
z =
-3.2506
z =
-3.5999
z =
-4.0426
z =
-4.5785
z =
-5.2078
z =
-9.9834
z =
-8.7651
z =
-7.6588
z =
-6.6645
z =
-5.7822
z =
-5.0118
z =
-4.3534
z =
-3.8070
z =
-3.3725
z =
-3.0500
z =
-2.8395
z =
-2.7409
z =
-2.7543
z =
-2.8797
z =
-3.1171
z =
-3.4664
z =
-3.9277
z =
-4.5009
z =
-5.1862
z =
-5.9834
z =
-10.6704
z =
-9.2842
z =
-8.0286
z =
-6.9036
z =
-5.9093
z =
-5.0456
z =
-4.3126
z =
-3.7102
z =
-3.2384
z =
-2.8972
z =
-2.6867
z =
-2.6068
z =
-2.6575
z =
-2.8389
z =
-3.1509
z =
-3.5935
z =
-4.1668
z =
-4.8707
z =
-5.7052
z =
-6.6704
z =
-11.2687
z =
-9.7145
z =
-8.3097
z =
-7.0541
z =
-5.9478
z =
-4.9908
z =
-4.1831
z =
-3.5247
z =
-3.0156
z =
-2.6558
z =
-2.4453
z =
-2.3840
z =
-2.4721
z =
-2.7094
z =
-3.0961
z =
-3.6320
z =
-4.3172
z =
-5.1518
z =
-6.1356
z =
-7.2687
z =
-11.7784
z =
-10.0563
z =
-8.5021
z =
-7.1159
z =
-5.8977
z =
-4.8474
z =
-3.9650
z =
-3.2506
z =
-2.7042
z =
-2.3257
z =
-2.1152
z =
-2.0726
z =
-2.1980
z =
-2.4913
z =
-2.9526
z =
-3.5819
z =
-4.3791
z =
-5.3442
z =
-6.4773
z =
-7.7784
z =
-12.1994
z =
-10.3094
z =
-8.6059
z =
-7.0891
z =
-5.7589
z =
-4.6153
z =
-3.6583
z =
-2.8879
z =
-2.3041
z =
-1.9070
z =
-1.6965
z =
-1.6725
z =
-1.8353
z =
-2.1846
z =
-2.7205
z =
-3.4431
z =
-4.3522
z =
-5.4480
z =
-6.7304
z =
-8.1994
z =
-12.5319
z =
-10.4738
z =
-8.6211
z =
-6.9736
z =
-5.5314
z =
-4.2945
z =
-3.2629
z =
-2.4365
z =
-1.8154
z =
-1.3996
z =
-1.1891
z =
-1.1838
z =
-1.3839
z =
-1.7892
z =
-2.3998
z =
-3.2156
z =
-4.2368
z =
-5.4632
z =
-6.8949
z =
-8.5319
z =
-12.7756
z =
-10.5496
z =
-8.5476
z =
-6.7695
z =
-5.2153
z =
-3.8851
z =
-2.7788
z =
-1.8965
z =
-1.2381
z =
-0.8036
z =
-0.5931
z =
-0.6065
z =
-0.8439
z =
-1.3051
z =
-1.9904
z =
-2.8995
z =
-4.0327
z =
-5.3897
z =
-6.9707
z =
-8.7756
z =
-12.9307
z =
-10.5368
z =
-8.3855
z =
-6.4767
z =
-4.8106
z =
-3.3871
z =
-2.2062
z =
-1.2678
z =
-0.5721
z =
-0.1190
z =
0.0916
z =
0.0595
z =
-0.2152
z =
-0.7325
z =
-1.4923
z =
-2.4948
z =
-3.7399
z =
-5.2276
z =
-6.9579
z =
-8.9307
z =
-12.9972
z =
-10.4353
z =
-8.1347
z =
-6.0953
z =
-4.3172
z =
-2.8004
z =
-1.5448
z =
-0.5505
z =
0.1825
z =
0.6543
z =
0.8648
z =
0.8141
z =
0.5021
z =
-0.0711
z =
-0.9057
z =
-2.0015
z =
-3.3585
z =
-4.9768
z =
-6.8564
z =
-8.9972
z =
-12.9751
z =
-10.2452
z =
-7.7953
z =
-5.6253
z =
-3.7352
z =
-2.1251
z =
-0.7949
z =
0.2554
z =
1.0258
z =
1.5163
z =
1.7268
z =
1.6574
z =
1.3081
z =
0.6788
z =
-0.2304
z =
-1.4194
z =
-2.8885
z =
-4.6374
z =
-6.6663
z =
-8.9751
z =
-12.8643
z =
-9.9665
z =
-7.3673
z =
-5.0666
z =
-3.0646
z =
-1.3611
z =
0.0437
z =
1.1500
z =
1.9577
z =
2.4668
z =
2.6774
z =
2.5893
z =
2.2027
z =
1.5174
z =
0.5336
z =
-0.7488
z =
-2.3298
z =
-4.2094
z =
-6.3875
z =
-8.8643
z =
-12.6648
z =
-9.5991
z =
-6.8506
z =
-4.4193
z =
-2.3053
z =
-0.5085
z =
0.9710
z =
2.1333
z =
2.9783
z =
3.5061
z =
3.7166
z =
3.6099
z =
3.1859
z =
2.4447
z =
1.3862
z =
0.0105
z =
-1.6825
z =
-3.6927
z =
-6.0201
z =
-8.6648
z =
-12.3767
z =
-9.1430
z =
-6.2452
z =
-3.6833
z =
-1.4574
z =
0.4327
z =
1.9869
z =
3.2051
z =
4.0875
z =
4.6339
z =
4.8444
z =
4.7191
z =
4.2578
z =
3.4606
z =
2.3275
z =
0.8584
z =
-0.9465
z =
-3.0873
z =
-5.5641
z =
-8.3767
z =
-12
z =
-8.5983
z =
-5.5512
z =
-2.8587
z =
-0.5208
z =
1.4626
z =
3.0914
z =
4.3657
z =
5.2853
z =
5.8504
z =
6.0609
z =
5.9169
z =
5.4183
z =
4.5651
z =
3.3573
z =
1.7950
z =
-0.1219
z =
-2.3934
z =
-5.0194
z =
-8
myplot3
ezplot( @pol )
close all;
ezplot( @pol )
sqr = @(x) x.^2
sqr =
@(x)x.^2
sqr( 4 )
ans =
16
ezplot( sqr )
edit fun1
fun1( 0, 1 )
ans =
-1
function z = fun1( t, y )
|
{Error: Function definitions are not permitted in this context.
}
n = 10; t = linspace( 0, 3, n );
t(1) = 1;
n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n )
t =
0 3
n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 )
t =
0 1.5000 3.0000
n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 );
h
h =
1.5000
n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 );
y(1) = 1;
for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
plot( t, y )
{Error using plot
Vectors must be the same length.
}
length(t)
ans =
3
length(y)
ans =
400
clear('y')
for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
{Undefined function or variable 'y'.
}
y(1) = 1;
for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
plot( t, y )
{Error using plot
Vectors must be the same length.
}
whos('y')
Name Size Bytes Class Attributes
y 1x2 16 double
n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 );
n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
whos('t')
Name Size Bytes Class Attributes
t 1x11 88 double
whos('n')
Name Size Bytes Class Attributes
n 1x1 8 double
whos('y')
Name Size Bytes Class Attributes
y 1x10 80 double
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
plot( t, y )
n = 100; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
close all; plot( t, y )
sol = @(t) exp(-t) * cos(5*t)
sol =
@(t)exp(-t)*cos(5*t)
sol( t )
{Error using *
Inner matrix dimensions must agree.
Error in @(t)exp(-t)*cos(5*t)
}
sol(0)
ans =
1
sol(3)
ans =
-0.0378
format long
sol(3)
ans =
-0.037822634055742
y(end)
ans =
-0.037896264491903
sol( y )
{Error using *
Inner matrix dimensions must agree.
Error in @(t)exp(-t)*cos(5*t)
}
sol = @(t) exp(-t) .* cos(5*t)
sol =
@(t)exp(-t).*cos(5*t)
sol( y )
ans =
Columns 1 through 4
0.104353486269682 0.052001516413462 -0.046423525102459 -0.191030853468242
Columns 5 through 8
-0.361377449593051 -0.504032992157408 -0.537622440228157 -0.387226981102216
Columns 9 through 12
-0.038987711551221 0.421975830440460 0.830344137655809 1.017721513498643
Columns 13 through 16
0.899292031348634 0.510123888024507 -0.027661349648993 -0.574261533046739
Columns 17 through 20
-1.029726606920796 -1.353858095511375 -1.553474278934048 -1.656562898834221
Columns 21 through 24
-1.689735241380445 -1.665931454361633 -1.582408263242207 -1.426428437523448
Columns 25 through 28
-1.185543840488392 -0.858835948927268 -0.464804531771425 -0.042059152862089
Columns 29 through 32
0.358444824922948 0.686932591735934 0.908416275033252 1.010738777254311
Columns 33 through 36
1.004475975275649 0.916117921078458 0.778463394847591 0.622191745495058
Columns 37 through 40
0.470849006204548 0.339452833987461 0.235629149993288 0.161869658486503
Columns 41 through 44
0.117812293338932 0.101952764834923 0.112611251310003 0.148220802411667
Columns 45 through 48
0.207110714150592 0.286996972213651 0.384408073239325 0.494276005816313
Columns 49 through 52
0.609890557322316 0.723329972289200 0.826344336739195 0.911515643039954
Columns 53 through 56
0.973408550181390 1.009409179037865 1.020038510656838 1.008686325749404
Columns 57 through 60
0.980875146776477 0.943269834286068 0.902669196272626 0.865163303433793
Columns 61 through 64
0.835551925033782 0.817035896080053 0.811139648288980 0.817804782837368
Columns 65 through 68
0.835601530687178 0.862021528679367 0.893828214366321 0.927443872421876
Columns 69 through 72
0.959345984648710 0.986436221473972 1.006340686432574 1.017605045073945
Columns 73 through 76
1.019763508905773 1.013282308949428 0.999399745750037 0.979899967869152
Columns 77 through 80
0.956862858114222 0.932427936689940 0.908599041963962 0.887102981764760
Columns 81 through 84
0.869303195938022 0.856161102756745 0.848233883355368 0.845697322251849
Columns 85 through 88
0.848384593224234 0.855835060955732 0.867350036155484 0.882054214350802
Columns 89 through 92
0.898961981318915 0.917047048465768 0.935312467396216 0.952856595779651
Columns 93 through 96
0.968929657112838 0.982975584438421 0.994655000747745 1.003847287408740
Columns 97 through 100
1.010632295432128 1.015254815173786 1.018076931939366 1.019524520608433
Column 101
1.020034264218266
exact = sol( y );
exact = sol( t );
max( abs(exact - y)./exact )
ans =
1.276252495531087
exact
exact =
Columns 1 through 4
1.000000000000000 0.959548476284976 0.899702023097390 0.822946687527225
Columns 5 through 8
0.732007024013916 0.629770445701126 0.519212289612792 0.403323252671911
Columns 9 through 12
0.285040705344865 0.167185214049475 0.052403407875472 -0.056881884773390
Columns 13 through 16
-0.158513522701115 -0.250633476673835 -0.331707527523356 -0.400541185954253
Columns 17 through 20
-0.456286984399144 -0.498443478086242 -0.526846460780452 -0.541653047698029
Columns 21 through 24
-0.543319401780100 -0.532572978398499 -0.510380236860953 -0.477910814610749
Columns 25 through 28
-0.436499182201738 -0.387604794945871 -0.332771732045996 -0.273588767943680
Columns 29 through 32
-0.211650755797764 -0.148522122024247 -0.085703176449320 -0.024599837774347
Columns 33 through 36
0.033502738289018 0.087462257701009 0.136296861520342 0.179198039258522
Columns 37 through 40
0.215538860828837 0.244877613115507 0.266957026344823 0.281699364624537
Columns 41 through 44
0.289197732789170 0.289704016949230 0.283613928140726 0.271449656801585
Columns 45 through 48
0.253840670390634 0.231503197555631 0.205218940384062 0.175813542231448
Columns 49 through 52
0.144135313443450 0.111034682189645 0.077344793981631 0.043863632743293
Columns 53 through 56
0.011337980097020 -0.019550530579308 -0.048197071193733 -0.074082856138344
Columns 57 through 60
-0.096781891179881 -0.115965225969549 -0.131402759155826 -0.142962697708025
Columns 61 through 64
-0.150608819314580 -0.154395727849825 -0.154462326330949 -0.151023759122699
Columns 65 through 68
-0.144362095184625 -0.134816036865100 -0.122769944266577 -0.108642463831234
Columns 69 through 72
-0.092875041957835 -0.075920590713622 -0.058232553704785 -0.040254596652364
Columns 73 through 76
-0.022411119983277 -0.005098760622651 0.011320981985338 0.026527893947810
Columns 77 through 80
0.040247901114203 0.052256594704873 0.062381425829242 0.070502596666932
Columns 81 through 84
0.076552704011380 0.080515215912718 0.082421883905718 0.082349211468062
Columns 85 through 88
0.080414113721293 0.076768913856897 0.071595828332551 0.065101095617511
Columns 89 through 92
0.057508902332347 0.049055256261602 0.039981948217213 0.030530734448400
Columns 93 through 96
0.020937858625074 0.011429017792938 0.002214860554999 -0.006512911469627
Columns 97 through 100
-0.014584785671251 -0.021855988703115 -0.028208327440439 -0.033551320221031
Column 101
-0.037822634055742
max( abs(exact - y) )
ans =
0.046678059686664
max( abs(exact - y)./exact )
ans =
1.276252495531087
max( (exact - y)./exact )
ans =
1.141713261727473
(y(end) - exact(end))/exact(end)
ans =
0.001946729465011
n = 1000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.272437623209290e-04
n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.272437623209290e-04
clear('t')
clear all
n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
{Undefined function or variable 'sol'.
}
sol = @(t) exp(-t) .* cos(5*t)
sol =
@(t)exp(-t).*cos(5*t)
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
-0.602534223273937
n = 1000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.272437623209290e-04
n = 10000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.799831062937499e-05
n = 100000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.852521557373846e-06
n = 1000000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1;
for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end
exact = sol( t ); (y(end) - exact(end))/exact(end)
ans =
7.857789108854612e-07
max(abs(y - exact))
ans =
4.681017783281227e-06
edit myeuler
myeuler( @fun1, 0, 3, 10, 1 )
ans =
Columns 1 through 4
1.000000000000000 0.700000000000000 -0.618443691672424 -0.549083037934104
Columns 5 through 8
0.211793004434057 0.274492599267961 -0.121799308067884 -0.187443606786559
Columns 9 through 11
0.030376076322544 0.094278448793071 -0.015033202622791
myeuler( @fun1, 0, 3, 100, 1 );
y = myeuler( @fun1, 0, 3, 100, 1 );
y(end)
ans =
-0.037896264491903
y = myeuler( @fun1, 0, 3, 100, 1 );
just DISPlays a string
it is just like in C:
y(y = myeuler( @fun1, 0, 3, 100, 1 );
just DISPlays a string
it is just like in C:
y(
y = myeuler( @fun1, 0, 3, 100, 1 );
just DISPlays a string
it is just like in C! y(y = myeuler( @fun1, 0, 3, 100, 1 );
just DISPlays a string
it is just like in C! y(101)= -0.037896y = myeuler( @fun1, 0, 3, 100, 1 );
just DISPlays a string
it is just like in C!
y(101)= -0.037896264492
doc fpirntf
edit sqrts.m
edit sqsqrt
edit sqrtsq
sqrts( 2, 7 )
7, 1.999999999999971, 2.000000000000000
sqrts( 2, 8 )
7, 1.999999999999971, 2.000000000000000
8, 2.000000000000024, 2.000000000000000
sqrts( 2, 9 )
7, 1.999999999999971, 2.000000000000000
8, 2.000000000000024, 2.000000000000000
9, 2.000000000000024, 2.000000000000000
sqrts( 2, 10 )
7, 1.999999999999971, 2.000000000000000
8, 2.000000000000024, 2.000000000000000
9, 2.000000000000024, 2.000000000000000
10, 2.000000000000024, Inf
clc
sqrts( 2.2, 10 )
7, 2.200000000000012, 2.200000000000000
8, 2.200000000000079, 2.200000000000000
9, 2.200000000000079, 2.200000000000000
10, 2.200000000000079, Inf
sqrts( 3.2, 10 )
7, 3.199999999999936, 3.200000000000000
8, 3.199999999999936, 3.200000000000000
9, 3.200000000000114, 3.200000000000000
10, 3.199999999999755, Inf
sqrts( .2, 10 )
7, 0.200000000000002, 0.200000000000000
8, 0.200000000000002, 0.200000000000000
9, 0.200000000000002, 0.000000000000000
10, 0.199999999999990, 0.000000000000000
clc
sqrts( 1.2, 12 )
7, 1.199999999999998, 1.200000000000000
8, 1.199999999999962, 1.200000000000000
9, 1.199999999999896, 1.200000000000000
10, 1.200000000000032, 1.200000000000000
11, 1.200000000000305, 1.200000000000000
12, 1.199999999999761, Inf
sqrts( 2.2, 12 )
7, 2.200000000000012, 2.200000000000000
8, 2.200000000000079, 2.200000000000000
9, 2.200000000000079, 2.200000000000000
10, 2.200000000000079, Inf
11, 2.200000000000079, Inf
12, 2.200000000000079, Inf
sqrts( 0.7, 12 )
7, 0.700000000000003, 0.700000000000000
8, 0.699999999999993, 0.700000000000000
9, 0.699999999999993, 0.700000000000000
10, 0.699999999999953, 0.700000000000000
11, 0.699999999999953, 0.699999999973900
12, 0.699999999999832, 0.000000000000000
sqrts( 0.7, 15 )
7, 0.700000000000003, 0.700000000000000
8, 0.699999999999993, 0.700000000000000
9, 0.699999999999993, 0.700000000000000
10, 0.699999999999953, 0.700000000000000
11, 0.699999999999953, 0.699999999973900
12, 0.699999999999832, 0.000000000000000
13, 0.699999999999513, 0.000000000000000
14, 0.699999999999513, 0.000000000000000
15, 0.699999999998245, 0.000000000000000
sqrts( 0.7, 20 )
7, 0.700000000000003, 0.700000000000000
8, 0.699999999999993, 0.700000000000000
9, 0.699999999999993, 0.700000000000000
10, 0.699999999999953, 0.700000000000000
11, 0.699999999999953, 0.699999999973900
12, 0.699999999999832, 0.000000000000000
13, 0.699999999999513, 0.000000000000000
14, 0.699999999999513, 0.000000000000000
15, 0.699999999998245, 0.000000000000000
16, 0.700000000000752, 0.000000000000000
17, 0.700000000000752, 0.000000000000000
18, 0.700000000000752, 0.000000000000000
19, 0.700000000000752, 0.000000000000000
20, 0.700000000000752, 0.000000000000000
sqrts( 0.5, 20 )
7, 0.499999999999999, 0.500000000000000
8, 0.499999999999999, 0.500000000000000
9, 0.499999999999999, 0.500000000000000
10, 0.499999999999999, 0.500000000000000
11, 0.499999999999999, 0.000000000000000
12, 0.500000000000114, 0.000000000000000
13, 0.500000000000114, 0.000000000000000
14, 0.500000000000571, 0.000000000000000
15, 0.500000000001479, 0.000000000000000
16, 0.500000000001479, 0.000000000000000
17, 0.500000000001479, 0.000000000000000
18, 0.500000000008752, 0.000000000000000
19, 0.500000000008752, 0.000000000000000
20, 0.500000000037885, 0.000000000000000
sqrts( 0.1, 20 )
7, 0.099999999999999, 0.100000000000000
8, 0.099999999999999, 0.100000000000000
9, 0.100000000000002, 0.000000000000000
10, 0.100000000000002, 0.000000000000000
11, 0.100000000000002, 0.000000000000000
12, 0.100000000000002, 0.000000000000000
13, 0.100000000000002, 0.000000000000000
14, 0.100000000000095, 0.000000000000000
15, 0.100000000000095, 0.000000000000000
16, 0.100000000000460, 0.000000000000000
17, 0.100000000000460, 0.000000000000000
18, 0.100000000000460, 0.000000000000000
19, 0.100000000003375, 0.000000000000000
20, 0.099999999997554, 0.000000000000000
sqrts( 4.1, 20 )
7, 4.099999999999977, 4.100000000000000
8, 4.100000000000105, 4.100000000000000
9, 4.100000000000337, Inf
10, 4.099999999999857, Inf
11, 4.100000000000778, Inf
12, 4.100000000000778, Inf
13, 4.100000000000778, Inf
14, 4.100000000008135, Inf
15, 4.099999999993023, Inf
16, 4.099999999993023, Inf
17, 4.100000000053106, Inf
18, 4.099999999933824, Inf
19, 4.100000000172273, Inf
20, 4.100000000648643, Inf
diary