n = 100; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
0.006048975982605
n = 1000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
6.076232396232373e-04
n = 10000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
6.078967064790568e-05
n = 100000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
6.079240612503426e-06
n = 1000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
6.0745346e-04
n = 10000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
1.2690121e-04
n = 100000; x = my_pi_up( n ); abs( x - pi6 )/pi6
ans =
1.2690121e-04
x
x =
1.6447253
n = 100000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447253 0.0001269
n = 10000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447253 0.0001269
n = 8000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447253 0.0001269
n = 6000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447253 0.0001269
n = 4000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447139 0.0001339
n = 5000; x = my_pi_up( n ); [x, abs( x - pi6 )/pi6]
ans =
1.6447253 0.0001269
n = 4000; xu = my_pi_up( n ); xd = my_pi_down( n ); [xu, abs( xu - pi6 )/pi6; xd, abs( xd - pi6 )/pi6]
ans =
1.6447139 0.0001339
1.6446841 0.0001520
n = 5000; xu = my_pi_up( n ); xd = my_pi_down( n ); [xu, abs( xu - pi6 )/pi6; xd, abs( xd - pi6 )/pi6]
ans =
1.6447253 0.0001269
1.6447340 0.0001216
n = 10000; xu = my_pi_up( n ); xd = my_pi_down( n ); [xu, abs( xu - pi6 )/pi6; xd, abs( xd - pi6 )/pi6]
ans =
1.6447253 0.0001269
1.6448340 0.0000608
n = 100000; xu = my_pi_up( n ); xd = my_pi_down( n ); [xu, abs( xu - pi6 )/pi6; xd, abs( xd - pi6 )/pi6]
ans =
1.6447253 0.0001269
1.6449240 0.0000061
n = 1000000; xu = my_pi_up( n ); xd = my_pi_down( n ); [xu, abs( xu - pi6 )/pi6; xd, abs( xd - pi6 )/pi6]
ans =
1.6447253 0.0001269
1.6449330 0.0000007
edit sqsqrt
x=2;p=1; [sqrtsq(x, p) sqsqrt(x, p)]
ans =
2.000000000000000 2.000000000000000
x=2;p=2; [sqrtsq(x, p) sqsqrt(x, p)]
ans =
2.000000000000000 2.000000000000000
x=1;p=10; [sqrtsq(x, p) sqsqrt(x, p)]
ans =
1 1
x=1;p=20; [sqrtsq(x, p) sqsqrt(x, p)]
ans =
1 1
x=pi/2;p=20; [sqrtsq(x, p) sqsqrt(x, p)]
ans =
Inf 1.570796326625687
x=pi/2;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-09 *
Inf 0.107721994469509
x=2;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-10 *
Inf 0.786792853091356
x=3;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-09 *
Inf 0.141214891632065
x=.5;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.000000000000000 0.000000000075771
x=.1;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.000000000000000 0.000000000024458
x=1;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
0 0
x=1.5;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-10 *
Inf 0.406317942254949
x=1.1;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-11 *
Inf 0.589447682583258
x=1.00001;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-09 *
0 0.106769746714549
x=1.0001;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-10 *
0 0.597364595767515
x=1.001;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-10 *
Inf 0.647822344109198
1.001^2
ans =
1.002001000000000
(1.001^2)^2
ans =
1.004006004000999
((1.001^2)^2)^2
ans =
1.008028056070055
((1.001^2)^2)^2^2
ans =
1.016120561824374
((1.001^2)^2)^2^2^2
ans =
1.032500996162281
((1.001^2)^2)^2^2^2^2
ans =
1.066058307076103
((1.001^2)^2)^2^2^2^2^2
ans =
1.136480314085966
((1.001^2)^2)^2^2^2^2^2^2
ans =
1.291587504304936
((1.001^2)^2)^2^2^2^2^2^2^2
ans =
1.668198281276653
((1.001^2)^2)^2^2^2^2^2^2^2^2
ans =
2.782885505654380
((1.0001^2)^2)^2^2^2^2^2^2^2^2
ans =
1.107820842039957
((1.00001^2)^2)^2^2^2^2^2^2^2^2
ans =
1.010292556489493
x=1.0001;p=20; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-10 *
0 0.597364595767515
x=1.0001;p=30; l=sqrtsq(x, p); r=sqsqrt(x, p); [abs(x-l)/abs(x) abs(x-r)/abs(x)]
ans =
1.0e-07 *
Inf 0.976157869554016
edit my_filter
edit signal
my_filter
my_filter
my_filter
my_filter
my_filter
my_filter
f =
Column 1
0.000000000000013
Column 2
1.562712527537314 -49.726318913663746i
Column 3
-0.041210800682674 + 0.655026919502409i
Column 4
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Column 5
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Column 6
-0.022337921944684 + 0.141036088512919i
Column 7
-0.014792004088384 + 0.077542400963851i
Column 8
-0.002496161356033 + 0.011167183967095i
Column 9
0.021446864741067 - 0.083530023210946i
Column 10
0.088676271138289 - 0.305225727272816i
Column 11
1.482386192152953 - 4.562315579325071i
Column 12
-0.223647939948333 + 0.621206050864438i
Column 13
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Column 14
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Column 15
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Column 16
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Column 17
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Column 18
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Column 19
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Column 20
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Column 21
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Column 22
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Column 23
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Column 24
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Column 25
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Column 26
-0.034167672019716 + 0.034167672019710i
Column 27
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Column 28
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Column 29
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Column 30
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Column 31
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Column 32
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Column 33
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Column 34
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Column 35
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Column 36
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Column 40
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Column 41
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Column 46
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Column 51
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Column 67
0.085574266768263 + 0.047044851263833i
Column 68
0.056984324873318 + 0.033700435785701i
Column 69
0.035505283751954 + 0.022532338233770i
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Column 73
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-0.034167672019716 - 0.034167672019710i
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-0.039224757744025 - 0.041770124460315i
Column 78
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-0.051950168869403 - 0.066973754146373i
Column 81
-0.055786551805610 - 0.076783601310671i
Column 82
-0.059632139743252 - 0.087746029018940i
Column 83
-0.063650625483001 - 0.100297336890515i
Column 84
-0.068069134017926 - 0.115098619833552i
Column 85
-0.073240036966033 - 0.133223132671828i
Column 86
-0.079776189991143 - 0.156569588565818i
Column 87
-0.088892177707600 - 0.188905493376168i
Column 88
-0.103449709792652 - 0.239058174364521i
Column 89
-0.132303512686234 - 0.334160528546582i
Column 90
-0.223647939948333 - 0.621206050864438i
Column 91
1.482386192152953 + 4.562315579325071i
Column 92
0.088676271138289 + 0.305225727272816i
Column 93
0.021446864741067 + 0.083530023210946i
Column 94
-0.002496161356033 - 0.011167183967095i
Column 95
-0.014792004088384 - 0.077542400963851i
Column 96
-0.022337921944684 - 0.141036088512919i
Column 97
-0.027683397157764 - 0.219136652917031i
Column 98
-0.032534286380315 - 0.344176799302718i
Column 99
-0.041210800682674 - 0.655026919502409i
Column 100
1.562712527537314 +49.726318913663746i
my_filter
f =
Column 1
0.000000000000013
Column 2
1.562712527537314 -49.726318913663746i
Column 3
-0.041210800682674 + 0.655026919502409i
Column 4
-0.032534286380315 + 0.344176799302718i
Column 5
-0.027683397157764 + 0.219136652917031i
Column 6
-0.022337921944684 + 0.141036088512919i
Column 7
-0.014792004088384 + 0.077542400963851i
Column 8
-0.002496161356033 + 0.011167183967095i
Column 9
0.021446864741067 - 0.083530023210946i
Column 10
0.088676271138289 - 0.305225727272816i
Column 11
1.482386192152953 - 4.562315579325071i
Column 12
-0.223647939948333 + 0.621206050864438i
Column 13
-0.132303512686234 + 0.334160528546582i
Column 14
-0.103449709792652 + 0.239058174364521i
Column 15
-0.088892177707600 + 0.188905493376168i
Column 16
-0.079776189991143 + 0.156569588565818i
Column 17
-0.073240036966033 + 0.133223132671828i
Column 18
-0.068069134017926 + 0.115098619833552i
Column 19
-0.063650625483001 + 0.100297336890515i
Column 20
-0.059632139743252 + 0.087746029018940i
Column 21
-0.055786551805610 + 0.076783601310671i
Column 22
-0.051950168869403 + 0.066973754146373i
Column 23
-0.047990782142613 + 0.058010890344138i
Column 24
-0.043788886520132 + 0.049668742128895i
Column 25
-0.039224757744025 + 0.041770124460315i
Column 26
-0.034167672019716 + 0.034167672019710i
Column 27
-0.028464919757314 + 0.026730338875191i
Column 28
-0.021928585991092 + 0.019332649113985i
Column 29
-0.014317687200596 + 0.011844620952266i
Column 30
-0.005312089413521 + 0.004120478918936i
Column 31
0.005527801989537 - 0.004016183231799i
Column 32
0.018826506256891 - 0.012794480440209i
Column 33
0.035505283751954 - 0.022532338233770i
Column 34
0.056984324873318 - 0.033700435785701i
Column 35
0.085574266768263 - 0.047044851263833i
Column 36
0.125302451695248 - 0.063844788022778i
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0.183865127688773 - 0.086520361650869i
Column 38
0.278021234068496 - 0.120310531346755i
Column 39
0.452449321276675 - 0.179137358854963i
Column 40
0.879190574358814 - 0.316528083562167i
Column 41
3.433836903554857 - 1.115721243616418i
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-2.597037498603043 + 0.754509141284061i
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-1.075632143033382 + 0.276175394139794i
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-0.730290184198702 + 0.163239196368248i
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-0.580410309123517 + 0.110719187938149i
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-0.498954908860839 + 0.079026693987107i
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-0.418969598519236 + 0.039604287478076i
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-0.399931593128983 + 0.025161563105942i
Column 50
-0.389511694163072 + 0.012240898127757i
Column 51
-0.386189209038676
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-0.389511694163072 - 0.012240898127757i
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-0.498954908860839 - 0.079026693987107i
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3.433836903554857 + 1.115721243616418i
Column 62
0.879190574358814 + 0.316528083562167i
Column 63
0.452449321276675 + 0.179137358854963i
Column 64
0.278021234068496 + 0.120310531346755i
Column 65
0.183865127688773 + 0.086520361650869i
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0.125302451695248 + 0.063844788022778i
Column 67
0.085574266768263 + 0.047044851263833i
Column 68
0.056984324873318 + 0.033700435785701i
Column 69
0.035505283751954 + 0.022532338233770i
Column 70
0.018826506256891 + 0.012794480440209i
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0.005527801989537 + 0.004016183231799i
Column 72
-0.005312089413521 - 0.004120478918936i
Column 73
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Column 74
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Column 75
-0.028464919757314 - 0.026730338875191i
Column 76
-0.034167672019716 - 0.034167672019710i
Column 77
-0.039224757744025 - 0.041770124460315i
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-0.043788886520132 - 0.049668742128895i
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Column 80
-0.051950168869403 - 0.066973754146373i
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-0.055786551805610 - 0.076783601310671i
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Column 83
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Column 84
-0.068069134017926 - 0.115098619833552i
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-0.073240036966033 - 0.133223132671828i
Column 86
-0.079776189991143 - 0.156569588565818i
Column 87
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Column 88
-0.103449709792652 - 0.239058174364521i
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Column 90
-0.223647939948333 - 0.621206050864438i
Column 91
1.482386192152953 + 4.562315579325071i
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Column 93
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Column 94
-0.002496161356033 - 0.011167183967095i
Column 95
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-0.022337921944684 - 0.141036088512919i
Column 97
-0.027683397157764 - 0.219136652917031i
Column 98
-0.032534286380315 - 0.344176799302718i
Column 99
-0.041210800682674 - 0.655026919502409i
Column 100
1.562712527537314 +49.726318913663746i
my_filter
my_filter
my_filter
my_filter
my_filter
my_filter
my_filter
my_filter
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 28
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 28
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 31
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 31
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 31
my_filter
{Warning: Imaginary parts of complex X and/or Y arguments ignored}
> In my_filter at 31
edit my_LU
my_LU( .1 )
ans =
1 0
10 1
[L, U] = my_LU( .1 )
L =
1 0
10 1
U =
0.100000000000000 -1.000000000000000
0 11.000000000000000
eps = .01; A = [ eps -1; 1 1];
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
ans =
0
eps = .00001; A = [ eps -1; 1 1];
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
ans =
6.861567364029007e-17
eps = .000000001; A = [ eps -1; 1 1];
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
ans =
6.861555644282676e-17
eps = 10^-7; A = [ eps -1; 1 1];
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
ans =
7.2224054e-16
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
L =
1 0
10000000 1
U =
1.0e+07 *
0.0000000 -0.0000001
0 1.0000001
ans =
7.2224054e-16
format long
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
L =
1 0
10000000 1
U =
1.0e+07 *
0.0000000 -0.0000001
0 1.0000001
ans =
7.2224054e-16
eps = 10^-8; A = [ eps -1; 1 1];
[L, U] = my_LU( eps ); norm( L*U - A )/norm( A )
ans =
0.6180340
L*A
ans =
1.0e+07 *
0.000000000000001 -0.000000100000000
0.000000200000000 -9.999999900000001