Physics307L:People/Mondragon/Poisson/Notebook/20090513
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Ok, for better results, I switched to using a 4000 by 4000 matrix to simulate the first counting experiment.
The first matrix table1_3 represents 4000 trails of 4000 counting experiments were the average number of counts in each counting experiment (or whatever the [math]\displaystyle{ \lambda }[/math] in [math]\displaystyle{ f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\! }[/math] means) is 1.3 ([math]\displaystyle{ \lambda = 1.3 }[/math]). Each row is a a trail run. If the entry on row [math]\displaystyle{ r }[/math] and column [math]\displaystyle{ c }[/math] is [math]\displaystyle{ x }[/math], then counting experiment [math]\displaystyle{ c }[/math] in trail run [math]\displaystyle{ r }[/math] had a count of [math]\displaystyle{ x }[/math] events.
The rows of histy are the histograms of each corresponding trail run. I ran the bins for this one out to 50, since even at [math]\displaystyle{ \lambda = 9 }[/math], the max count in the 4000 by 4000 matrix above should be around 26 or so. Rows represent the test run, columns represent how many times a count of [math]\displaystyle{ column number - 1 }[/math] happened in that trail run. histy should be 4000 by 51. If the entry on row [math]\displaystyle{ r }[/math] and column [math]\displaystyle{ c }[/math] is [math]\displaystyle{ x }[/math], then there was [math]\displaystyle{ x }[/math] occurrences of a count of [math]\displaystyle{ c - 1 }[/math] in trail run [math]\displaystyle{ r }[/math].
The rows of histyy are histograms of the results in histy. If the entry on row [math]\displaystyle{ r }[/math] and column [math]\displaystyle{ c }[/math] is [math]\displaystyle{ x }[/math], then there was [math]\displaystyle{ x }[/math] trail runs were a count of [math]\displaystyle{ r- 1 }[/math] happened [math]\displaystyle{ c-1 }[/math] times.
it is histyy that I am really interested in. It should show what trends values in a Poisson plots tend to take. As I thought, values near [math]\displaystyle{ \lambda }[/math] have a Gaussian spread and values far from [math]\displaystyle{ \lambda }[/math] have a Poisson spread.
diary
octave:2> diary on
octave:3> load table1_3.asc
octave:4> who
*** dynamically linked functions:
builtin:find builtin:max builtin:min dispatch
*** currently compiled functions:
findstr ispc pkg split strrep
fullfile isscalar repmat strcat
*** local user variables:
__nargin__ table1_3
octave:5> maxbin = max(max(table1_3))
maxbin = 10
octave:6> minbin = min(min(table1_3))
minbin = 0
octave:7> t=poissrnd(5,50,50);
octave:8> max(max(t))
ans = 15
octave:9> t=poissrnd(5,50,50);
octave:10> max(max(t))
ans = 14
octave:11> t=poissrnd(9,50,50);
octave:12> max(max(t))
ans = 20
octave:13> t=poissrnd(9,50,50);
octave:14> max(max(t))
ans = 19
octave:15> t=poissrnd(9,50,50);
octave:16> max(max(t))
ans = 23
octave:17> t=poissrnd(10,50,50);
octave:18> max(max(t))
ans = 24
octave:19> t=poissrnd(10,50,50);
octave:20> max(max(t))
ans = 22
octave:21> t=poissrnd(10,50,50);
octave:22> max(max(t))
ans = 22
octave:23> t=poissrnd(10,50,50);
octave:24> max(max(t))
ans = 24
octave:25> t=poissrnd(10,50,50);
octave:26> max(max(t))
ans = 25
octave:27> t=poissrnd(10,50,50);
octave:28> max(max(t))
ans = 22
octave:29> ok, 30
error: `ok' undefined near line 29 column 1
octave:29> bins=0:30;
octave:30> for i=1:500
> [histx(i,:), histy(i,:)] = hist(table1_3),bins);
parse error:
syntax error
>>> [histx(i,:), histy(i,:)] = hist(table1_3),bins);
^
octave:30> for i=1:500
> [histx(i,:), histy(i,:)] = hist(table1_3),bins));
parse error:
syntax error
>>> [histx(i,:), histy(i,:)] = hist(table1_3),bins));
^
octave:30> [histx(i,:), histy(i,:)] = hist((table1_3),bins);
error: number of columns must match (1 != 1500)
error: evaluating argument list element number 1
error: evaluating if command near line 100, column 3
error: called from `hist' in file `/usr/share/octave/3.0.0/m/plot/hist.m'
octave:30> for i=1:500
> [histx(i,:), histy(i,:)] = hist((table1_3),bins);
> end
error: number of columns must match (1 != 1500)
error: evaluating argument list element number 1
error: evaluating if command near line 100, column 3
error: called from `hist' in file `/usr/share/octave/3.0.0/m/plot/hist.m'
error: evaluating for command near line 30, column 1
octave:30> for i=1:500
> [histx(i,:), histy(i,:)] = hist((table1_3(i,:)),bins);
> end
octave:31> plot
usage: plot (y)
plot (x, y, ...)
plot (x, y, fmt, ...) plot (x, y, property, value, ...)
error: evaluating if command near line 28, column 3
error: called from `__plt__' in file `/usr/share/octave/3.0.0/m/plot/__plt__.m'
error: evaluating assignment expression near line 187, column 9
error: called from `plot' in file `/usr/share/octave/3.0.0/m/plot/plot.m'
octave:31> plot(histx(1,:),histy(2,:))
octave:32> bar(histx(1,:), histy(1,:))
error: bar: x vector values must be in ascending order
error: evaluating if command near line 108, column 3
error: called from `__bar__' in file `/usr/share/octave/3.0.0/m/plot/__bar__.m'
error: called from `bar' in file `/usr/share/octave/3.0.0/m/plot/bar.m'
octave:32> bar( histy(1,:))
octave:33> histy
histy =
octave:34> bar( histx(1,:))
octave:35> bar( histx(51,:))
octave:36> for 1:500
parse error:
syntax error
>>> for 1:500
^
octave:36> for i=1:500
> bar( histx(i,:))
> end
octave:37> histx(64,:)
ans =
Columns 1 through 13:
390 553 332 159 52 12 2 0 0 0 0 0 0
Columns 14 through 26:
0 0 0 0 0 0 0 0 0 0 0 0 0
Columns 27 through 31:
0 0 0 0 0
octave:38> histx(:,1)
ans =
octave:39> bar(histx(:,1))
octave:40> ooooooo that looks like its possibly gaussian, just as I thought it would
parse error:
syntax error
>>> ooooooo that looks like its possibly gaussian, just as I thought it would
^
octave:40> max(histx(:,1))
ans = 462
octave:41> min(histx(:,1))
ans = 351
octave:42> hist(histx(:,1), 351:462)
octave:43> size(table1_3)
ans =
1500 1500
octave:44> oops
error: `oops' undefined near line 44 column 1
octave:44> for i=1:1500
> histy(i,:) = hist((table1_3(i,:)),bins);
> end
octave:45> max(histy(:,1))
ans = 470
octave:46> min(histy(:,1))
ans = 341
octave:47> hist(histy(:,1), 341:470)
octave:48> table1_3 = poissrnd(1.3,4000,4000);
octave:49> for i=1:4000
> end
octave:50> maxbin = max(max(table1_3))
maxbin = 10
octave:51> minbin = min(min(table1_3))
minbin = 0
octave:52> bins = 0:50;
octave:53> for i=1:4000
> histy(i,:) = hist((table1_3(i,:)),bins);
> end
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 54, column 12
error: evaluating for command near line 53, column 1
octave:53> histy(56,:) = hist((table1_3(56,:)),bins);
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 53, column 13
octave:53> table1_3 = poissrnd(1.3,3000,3000);
octave:54> histy(56,:) = hist((table1_3(56,:)),bins);
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 54, column 13
octave:54> bins
bins =
Columns 1 through 20:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Columns 21 through 40:
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Columns 41 through 51:
40 41 42 43 44 45 46 47 48 49 50
octave:55> histy(56,:) = hist((table1_3(56,:),bins);
parse error:
syntax error
>>> histy(56,:) = hist((table1_3(56,:),bins);
^
octave:55> histy(56,:) = hist(table1_3(56,:),bins);
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 55, column 13
octave:55> histy(56,:) = hist(table1_3(56,:));
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 55, column 13
octave:55> table1_3(56,:)
ans =
octave:56> size(table1_3)
ans =
3000 3000
octave:57> is 3000 by 3000 just too big?
parse error:
syntax error
>>> is 3000 by 3000 just too big?
^
octave:57> table1_3 = poissrnd(1.3,2000,2000);
octave:58> histy(56,:) = hist(table1_3(56,:));
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 58, column 13
octave:58> table1_3 = poissrnd(1.3,1500,1500);
octave:59> histy(56,:) = hist(table1_3(56,:));
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 59, column 13
octave:59> histy(56) = hist(table1_3(56,:));
error: A(I) = X: X must be a scalar or a matrix with the same size as I
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 59, column 11
octave:59> hist(table1_3(56,:));
octave:60> ans
ans =
3000 3000
octave:61> x=hist(table1_3(56,:));
octave:62> x
x =
451 516 320 151 46 0 13 2 0 1
octave:63> x(56)=hist(table1_3(56,:));
error: A(I) = X: X must be a scalar or a vector with same length as I
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 63, column 6
octave:63> x(56,:)=hist(table1_3(56,:));
octave:64> histy(56,:)=hist(table1_3(56,:));
error: A(IDX-LIST) = X: X must be a scalar or size of X must equal number of elements indexed by IDX-LIST
error: assignment failed, or no method for `matrix = matrix'
error: evaluating assignment expression near line 64, column 12
octave:64> clear all
octave:65> clear -all
octave:66> who
*** dynamically linked functions:
dispatch
*** currently compiled functions:
pkg
*** local user variables:
__nargin__
octave:67> table1_3 = poissrnd(1.3,4000,4000);
octave:68> x(56,:)=hist(table1_3(56,:));
octave:69> histy(56,:)=hist(table1_3(56,:));
octave:70> memory was cluttered?
parse error:
syntax error
>>> memory was cluttered?
^
octave:70> clear all
octave:71> table1_3 = poissrnd(1.3,4000,4000);
octave:72> for i=1:4000
> histy(i,:)=hist(table1_3(i,:),0:50);
> end
octave:73> bins = 0:50;
octave:74> save -text table1_3.asc table1_3 histy bins
octave:75> min(histy(:,1))
ans = 993
octave:76> max(histy(:,1))
ans = 1186
octave:77> hist(histy(:,1),993:1186)
octave:78> max(max(histy))
ans = 1527
octave:79> min(min(histy))
ans = 0
octave:80> size(histy)
ans =
4000 51
octave:81> for i = bins
> histyy(i,:)=hist(histy(:,i),0:2000);
> end
error: invalid column index = 0
error: evaluating argument list element number 1
error: evaluating assignment expression near line 82, column 12
error: evaluating for command near line 81, column 1
octave:81> for i = bins+1
> histyy(i,:)=hist(histy(:,i),0:2000);
> end
octave:82> bar(histyy(1,:),0:2000)
error: bar: x vector values must be in ascending order
error: evaluating if command near line 108, column 3
error: called from `__bar__' in file `/usr/share/octave/3.0.0/m/plot/__bar__.m'
error: called from `bar' in file `/usr/share/octave/3.0.0/m/plot/bar.m'
octave:82> bar(0:2000,histyy(1,:))
octave:83> bar(0:2000,histyy(2,:))
octave:84> bar(0:2000,histyy(3,:))
octave:85> bar(0:2000,histyy(9,:))
octave:86> axis([0,10])
octave:87> bar(0:2000,histyy(7,:))
octave:88> axis([0,10])
octave:89> axis([0,30])
octave:90> save -text table1_3.asc table1_3 histy bins histyy
octave:91> clear histyy
octave:92> who
*** dynamically linked functions:
builtin:find builtin:min gnuplot_binary regexp
builtin:kron cellfun issparse sort
builtin:max dispatch randp
*** currently compiled functions:
__bar__ diff lower
__bars__ drawnow newplot
__gnuplot_version__ findstr patch
__go_draw_axes__ gca pkg
__go_draw_figure__ gcf poissrnd
__next_line_color__ hist rem
__patch__ image_viewer repmat
__plt_get_axis_arg__ isa split
ancestor ismember str2num
axes isscalar strcat
axis isstr strcmpi
bar isvector xor
compare_versions logical
*** local user variables:
__nargin__ ans bins histy i table1_3
octave:93> bins2 = 0:2500;
octave:94> for i = bins+1
> histyy(i,:)=hist(histy(:,i),bars2);
> end
error: `bars2' undefined near line 95 column 29
error: evaluating argument list element number 2
error: evaluating assignment expression near line 95, column 12
error: evaluating for command near line 94, column 1
octave:94> for i = bins+1
> histyy(i,:)=hist(histy(:,i),bins2);
> end
octave:95> save -text table1_3.asc table1_3 histy bins histyy bins2
octave:96> size(histyy)
ans =
51 2501
octave:97> [xx,yy]=meshgrid(bins, bins2);
octave:98> mesh(xx,yy,histyy)
error: surface: x, y, and z must have same dimensions
error: evaluating if command near line 114, column 7
error: evaluating if command near line 106, column 5
error: evaluating if command near line 76, column 3
error: called from `surface:__surface__' in file `/usr/share/octave/3.0.0/m/plot/surface.m'
error: called from `surface' in file `/usr/share/octave/3.0.0/m/plot/surface.m'
error: evaluating assignment expression near line 37, column 7
error: called from `mesh' in file `/usr/share/octave/3.0.0/m/plot/mesh.m'
octave:98> [xx,yy]=meshgrid(bins2, bins);
octave:99> size(xx)
ans =
51 2501
octave:100> mesh(xx,yy,histyy)
octave:101>
octave:101> diary off
important excerpts
octave:71> table1_3 = poissrnd(1.3,4000,4000); octave:72> for i=1:4000 > histy(i,:)=hist(table1_3(i,:),0:50); > end octave:73> bins = 0:50; octave:93> bins2 = 0:2500; octave:94> for i = bins+1 > histyy(i,:)=hist(histy(:,i),bins2); > end
