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An Octave cookbook. Each entry should go in a separate section and have the following subsection: problem, solution, discussion and maybe a see also. | An Octave cookbook. Each entry should go in a separate section and have the following subsection: problem, solution, discussion and maybe a see also. | ||
== Programs, Libraries, and Packages == | == Programs, Libraries, and Packages == | ||
Line 17: | Line 15: | ||
This is a list of possible tests to check for features: | This is a list of possible tests to check for features: | ||
## support for 64 bit indexing | |||
## support for 64 bit indexing | sizemax () > intmax ("int32") | ||
sizemax () > intmax ("int32") | |||
## built with support for java | ## built with support for java | ||
usejava ("jvm") | usejava ("jvm") | ||
## Image IO with support for tif files | ## Image IO with support for tif files | ||
any (cellfun (@(x) ismember ("tif", x), {imformats.ext})) | any (cellfun (@(x) ismember ("tif", x), {imformats.ext})) | ||
## Image IO with support for png files | ## Image IO with support for png files | ||
any (cellfun (@(x) ismember ("png", x), {imformats.ext})) | any (cellfun (@(x) ismember ("png", x), {imformats.ext})) | ||
=== Find if a package is installed === | === Find if a package is installed === | ||
Line 41: | Line 37: | ||
Use {{codeline|pkg ("list", pkg-name)}} like so: | Use {{codeline|pkg ("list", pkg-name)}} like so: | ||
if (! isempty (pkg ("list", "foo"))) | |||
if (! isempty (pkg ("list", "foo"))) | ## use functions from package foo, the prefered way | ||
elseif (! isempty (pkg ("list", "bar"))) | |||
elseif (! isempty (pkg ("list", "bar"))) | ## use functions from package bar, not so optimal | ||
else | |||
else | ## default case | ||
endif | |||
endif | |||
==== Discussion ==== | ==== Discussion ==== | ||
Line 62: | Line 56: | ||
then you might as well not catch it in the first place. | then you might as well not catch it in the first place. | ||
## This contraption doesn't add anything. If 'pkg load' fails, it | |||
## This contraption doesn't add anything. If 'pkg load' fails, it | ## will already give an error message to the user. | ||
## will already give an error message to the user. | try | ||
try | pkg load foo; | ||
catch | |||
catch | error ("failed to load foo: %s", lasterr ()); | ||
end_try_catch | |||
end_try_catch | |||
## Again, doesn't add anything. The failure of 'pkg load' is enough | ## Again, doesn't add anything. The failure of 'pkg load' is enough | ||
if (isempty (pkg ("list", "foo"))) | if (isempty (pkg ("list", "foo"))) | ||
error ("program: package foo is not installed"); | |||
endif | endif | ||
Beware that an installed package is not always a guarantee that a function | Beware that an installed package is not always a guarantee that a function | ||
will be available. Some packages may disable functions at build time, or | will be available. Some packages may disable functions at build time, or | ||
specific functions may have specific runtime requirements. | specific functions may have specific runtime requirements. | ||
== Structures == | == Structures == | ||
=== Retrieve a field value from all entries in a struct array === | === Retrieve a field value from all entries in a struct array === | ||
==== Problem ==== | ==== Problem ==== | ||
You have a struct array with multiple fields, and you want to access the value from a specific field from all elements. For example, you want to return the age from all patients in the following case: | You have a struct array with multiple fields, and you want to access the value from a specific field from all elements. For example, you want to return the age from all patients in the following case: | ||
samples = struct ("patient", {"Bob", "Kevin", "Bob" , "Andrew"}, | |||
samples = struct ("patient", {"Bob", "Kevin", "Bob" , "Andrew"}, | "age", { 45 , 52 , 45 , 23 }, | ||
"protein", {"H2B", "CDK2" , "CDK2", "Tip60" }, | |||
"tube" , { 3 , 5 , 2 , 18 } | |||
); | |||
==== Solution ==== | ==== Solution ==== | ||
Indexing the struct returns a comma separated list so use them to create a matrix. | Indexing the struct returns a comma separated list so use them to create a matrix. | ||
[samples(:).age] | |||
[samples(:).age] | |||
This however does not keep the original structure of the data, instead returning all values in a single column. To fix this, use {{Codeline|reshape()}}. | This however does not keep the original structure of the data, instead returning all values in a single column. To fix this, use {{Codeline|reshape()}}. | ||
reshape ([samples(:).age], size (samples)) | |||
reshape ([samples(:).age], size (samples)) | |||
==== Discussion ==== | ==== Discussion ==== | ||
Returning all values in a comma separated lists allows you to make anything out of them. If numbers are expected, create a matrix by enclosing them in square brackets. But if strings are to be expected, a cell array can also be easily generated with curly brackets | |||
{samples(:).patient} | |||
{samples(:).patient} | |||
You are also not limited to return all elements, you may use logical indexing from other fields to get values from the others: | You are also not limited to return all elements, you may use logical indexing from other fields to get values from the others: | ||
[samples([samples(:).age] > 34).tube] ## return tube numbers from all samples from patients older than 34 | |||
[samples([samples(:).age] > 34).tube] ## return tube numbers from all samples from patients older than 34 | [samples(strcmp({samples(:).protein}, "CDK2")).tube] ## return all tube numbers for protein CDK2 | ||
[samples(strcmp({samples(:).protein}, "CDK2")).tube] ## return all tube numbers for protein CDK2 | |||
== Array manipulation == | == Array manipulation == | ||
Line 152: | Line 109: | ||
==== Problem ==== | ==== Problem ==== | ||
For an array {{Codeline|A}} with arbitrary number of dimensions, select, for example, the first column. | For an array {{Codeline|A}} with arbitrary number of dimensions, select, for example, the first column. This would be {{Codeline|A(:, 1)}} if {{Codeline|A}} was 2-D, {{Codeline|A(:, 1, :)}} if {{Codeline|A}} was 3-D, and so on. | ||
This would be {{Codeline|A(:, 1)}} if {{Codeline|A}} was 2-D, {{Codeline|A(:, 1, :)}} if {{Codeline|A}} was 3-D, and so on. | |||
==== Solution ==== | ==== Solution ==== | ||
One possibility is to use {{ | One possibility is to use {{Codeline|subsref}} with the input {{Codeline|idx}} created dynamically with {{Codeline|repelems}} to have the right number of dimensions. This can be written as a function: | ||
This can be written as a function: | |||
<syntaxhighlight lang=" | {{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | ||
function [B]= array_slice (A,k,d) | function [B]= array_slice (A,k,d) | ||
#return the k-th slice (row, column...) of A, with d specifying the dimension to slice on | #return the k-th slice (row, column...) of A, with d specifying the dimension to slice on | ||
Line 179: | Line 135: | ||
%! A=rand(2, 3, 4, 5, 6); | %! A=rand(2, 3, 4, 5, 6); | ||
%!assert (array_slice (A,2,3), A(:, :, 2, :, :)) | %!assert (array_slice (A,2,3), A(:, :, 2, :, :)) | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
To remove the singleton dimension {{Codeline|d}} from the result {{Codeline|B}}, use | To remove the singleton dimension {{Codeline|d}} from the result {{Codeline|B}}, use | ||
{{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | |||
<syntaxhighlight lang=" | |||
B = reshape(B, [size(B)([1:d-1 d+1:end])]); | B = reshape(B, [size(B)([1:d-1 d+1:end])]); | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
== Input/output == | == Input/output == | ||
=== Display matched elements from different arrays === | === Display matched elements from different arrays === | ||
==== Problem ==== | ==== Problem ==== | ||
You have two, or more, arrays with paired elements and want to print out a string about them. For example: | You have two, or more, arrays with paired elements and want to print out a string about them. For example: | ||
keys = {"human", "mouse", "chicken"}; | |||
keys = {"human", "mouse", "chicken"}; | values = [ 64 72 70 ]; | ||
values = [ 64 72 70 ]; | |||
and you want to display: | and you want to display: | ||
Calculated human genome GC content is 64% | |||
Calculated mouse genome GC content is 72% | |||
Calculated chicken genome GC content is 70% | |||
==== Solution ==== | ==== Solution ==== | ||
Make a two rows cell array, with each paired data in a column and supply a cs-list to printf | |||
values = num2cell (values); | |||
new = {keys{:}; values{:}}; | |||
printf ("Calculated %s genome GC content is %i%%\n", new{:}) | |||
values = num2cell (values); | |||
new = {keys{:}; values{:}}; | |||
printf ("Calculated %s genome GC content is %i%%\n", new{:}) | |||
or in a single line: | or in a single line: | ||
printf ("Calculated %s genome GC content is %i%%\n", {keys{:}; num2cell(values){:}}{:}) | |||
printf ("Calculated %s genome GC content is %i%%\n", {keys{:}; num2cell(values){:}}{:}) | |||
==== Discussion ==== | ==== Discussion ==== | ||
{{Codeline|printf}} and family do not accept cell arrays as values. However, they keep repeating the template given as long as it has enough arguments to keep going. As such, the trick is on supplying a cs-list of elements which can be done by using a cell array and index it with {{Codeline|<nowiki>{}</nowiki>}}. | |||
Since values are stored in column-major order, paired values need to be on the same column. A new row of data can then be added later with {{Codeline|new(end+1,:) <nowiki>= {"Andrew", "Bob", "Kevin"}</nowiki>}}. Note that normal brackets are now being used for indexing. | |||
Since values are stored in column-major order, paired values need to be on the same column. | |||
A new row of data can then be added later with | |||
new(end+1,:) = {"Andrew", "Bob", "Kevin"} | |||
</ | |||
Note that normal brackets are now being used for indexing. | |||
=== Swap values === | === Swap values === | ||
If you want to exchange the value between two variables without creating a dummy one, you can simply do: | If you want to exchange the value between two variables without creating a dummy one, you can simply do: | ||
<syntaxhighlight lang=" | {{Code|Swap values without dummy variable|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
[b,a] = deal (a,b); | [b,a] = deal (a,b); | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
=== Collect all output arguments of a function === | === Collect all output arguments of a function === | ||
If you have a function that returns several values, e.g. | If you have a function that returns several values, e.g. | ||
<syntaxhighlight lang=" | {{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | ||
function [a b c]= myfunc () | function [a b c]= myfunc () | ||
[a,b,c] = deal (1,2,3); | [a,b,c] = deal (1,2,3); | ||
endfunction | endfunction | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
and you want to collect them all into a single cell (similarly to Python's zip() function) you can do: | and you want to collect them all into a single cell (similarly to Python's zip() function) you can do: | ||
<syntaxhighlight lang=" | {{Code|Collect multiple output arguments|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
outargs = nthargout (1:3, @myfunc) | outargs = nthargout (1:3, @myfunc) | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
=== Create a text table with fprintf=== | === Create a text table with fprintf=== | ||
(a.k.a. A funny formatting trick with fprintf found by chance) | |||
Imagine that you want to create a text table with | Imagine that you want to create a text table with fprintf with 2 columns of 15 characters width and both right justified. How to do this thing? | ||
How to do this thing? | |||
That's easy: | That's easy: | ||
If the variable Text is a cell array of strings (of length < 15) with two columns and a certain number of rows, simply type for the | If the variable Text is a cell array of strings (of length <15) with two columns and a certain number of rows, simply type for the kth row of Text | ||
{{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | |||
fprintf('%15.15s | %15.15s\n', Text{k,1}, Text{k,2}); | |||
</syntaxhighlight>}} | |||
The syntax '%<n>.<m>s' allocates '<n>' places to write chars and display the '<m>' first characters of the string to display. | |||
<syntaxhighlight lang=" | Example: | ||
fprintf('%15.15s | %15.15s\n', Text{ | {{Code|Example create a text table with fprintf|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
</syntaxhighlight> | octave:1> Text={'Hello','World'}; | ||
octave:2> fprintf('%15.15s | %15.15s\n', Text{1,1}, Text{1,2}) | |||
Hello | World | |||
</syntaxhighlight>}} | |||
===Load comma separated values (*.csv) files=== | |||
{{Code|Load comma separated values files|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
A=textread("file.csv", "%d", "delimiter", ","); | |||
B=textread("file.csv", "%s", "delimiter", ","); | |||
inds = isnan(A); | |||
B(!inds) = num2cell(A(!inds)) | |||
</syntaxhighlight>}} | |||
< | This gets you a 1 column cell array. You can reshape it to the original size by using the <code>reshape</code> function | ||
</ | |||
The next version of octave (3.6) implements the <code>CollectOutput</code> switch as seen in example 8 here: http://www.mathworks.com/help/techdoc/ref/textscan.html | |||
Another option is to use the function <code>csvread</code>, however this function can't handle non-numerical data. | |||
The probably best option is to use the function csv2cell() from the io package. This function can read mixed-type (numerical and text) .csv files, allows to specify other field separators than a comma and other text protection characters (default: " double quote) and can skip headerlines. If you have the io package installed and loaded, type "help csv2cell" at the Octave prompt for more info. | |||
===Load XML files=== | ===Load XML files=== | ||
Reading XML in octave can be achieved using the java library [ | Reading XML in octave can be achieved using the java library [http://xerces.apache.org/ Xerces] (from apache). | ||
It seems that the | It seems that the matlab's xmlread is just a thin wrapper around the Xerces library. One should note however, that Java functions have the working directory set to the working directory when octave starts and the working directory is not modified by a cd in octave. Matlab has the same behavior, as Java does not provide a way to change the current working directory (http://bugs.java.com/bugdatabase/view_bug.do?bug_id=4045688). To avoid any issues, it is thus better to use the absolute path to the XML file. | ||
One should note however, that Java functions have the working directory set to the working directory when octave starts and the working directory is not modified by a | |||
Matlab has the same behavior, as Java does not provide a way to change the current working directory (http://bugs.java.com/bugdatabase/view_bug.do?bug_id=4045688). | |||
To avoid any issues, it is thus better to use the absolute path to the XML file. | |||
You need the jar files | You need the jar files xercesImpl.jar and xml-apis.jar from e.g. https://www.apache.org/dist/xerces/j/Xerces-J-bin.2.11.0.tar.gz (check for the latest version). | ||
Use | Use javaaddpath to include these files: | ||
<syntaxhighlight lang=" | {{Code|Define java path|<syntaxhighlight lang="octave" style="font-size:1.1em"> | ||
javaaddpath ( | javaaddpath('/path/to/xerces-2_11_0/xercesImpl.jar'); | ||
javaaddpath ( | javaaddpath('/path/to/xerces-2_11_0/xml-apis.jar'); | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
A sample script: | |||
<syntaxhighlight lang=" | {{Code|Load XML file|<syntaxhighlight lang="octave" style="font-size:1.1em"> | ||
filename = | filename = 'sample.xml'; | ||
% These 3 lines are equivalent to xDoc = xmlread(filename) in matlab | |||
parser = javaObject('org.apache.xerces.parsers.DOMParser'); | |||
parser.parse(filename); | |||
xDoc = parser.getDocument; | |||
% get first data element | |||
elem = xDoc.getElementsByTagName('data').item(0); | |||
% get text from child | |||
data = elem.getFirstChild.getTextContent | |||
% get attribute named att | |||
att = elem.getAttribute('att') | |||
</syntaxhighlight>}} | |||
The file <tt>sample.xml</tt>: | |||
{{Code|Sample XML file|<syntaxhighlight lang="xml" style="font-size:1.1em"> | |||
<root> | |||
<data att="1">hello</data> | |||
</root> | |||
{{ | |||
<syntaxhighlight lang="xml"> | |||
<root> | |||
</root> | |||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||
Line 339: | Line 275: | ||
For example, to plot data using a string variable as a legend: | For example, to plot data using a string variable as a legend: | ||
Option 1 (simplest): | |||
{{Code|Using variable strings in commands. op1|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
legend = "-1;My data;"; | legend = "-1;My data;"; | ||
plot (x, y, legend); | plot(x, y, legend); | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
Option 2 (to insert variables): | |||
{{Code|Using variable strings in commands. op2|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
plot(x, y, sprintf("-1;%s;", dataName)); | |||
plot (x, y, sprintf("-1;%s;", dataName)); | </syntaxhighlight>}} | ||
</syntaxhighlight> | |||
Option 3 (not as neat): | |||
legend = | {{Code|Using variable strings in commands. op3|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
plot_command = [ | legend = 'my legend'; | ||
eval (plot_command); | plot_command = ['plot(x,y,\';',legend,';\')']; | ||
</syntaxhighlight> | eval(plot_command); | ||
</syntaxhighlight>}} | |||
These same tricks are useful for reading and writing data files with unique names, etc. | These same tricks are useful for reading and writing data files with unique names, etc. | ||
== Combinatorics == | == Combinatorics == | ||
=== Combinations with string characters === | === Combinations with string characters === | ||
==== Problem ==== | ==== Problem ==== | ||
You want to get all combinations of different letters but {{codeline|nchoosek}} only accepts numeric input. | |||
You want to get all combinations of different letters but {{ | |||
==== Solution ==== | ==== Solution ==== | ||
Convert your string to numbers and then back to characters. | Convert your string to numbers and then back to characters. | ||
<syntaxhighlight lang=" | {{Code||<syntaxhighlight lang="octave"> | ||
char (nchoosek (uint8 (string), n)) | char (nchoosek (uint8 (string), n)) | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
==== Discussion ==== | ==== Discussion ==== | ||
A string in Octave is just a character matrix and can easily be converted to numeric form back and forth. Each character has an associated number (the {{codeline|asci}} function of the {{forge|miscellaneous}} package displays a nicely formatted conversion table). | |||
A string in Octave is just a character matrix and can easily be converted to numeric form back and forth. | |||
Each character has an associated number (the {{codeline|asci}} function of the {{forge|miscellaneous}} package displays a nicely formatted conversion table). | |||
=== Permutations with repetition === | === Permutations with repetition === | ||
==== Problem ==== | ==== Problem ==== | ||
You want to generate all possible permutations of a vector with repetition. | You want to generate all possible permutations of a vector with repetition. | ||
==== Solution ==== | ==== Solution ==== | ||
Use {{codeline|ndgrid}} | |||
{{Code||<syntaxhighlight lang="octave"> | |||
[x y z] = ndgrid ([1 2 3 4 5]); | |||
<syntaxhighlight lang=" | [x(:) y(:) z(:)] | ||
[x | </syntaxhighlight>}} | ||
[x(:) | |||
</syntaxhighlight> | |||
==== Discussion ==== | ==== Discussion ==== | ||
It is possible to expand the code above and make it work for any length of permutations. | It is possible to expand the code above and make it work for any length of permutations. | ||
<syntaxhighlight lang=" | {{Code||<syntaxhighlight lang="octave"> | ||
cart = nthargout ([1:n], @ndgrid, vector); | cart = nthargout ([1:n], @ndgrid, vector); | ||
combs = cell2mat (cellfun (@(c) c(:), cart, "UniformOutput", false)); | combs = cell2mat (cellfun (@(c) c(:), cart, "UniformOutput", false)); | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
== Mathematics == | == Mathematics == | ||
=== Test if a number is a integer === | |||
=== Test if a number is | There are several methods to do this. The simplest method is probably {{Codeline|<nowiki>fix (x) == x</nowiki>}} | ||
The simplest method is probably {{ | |||
< | |||
fix (x) == x | |||
</ | |||
=== Find if a number is even/odd === | === Find if a number is even/odd === | ||
==== Problem ==== | ==== Problem ==== | ||
You have a number, or an array or matrix of them, and want to know if any of them is an odd or even number, i.e., their parity. | You have a number, or an array or matrix of them, and want to know if any of them is an odd or even number, i.e., their parity. | ||
==== Solution ==== | ==== Solution ==== | ||
Check the remainder of a division by two. If the remainder is zero, the number is even. | Check the remainder of a division by two. If the remainder is zero, the number is even. | ||
mod (value, 2) ## 1 if odd, zero if even | |||
mod (value, 2) | |||
Since {{ | Since {{Codeline|mod()}} acceps a matrix, the following can be done: | ||
any (mod (values, 2)) ## true if at least one number in values is even | |||
any (mod (values, 2)) | all (mod (values, 2)) ## true if all numbers in values are odd | ||
all (mod (values, 2)) | |||
any (!logical (mod (values, 2))) ## true if at least one number in values is even | |||
any (!logical (mod (values, 2))) | all (!logical (mod (values, 2))) ## true if all numbers in values are even | ||
all (!logical (mod (values, 2))) | |||
==== Discussion ==== | ==== Discussion ==== | ||
Since we are checking for the remainder of a division, the first choice would be to use {{Codeline|rem()}}. However, in the case of negative numbers {{Codeline|mod()}} will still return a positive number making it easier for comparisons. Another alternative is to use {{Codeline|bitand (X, 1)}} or {{Codeline|bitget (X, 1)}} but those are a bit slower. | |||
Note that this solution applies to integers only. Non-integers such as 1/2 or 4.201 are neither even nor odd. If the source of the numbers are unknown, such as user input, some sort of checking should be applied for NaN, Inf, or non-integer values. | |||
==== See also ==== | |||
Find if a number is an integer. | |||
=== Parametrized Functions === | === Parametrized Functions === | ||
==== Problem ==== | ==== Problem ==== | ||
Line 459: | Line 366: | ||
==== Solution ==== | ==== Solution ==== | ||
We could solve the problem with the following code: | |||
{{Code|Solve spring equation for different values of the spring constant|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
<syntaxhighlight lang=" | |||
t = linspace (0, 10, 100); | t = linspace (0, 10, 100); | ||
function sprime = spring (s, t, k) | function sprime = spring (s, t, k) | ||
Line 476: | Line 382: | ||
plot (t, x1, t, x2) | plot (t, x1, t, x2) | ||
legend ('x1', 'x2') | legend ('x1', 'x2') | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
[[File:solparfun.png|400px]] | [[File:solparfun.png|400px]] | ||
Line 485: | Line 391: | ||
The [http://www.gnu.org/software/octave/doc/interpreter/Anonymous-Functions.html#Anonymous-Functions anonymous function] | The [http://www.gnu.org/software/octave/doc/interpreter/Anonymous-Functions.html#Anonymous-Functions anonymous function] | ||
{{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | |||
@(x, t) sprime (x, t, k) | |||
</syntaxhighlight>}} | |||
is a function of only <math>x, t</math> where the parameter <math>k</math> is 'frozen' to the value it has at the moment in the current scope. | |||
is a function of only <math>x, t</math> where the parameter <math>k</math> is | |||
=== Distance between points === | === Distance between points === | ||
==== Problem ==== | ==== Problem ==== | ||
Given a set of points in space we want to calculate the distance between all of them. Each point is described by its components <math> (x_i,y_i,\ldots)</math>. Asusme that the points are saved in a matrix '''<tt>P</tt>''' with '''<tt>N</tt>''' rows (one for each point) and '''<tt>D</tt>''' columns, one for each component. | |||
Given a set of points in space we want to calculate the distance between all of them. | |||
Each point is described by its components <math> (x_i,y_i,\ldots)</math>. | |||
==== Solution ==== | ==== Solution ==== | ||
One way of proceeding is to use the broadcast properties of operators in GNU Octave. The square distance between the points can be calculated with the code | |||
One way of proceeding is to use the broadcast properties of operators in GNU Octave. | <!-- {{SyntaxHighlight| --> | ||
The square distance between the points can be calculated with the code | {{Code|Calculate square distance between points|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
[N, dim] = size (P); | |||
<syntaxhighlight lang=" | Dsq = zeros (N); | ||
[ | for i = 1:dim | ||
Dsq = zeros ( | |||
for i = 1: | |||
Dsq += (P(:,i) - P(:,i)').^2; | Dsq += (P(:,i) - P(:,i)').^2; | ||
endfor | endfor | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
This matrix is symmetric with zero diagonal. | This matrix is symmetric with zero diagonal. | ||
Similarly the vectors pointing from one point to the another is | Similarly the vectors pointing from one point to the another is | ||
<!-- {{SyntaxHighlight| --> | |||
<syntaxhighlight lang=" | {{Code|Calculate radius vector between points|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
R = zeros ( | R = zeros (N,N,dim); | ||
for i = 1: | for i = 1:dim | ||
R(:,:,i) = P(:,i) - P(:,i)'; | R(:,:,i) = P(:,i) - P(:,i)'; | ||
endfor | endfor | ||
</syntaxhighlight> | </syntaxhighlight>}} | ||
The relation between < | The relation between <tt>Dsq</tt> and <tt>R</tt> is | ||
<!-- {{SyntaxHighlight| --> | |||
<syntaxhighlight lang=" | {{Code||<syntaxhighlight lang="octave" style="font-size:13px"> | ||
Dsq = sumsq (R, 3); | Dsq = sumsq (R,3); | ||
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==== Discussion ==== | ==== Discussion ==== | ||
The calculation can be implemented using functions like <tt>cellfun</tt> and avoid the loop over components of the points. However in most cases we will have more points than components and the improvement, if any, will be minimal. | |||
Another observation is that the matrix Dsq is symmetric and we could store only the lower or upper triangular part. To use this optimization in a practical way check the help of the functions <tt>vech</tt> and <tt>unvech</tt> (this one is in the Forge package ''general''). Two functions that haven't seen the light yet are <tt>sub2ind_tril</tt> and <tt>ind2sub_tril</tt> (currently private functions in the [[Mechanics_package | Forge package mechanics]]) that are useful to index the elements of a vector constructed with the function <tt>vech</tt>. Each page (the third index) of the multidimensional array <tt>R</tt> is an anti-symmetric matrix and we could also save some memory by keeping only one of the triangular submatrices. | |||
Another observation is that the matrix | |||
To use this optimization in a practical way check the help of the functions < | |||
Two functions that haven't seen the light yet are < | |||
Each page (the third index) of the multidimensional array < | |||
Check the [[Geometry package]] for many more distance functions (points, lines, polygons, etc.). | Check the [[Geometry package]] for many more distance functions (points, lines, polygons, etc.). | ||
[[Category: | [[Category:Tutorials]] |