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I try to solve a differential equation in Octave. In a first attempt, all my independent variables are set constant (n,y,w). This is my code:
function xdot= f(x,t);
% xdot=zeros(1,1);
X=1.44221E+12;
IO=5.318E+11;
GO=6.81E+11;
beta=0;
gamma=0;
y=58.5021088;
w= 31.29;
n=1363.5;
tw=0.4;
tp=0.3;
sw=0.07;
sp=0.25;
mw=0.593941689;
mp=0.593941689;
% aw=(1-tw)(sw+mw)
% ap=(1-tp)(sp+mp)
xdot=-(X+IO*(1+gamma*(diff(n)/n+diff(y)/y))+GO*beta(tw(diff(n)/n+diff(w)/w)+tp(diff(y)/y-diff(w)/w)-(x*n)/((y-w)((1-tp)(sp+mp)+tp)+((1-tw)(sw+mw)+tw)*w))*x)/(IO*gamma+GO*beta*tw);
endfunction
When I add
t = [0:(1/360):10]
x = lsode ("f", 39290000, t);
to solve the equation in the command line, I get this error:
error: index (0.843942): subscripts must be either integers 1 to (2^31)-1 or logicals
error: lsode: evaluation of user-supplied function failed
error: called from
f at line 23 column 7
It seems to me, in some way I misunderstood how to make the function.
Any help?
EDIT:
This is my new code:
function xdot= f(x,t);
X=1.44221E+12;
IO=5.318E+11;
GO=6.81E+11;
beta=0;
gamma=0;
y=58.5021088;
w= 31.29;
n=1363.5;
tw=0.4;
tp=0.3;
sw=0.07;
sp=0.25;
mw=0.593941689;
mp=0.593941689;
xdot=-X+IO-(x*n)/((y-w)*((1-tp)*(sp+mp)+tp)+w*(tw+(1-tp)*(sp+mp)))
endfunction
It does work if I copy it into the command line but if I start it as programm (f.m) and solve it then I get this error:
error: 'x' undefined near line 25 column 15
error: called from
f at line 25 column 7
From the documentation of lsode:
Syntax: [x, istate, msg] = lsode (fcn, x_0, t)
...
The first argument, fcn, is a string, inline, or function handle that names the function f to call to compute the vector of right hand sides for the set of equations. The function must have the form
xdot = f (x, t)
in which xdot and x are vectors and t is a scalar.
So firstly, your f function is of the wrong form to the one expected by lsode, since it takes 5 arguments as opposed to 2.
Secondly, inside your f function, the variables y, w, and n are overwritten, regardless of whether they were supplied, whereas t and x need to be supplied by the user.
When lsode calls the handle f, it calls it with two arguments as per its specification, which means it instantiates t and y, and calls the function with the remaining input arguments undefined. Of the remaining arguments, w and n are given values inside the function, as we pointed out above, but x remains undefined. So when you run the final calculation which relies on x, you get an error saying it has not yet been defined during the call to this function.
So, to fix this issue, rewrite your function such that its signature is f(x, t), which you can do so easily since y, w, and n are defined inside your function anyway, so they don't really need to be given as inputs.
Unlike Matlab, Octave Symbolic has no piecewise function. Is there a work around? I would like to do something like this:
syms x
y = piecewise(x0, 1)
Relatedly, how does one get pieces of a piecewise function? I ran the following:
>> int (exp(-a*x), x, 0, t)
And got the following correct answer displayed and stored in a variable:
t for a = 0
-a*t
1 e
- - ----- otherwise
a a
But now I would like to access the "otherwise" part of the answer so I can factor it. How do I do that?
(Yes, I can factor it in my head, but I am practicing for when more complicated expressions come along. I am also only really looking for an approach using symbolic expressions -- even though in any single case numerics may work fine, I want to understand the symbolic approach.)
Thanks!
Matlab's piecewise function seems to be fairly new (introduced in 2016b), but it basically just looks like a glorified ternary operator. Unfortunately I don't have 2016 to check if it performs any checks on the inputs or not, but in general you can recreate a 'ternary' operator in octave by indexing into a cell using logical indexing. E.g.
{#() return_A(), #() return_B(), #() return_default()}([test1, test2, true]){1}()
Explanation:
Step 1: You put all the values of interest in a cell array. Wrap them in function handles if you want to prevent them being evaluated at the time of parsing (e.g. if you wanted the output of the ternary operator to be to produce an error)
Step 2: Index this cell array using logical indexing, where at each index you perform a logical test
Step 3: If you need a 'default' case, use a 'true' test for the last element.
Step 4: From the cell (sub)array that results from above, select the first element and 'run' the resulting function handle. Selecting the first element has the effect that if more than one tests succeed, you only pick the first result; given the 'default' test will always succeed, this also makes sure that this is not picked unless it's the first and only test that succeeds (which it does so by default).
Here are the above steps implemented into a function (appropriate sanity checks omitted here for brevity), following the same syntax as matlab's piecewise:
function Out = piecewise (varargin)
Conditions = varargin(1:2:end); % Select all 'odd' inputs
Values = varargin(2:2:end); % Select all 'even' inputs
N = length (Conditions);
if length (Values) ~= N % 'default' case has been provided
Values{end+1} = Conditions{end}; % move default return-value to 'Values'
Conditions{end} = true; % replace final (ie. default) test with true
end
% Wrap return-values into function-handles
ValFuncs = cell (1, N);
for n = 1 : N; ValFuncs{n} = #() Values{n}; end
% Grab funhandle for first successful test and call it to return its value
Out = ValFuncs([Conditions{:}]){1}();
end
Example use:
>> syms x t;
>> F = #(a) piecewise(a == 0, t, (1/a)*exp(-a*t)/a);
>> F(0)
ans = (sym) t
>> F(3)
ans = (sym)
-3⋅t
ℯ
─────
9
I have created a function that returns the magnitude of a vector.the output is 360x3 dimension matrix. the input is 360x2.
Everything works fine outside the function. how do i get it to work ?
clc
P_dot_ij_om_13= rand(360,2); // 360x2 values of omega in vectors i and j
//P_dot_ij_om_13(:,3)=0;
function [A]=mag_x(A)
//b="P_dot_ijOmag_"+ string(k);
//execstr(b+'=[]'); // declare indexed matrix P_dot_ijOmag_k
//disp(b)
for i=1:1:360
//funcprot(0);
A(i,3)=(A(i,2)^2+A(i,1)^2)^0.5; //calculates magnitude of i and j and adds 3rd column
disp(A(i,3),"vector magnitude")
end
funcprot(1);
return [A] // should return P_dot_ijOmag_k in the variable browser [360x3 dim]
endfunction
mag_x(P_dot_ij_om_13);
//i=1;
//P_dot_ij_om_13(i,3)= (P_dot_ij_om_13(i,2)^2+P_dot_ij_om_13(i,1)^2)^0.5;// example
You never assigned mag_x(P_dot_ij_om_13) to any variable, so the output of this function disappears into nowhere. The variable A is local to this function, it does not exist outside of it.
To have the result of calculation available, assign it to some variable:
res = mag_x(P_dot_ij_om_13)
or A = mag_x(P_dot_ij_om_13) if you want to use the same name outside of the function as was used inside of it.
By the way, the Scilab documentation discourages the use of return, as it leads to confusion. The Scilab / Matlab function syntax is different from the languages in which return specifies the output of a function:
function y = sq(x)
y = x^2
endfunction
disp(sq(3)) // displays 9
No need for return here.
I have a matrix with rows of 4 integers, with an unspecified number of columns (depends on the text file).
I'm wanting to apply a function to each row of the matrix, independently. The function has 4 inputs, and 2 outputs.
I'm trying to use the arrayfun function to do this, but whenever I call the function, I get an error saying: "Not enough input arguments."
Here is the function call:
[gain,phase]=arrayfun(#(x) GainPhaseComp(B(x,1:4)), 1:size(B));
where b is an n by 4 matrix.
Here is the function:
function [gain,phase] = GainPhaseComp(InAmp,InPhase,OutAmp,OutPhase)
gain = 20*log10(OutAmp\InAmp);
phase = (OutPhase - InPhase);
end
Any help would be greatly appreciated!
Your function GainPhaseComp has 4 input arguments, but you pass only 1 row vector. Vector with 4 elements is still one variable, not 4. You need either to change the function definition or split the vector elements.
1st option:
function [gain,phase] = GainPhaseComp(inputvector)
% function body
2nd option:
[gain,phase]=arrayfun(#(x) GainPhaseComp(B(x,1),B(x,2),B(x,3),B(x,4)), 1:size(B,1));
This is a general question, not related to a particular operation. I would like to be able to write the results of an arbitrary function into elements of a cell array without regard for the data type the function returns. Consider this pseudocode:
zout = cell(n,m);
myfunc = str2func('inputname'); %assume myfunc puts out m values to match zout dimensions
zout(1,:) = myfunc(x,y);
That will work for "inputname" == "strcat" , for example, given that x and y are strings or cells of strings with appropriate dimension. But if "inputname" == "strcmp" then the output is a logical array, and Matlab throws an error. I'd need to do
zout(1,:) = num2cell(strcmp(x,y));
So my question is: is there a way to fill the cell array zout without having to test for the type of variable generated by myfunc(x,y ? Should I be using a struct in the first place (and if so, what's the best way to populate it)?
(I'm usually an R user, where I could just use a list variable without any pain)
Edit: To simplify the overall scope, add the following "requirement" :
Let's assume for now that, for a function which returns multiple outputs, only the first one need be captured in zout . But when this output is a vector of N values or a vector of cells (i.e. Nx1 cell array), these N values get mapped to zout(1,1:N) .
So my question is: is there a way to fill the cell array zout without having to test for the type of variable generated by myfunc(x,y) ? Should I be using a struct in the first place (and if so, what's the best way to populate it)?
The answer provided by #NotBoStyf is almost there, but not quite. Cell arrays are the right way to go. However, the answer very much depends on the number of outputs from the function.
Functions with only one output
The function strcmp has only one output, which is an array. The reason that
zout{1,:} = strcmp(x,y)
gives you an error message, when zout is dimensioned N x 2, is that the left-hand side (zout{1,:}) expects two outputs from the right-hand side. You can fix this with:
[zout{1,:}] = num2cell(strcmp(x,y)); % notice the square brackets on the LHS
However, there's really no reason to do this. You can simply define zout as an N x 1 cell array and capture the results:
zout = cell(1,1);
x = 'a';
y = { 'a', 'b' };
zout{1} = strcmp(x,y);
% Referring to the results:
x_is_y_1 = zout{1}(1);
x_is_y_2 = zout{1}(2);
There's one more case to consider...
Functions with multiple outputs
If your function produces multiple outputs (as opposed to a single output that is an array), then this will only capture the first output. Functions that produce multiple outputs are defined like this:
function [outA,outB] = do_something( a, b )
outA = a + 1;
outB = b + 2;
end
Here, you need to explicitly capture both output arguments. Otherwise, you just get a. For example:
outA = do_something( [1,2,3], [4,5,6] ); % outA is [2,3,4]
[outA,outB] = do_something( [1,2,3], [4,5,6] ); % outA is [2,3,4], outB is [6,7,8]
Z1 = cell(1,1);
Z1{1,1} = do_something( [1,2,3], [4,5,6] ); % Z1{1,1} is [2,3,4]
Z2 = cell(1,2);
Z2{1,1:2} = do_something( [1,2,3], [4,5,6] ); % Same error as above.
% NB: You really never want to have a cell expansion that is not surrounded
% by square brackets.
% Do this instead:
[Z2{1,1:2}] = do_something( [1,2,3], [4,5,6] ); % Z2{1,1} is [2,3,4], Z2{1,2} is [6,7,8]
This can also be done programmatically, with some limits. Let's say we're given function
func that takes one input and returns a constant (but unknown) number of outputs. We
have cell array inp that contains the inputs we want to process, and we want to collect the results in cell around outp:
N = numel(inp);
M = nargout(#func); % number of outputs produced by func
outp = cell(N,M);
for i=1:N
[ outp{i,:} ] = func( inp{i} );
end
This approach has a few caveats:
It captures all of the outputs. This is not always what you want.
Capturing all of the outputs can often change the behavior of the function. For example, the find function returns linear indices if only one output is used, row/column indices if two outputs are used, and row/column/value if three outputs are used.
It won't work for functions that have a variable number of outputs. These functions are defined as function [a,b,...,varargout] = func( ... ). nargout will return a negative number if the function has varargout declared in its output list, because there's no way for Matlab to know how many outputs will be produced.
Unpacking array and cell outputs into a cell
All true so far, but: what I am hoping for is a generic solution. I can't use num2cell if the function produces cell outputs. So what worked for strcmp will fail for strcat and vice versa. Let's assume for now that, for a function which returns multiple outputs, only the first one need be captured in zout – Carl Witthoft
To provide a uniform output syntax for all functions that return either a cell or an array, use an adapter function. Here is an example that handles numeric arrays and cells:
function [cellOut] = cellify(input)
if iscell(input)
cellOut = input;
elseif isnumeric(input)
cellOut = num2cell(input);
else
error('cellify currently does not support structs or objects');
end
end
To unpack the output into a 2-D cell array, the size of each output must be constant. Assuming M outputs:
N = numel(inp);
% M is known and constant
outp = cell(N,M);
for i=1:N
outp(i,:) = cellify( func( inp{i} ) ); % NB: parentheses instead of curlies on LHS
end
The output can then be addressed as outp{i,j}. An alternate approach allows the size of the output to vary:
N = numel(inp);
% M is not necessary here
outp = cell(N,1);
for i=1:N
outp{i} = cellify( func( inp{i} ) ); % NB: back to curlies on LHS
end
The output can then be addressed as outp{i}{j}, and the size of the output can vary.
A few things to keep in mind:
Matlab cells are basically inefficient pointers. The JIT compiler does not always optimize them as well as numeric arrays.
Splitting numeric arrays into cells can cost quite a bit of memory. Each split value is actually a numeric array, which has size and type information associated with it. In numeric array form, this occurs once for each array. When the array is split, this incurs once for each element.
Use curly braces instead when asigning a value.
Using
zout{1,:} = strcmp(x,y);
instead should work.