Tips and tricks
C++
Real matrix operations
This is a table of matrix operations commonly performed in Octave and their equivalents in C++ when using the octave libraries.
| Operation | Octave | C++ |
| add | A+B | A+B |
| subtract | A-B | A-B |
| matrix multiplication | A*B | A*B |
| element multiplication | A.*B | product(A,B) |
| element division | A./B | quotient(A,B) |
| transpose* | A' | A.transpose() |
| select element m,n of A** | A(m,n) | A(m-1,n-1) |
| select row N of A** | A(N,:) | A.row(N-1) |
| select column N of A** | A(:,N) | A.column(N-1) |
| extract submatrix of A | A(a:b,c:d) | A.extract(a-1,c-1,b-1,d-1) |
| absolute value of A | abs(A) | A.abs() |
| comparison to scalar*** | A>2 | mx_el_gt(A,2) |
A<2 | mx_el_lt(A,2) | |
A==2 | mx_el_eq(A,2) | |
A~=2 | mx_el_ne(A,2) | |
A>=2 | mx_el_ge(A,2) | |
A<=2 | mx_el_le(A,2) | |
| matrix of zeros | A=zeros(m,n) | A.fill(0.0) |
| matrix of ones | A=ones(m,n) | A.fill(1.0) |
| identity matrix | eye(N) | identity_matrix(N,N) |
| inverse of A | inv(A) | A.inverse() |
| pseudoinverse of A | pinv(A) | A.pseudo_inverse() |
| diagonal elements of A | diag(A) | A.diag() |
| column vector | A(:) | ColumnVector(A.reshape (dim_vector(A.length()))) |
| row vector | A(:)' | RowVector(A.reshape (dim_vector(A.length()))) |
| check for Inf or <a href="wiki.pl?NaN">NaN</a> | any(~isfinite(A)) | A.any_element_is_inf_or_nan() |
| stack two matrices vertically | A=[B;C] | B.stack(C) |
| uniform random matrix | rand(a,b) | octave_rand::distribution("uniform"); octave_rand::matrix(a,b) |
| normal random matrix | randn(a,b) | octave_rand::distribution("normal"); octave_rand::matrix(a,b) |
| sum squares of columns | sumsq(A) | A.sumsq() |
| sum along columns | sum(A,1) | A.sum(0) |
| sum along rows | sum(A,2) | A.sum(1) |
| product along columns | prod(A,1) | A.prod(0) |
| product along rows | prod(A,2) | A.prod(1) |
| cumsum along columns | cumsum(A,1) | A.cumsum(0) |
| cumsum along rows | cumsum(A,2) | A.cumsum(1) |
| cumproduct along columns | cumprod(A,1) | A.cumprod(0) |
| cumproduct along rows | cumprod(A,2) | A.cumprod(1) |
| number of rows | size(A,1) | A.rows() |
| number of columns | size(A,2) | A.cols() |
Notes: *Transpose, addition, and multiplication operations also apply to RowVector, ComplexRowVector, ColumnVector, and ComplexColumnVector data types when the dimensions are in agreement. **The difference is due to the fact that arrays are zero-based in C++, but one-based in Octave. ***The names of Octave internal functions, such as mx_el_gt, are not documented and are subject to change. Functions such as mx_el_gt may eventually be available at both the scripting level and in C++ under more common names such as gt.
Complex Matrix Operations
| Operation | Octave | C++ |
| conjugate tranpose | A' | A.hermitian() |
General
How to declare functions inside a test block
function experience %!test %! experience_design_mat %! experience_obs_eqs %! assert (experience_design_mat == pi); %! assert (experience_obs_eqs == exp(1)); %! %! endfunction % this is a trick. %! % now we can declare functions to be used by the test above. %! %! function a = experience_design_mat %! a = pi; %! endfunction %! %! function b = experience_obs_eqs %! b = exp(1); %! % endfunction: don't add it here. Let test() do it.
A funny formatting trick with fprintf found by chance
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?
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 kth row of Text
fprintf('%15.15s | %15.15s\n', Text{k,1}, Text{k,2});
The syntax '%<n>.<m>s' allocates '<n>' places to write chars and display the '<m>' first characters of the string to display.
Example:
octave:1> Text={'Hello','World'};
octave:2> fprintf('%15.15s | %15.15s\n', Text{1,1}, Text{1,2})
Hello | World
Load Comma Separated Values (*.csv) files
A=textread("file.csv", "%d", "delimiter", ",");
B=textread("file.csv", "%s", "delimiter", ",");
inds = isnan(A);
B(!inds) = num2cell(A(!inds))
This gets you a 1 column cell array. You can reshape it to the original size by using the reshapefunction
The next version of octave (3.6) implements the CollectOutput switch as seen in example 8 here: http://www.mathworks.com/help/techdoc/ref/textscan.html
Using Variable Strings in Octave Commands
For example, to plot data using a string variable as a legend:
Option 1 (simplest):
legend = "-1;My data;"; plot(x, y, legend);
Option 2 (to insert variables):
plot(x, y, sprintf("-1;%s;", dataName));
Option 3 (not as neat):
legend = 'my legend'; plot_command = ['plot(x,y,\';',legend,';\')']; eval(plot_command);
These same tricks are useful for reading and writing data files with unique names, etc.
Vectorizing Tricks
You can easily fill a vector with an index:
for i=1:n, x(i) = i; end
x = [1:n];
This works for expressions on the index by wrapping the index in an expression:
for i=1:n, x(i) = sin(2*pi*i*f/r); end
x = sin(2*pi*[1:n]*f/r);
You can also work with other vectors this way:
for i=1:n, x(i) = sin(2*pi*y(i)*f/r); end
x = sin(2*pi*y*f/r);
Conditionals in the for loop are a little bit tricky. We need to create an index vector for the true condition, and another for the false condition, then calculate the two independently.
for i=1:n, if y(i)<1, x(i)=y(i); else x(i) = 2*y(i); endif
idx = y < 1; x(idx) = y(idx); x(!idx) = 2*y(!idx);
FIXME: add the following
- examples from matrices
- tricks with sort and cumsum (e.g., hist, lookup)
- counter-examples such as a tridiagonal solver
- sparse matrix tricks
- tricks relying on fortran indexing
Other references
- MATLAB array manipulation tips and tricks by Peter Acklam: http://home.online.no/~pjacklam/matlab/doc/mtt/index.html
- The MathWorks: Code Vectorization Guide: http://www.mathworks.com/support/tech-notes/1100/1109.html