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===Vectorizing Tricks=== | ===Vectorizing Tricks=== |
Revision as of 06:52, 21 September 2012
Contents
Tiny helper functions
This is a list of tiny helper functions (the equivalent of e.g., shell aliases), the kind one would have on its .octaverc file.
replace help with man
If you use octave too much, you'll find yourself trying to use help
instead of man
on bash. This function will fix that so you can use man
in your octave instance (you can also do the opposite, create a help
alias in bash but man
has less characters).
Code: alias to help |
function man (name) help (char (name)) endfunction |
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 NaN | 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
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