Matlab course at. P. Ciuciu 1,2. 1: CEA/NeuroSpin/LNAO 2: IFR49

Transcription

1 Matlab course at NeuroSpin P. Ciuciu 1,2 1: CEA/NeuroSpin/LNAO 2: IFR49 Feb 26, 2009

2 Outline 2/9 Lesson0: Getting started: environment,.m and.mat files Lesson I: Scalar, vectors, matrices and related operations Lesson II: String manipulations, cell array, files, structures Lesson III: Basic coding: instructions, tests (if), loops (for, while, switch) Lesson IV: Visualization tools + Exercises (fft, conv,...) Lesson V: Scripts, functions, API management (varargin, varargout), debugging Lesson VI: Coding sprint and interaction with SPM5

3 Lesson Two main 0: Getting issues in started fmri 3/9 Accessing Matlab matlab ; matlab -nodesktop quit or exit (kill matlab) Visiting the Matlab Java Runtime environment command, history and workspace windows Matlab files: source files (.m); binary.mat files for saving results; ASCII.dat files for saving strings : see later the load and save functions Add directories to MATLABPATH: path addpath /data/home/i2bm/work/matlabcourse/ rmpath /data/home/i2bm/work/matlabcourse/ addpath /data/home/i2bm/work/matlabcourse/ -begin

4 Lesson Two main 0: Getting issues in started fmri 4/9 Basic tools: Change directory: cd Get current working directory : pwd List files in the cwd : ls or dir List of variables: who and whos List of mfiles: what Unix mode (pass a system command):! rm toto.txt Command line editing and recall use up/down arrows to scroll through the stack of previous commands. CtrlA, CtrlK, CtrlE Help help save: provides the feature of the save routine lookfor save: list all functions including save in their help Web resouces:

5 5/9 Scalar computations: result saved in ANS variable ; x=2 z= 3 + i* 2 real(z), imag(z), angle(z), abs(z) Entering vector and matrices row/column vect.: x= [3,4,5]; length(x); y =[3;4;5] A = [1 2 3; 4 5 6; 7 8 9] ; matrix size: size(a) ; B=A' or B = A.' Matrix initialization : C=ones(3);D=zeros(3,4) Matrix operations, array operations: Addition (+), subtraction(-), Multiplication (*), power(^), transpose (') Left division (\), right division (/)

6 6/9 Matrix operations, array operations: The "matrix division" operations deserve special comment. If A is an invertible square matrix and b is a compatible column, resp. row, vector, then x = A \ b is the solution of A * x = b and, resp., x = b / A is the solution of x * A = b. In left division, if A is square, then it is factored using Gaussian elimination and these factors are used to solve A * x = b. If A is not square, it is factored using Householder orthogonalization with column pivoting and the factors are used to solve the under- or overdetermined system in the least squares sense. Right division is defined in terms of left division by b / A = (A' \ b')'. Example

7 7/9 Matrix building functions eye, zeros, ones: B = [A, zeros(3,2); zeros(2,3), eye(2)] triu, tril, rand, hilb magic, toeplitz x = diag(a); diag(x) Scalar functions sin asin exp abs round cos acos log (natural log) sqrt floor tan atan rem (remainder) sign ceil Vector functions max sum median any min prod mean all sort std max(a) and max(a(:)) or max(max(a))

8 8/9 Matrix functions eig eigenvalues and eigenvectors chol cholesky factorization svd singular value decomposition inv inverse lu LU factorization qr QR factorization hess hessenberg form schur schur decomposition expm matrix exponential sqrtm matrix square root poly characteristic polynomial det determinant size size norm 1-norm, 2-norm, F-norm, <infinity>-norm* cond condition number in the 2-norm rank rank

9 9/9 Submatrices and column notations x=[ ] or x=1:5, y=5:-1:1; z=0.2:0.2:1.2 y = rand(10,1) ; z=y(5:end) t=sin(z); [z t]: since sin operates entry-wise, it produces a vector y from the vector x. A= rand(5); Asubcol3 = A(1:4,3) or Acol3 = A(:,3) Asubrow4 = A(4,1:3); Arow4 = A(:,4); Arbitrary integral vectors can be used as subscripts: A(:,[2 4]) Subscripting can be used on both sides of an assignment statement: A(:,[2 4 5]) = B(:,1:3) A(:,[2,4]) = A(:,[2,4])*[1 2;3 4] x=a(:,1) ; what is the effect of x(end:-1:1) fliplr and flipud