Lecture 2 Scip, Matrix handling HA, 24.10.2018
Contents
Extracring and decomposing (parts of) matrices
clear % Remove variables from workspace (memory) clc % Clear screen close all % Close grapics windows format compact % Compress away extra blank lines from results. A=reshape(1:6,2,3),B=ones(2,2),C=diag(1:3)
A = 1 3 5 2 4 6 B = 1 1 1 1 C = 1 0 0 0 2 0 0 0 3
Side by side
side_by_side=[A B]
% Stack vertically:
pile = [A;C]
side_by_side = 1 3 5 1 1 2 4 6 1 1 pile = 1 3 5 2 4 6 1 0 0 0 2 0 0 0 3
Link to indexing (works after "publish")
Some Finish explanation of lofical indexing (can ignore now)
Indexing vectors with vector indices
clear close all format compact clc
v = [13 5 9 -1]
v = 13 5 9 -1
v(2) % 2. element -> 5
ans = 5
v([1 3 end]) % elements 1 3 end -> 13 9 -1
ans = 13 9 -1
v(1:3) % elements 1 2 3 -> 13 5 9
ans = 13 5 9
v(1:3)=-[1 2 3] % Update part chosen part of vector. % % Same size or scalar
v = -1 -2 -3 -1
v([1 1 end-1 2 1]) % Repetition and changing order allowed.
ans = -1 -1 -3 -2 -1
v([1 3])=NaN % A form of scalar expansion % NaN -2.0000 NaN -1
v = NaN -2 NaN -1
Indexing matrices
clc
clear
format compact
A=[3 33;9 8]
A = 3 33 9 8
A(1,1) % --> 3 A(1,2) % --> 33
ans = 3 ans = 33
Linear indexing, "slicing" matrix into a long column A(:)
%{ Can index with one index running along columns. This is called linear indexing. Think of A "queued" along columns, i.e. A(:) %} A(3) % <--> A(2,1) [A(3) A(1,2)] sub2ind([2,2],1,2) %
ans = 33 ans = 33 33 ans = 3
Some more cases of indexing matrices:
A = magic(6)
A = 35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11
B = A(3,5)
B = 27
C = A([1,2,3],4) % Sarakkeen 4 alkiot riveilta 1 2 3
C = 26 21 22
D = A(4,[1,1,1]) % [A(4,1) A(4,1) A(4,1)]
D = 8 8 8
E = A([2,5],[3,1]) % Rivien 2 5 sarakkeet 3 1
E = 7 3 34 30
F = A(:,4) % Koko 4. sarake
F = 26 21 22 17 12 13
G = A(4,:) % Koko 4. rivi
G = 8 28 33 17 10 15
H = A(:) % Columns of A "sliced" into one long column:
size(H)
H = 35 3 31 8 30 4 1 32 9 28 5 36 6 7 2 33 34 29 26 21 22 17 12 13 19 23 27 10 14 18 24 25 20 15 16 11 ans = 36 1
H' % Show transposed to save display space. A(1:3,[2 3 end-1])=NaN % Update as before with vectors. %
ans = Columns 1 through 13 35 3 31 8 30 4 1 32 9 28 5 36 6 Columns 14 through 26 7 2 33 34 29 26 21 22 17 12 13 19 23 Columns 27 through 36 27 10 14 18 24 25 20 15 16 11 A = 35 NaN NaN 26 NaN 24 3 NaN NaN 21 NaN 25 31 NaN NaN 22 NaN 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11