attachment:Example Scripts 26Feb13.m of EssentialsofMRIAnalysis 2013 - MRC CBU Imaging Wiki
location: attachment:Example Scripts 26Feb13.m of EssentialsofMRIAnalysis 2013

## Attachment 'Example Scripts 26Feb13.m'

```   1 %% Vector basics
2
3 % Row vector
4 x = [1 1 1 1]
5
6 % Column vector
7 y = [1 1 1 1]'
8
9 % create vector with sequence of numbers
10 z = [1:10]
11 z = [-1:0.01:1]
12
13 % Getting an element out of a vector
14 z(2)
15 z(2:3)
16
17 % Add or multiply values etc.
18 x + 10
19 2*x
20
21
22 %% Vector multiplication
23 % Transpose vectors
24 x
25 x'
26
27 % Vector multiplication: row vector * column vector (for time being)
28 x,y    % just for display
29 x*y
30
31 % Common error: multiply vectors of different lengths:
32 z = [1 1 1]'
33 x*z
34
35 % Define two parallel vectors:
36 x = [1 0 1 0]
37 y = [1 0 1 0]'
38
39 % Multiply vectors
40 x*y
41
42 % Define two orthogonal vectors:
43 x = [1 0 1 0]
44 y = [0 1 0 1]'
45
46 % Multiply vectors
47 x*y
48
49
50 %% Some things you can do with vectors
51 % Define a vector
52 x = [1 2 3 4]
53
54 % Define another vector
55 y = [0 0 1 0]'   % note the transpose
56
57 % Multiply the vectors
58 x*y
59
60 % Define another vector
61 z = [1 1 1 1]'
62
63 % Sum of elements of x:
64 x*z
65
66 % Average of elements of x
67 x*z / length(x)
68
69 % Define another vector
70 y = [1 -1 1 -1]'
71
72 % Subtract sum of even from sum of odd elements in x:
73 x*y
74
75 clear
76 %% Matrices
77
78 % Define a (diagonal) matrix
79 x = [1 1 1; 2 2 2]
80
81 % Getting elements out of matrices
82 x(1,2)
83 x(:,1)
84 x(2,:)
85
86 % Matrix transpose
87 x
88 y = x'
89
91 x + 2
92 2 * x
93
94 % Define another matrix
95 z = [1 2 3; 4 5 6]
96
97 % Subtract z from x
98 x - z
99
100 % Add z to x
101 x + z
102
103 % Elementwise multiplication (NOT "matrix multiplication": "*")
104 x .* z
105
106 % Try... (matrix multiplication)
107 x * z
108
109 % Elementwise division (NOT "matrix division/inversion": "/")
110 x ./ z
111
112 % Try... (matrix inversion)
113 x / z
114
115 %% Multiplying matrix and vector
116 % Define a vector
117 v = [1 1 1]'
118
119 % Mutliply matrix x with vector v (and obtain sum within each row of x)
120 x
121 v
122 x * v
123
124 % matrix and vector dimensions must agree
125 v * x % does not work
126
127 %% interpretation as sum of column vectors
128 % x * v results in the sum of column vectors in x
129 x * v
130 1*x(:,1) + 1*x(:,2) + 1*x(:,3)
131
132 %% Matrix multiplication
133 % Multiply two matrices
134 x * y
135
136 % Multiply two matrices
137 y * x
138
139 % Note: x*y is not necessarily y*x!!!
140
141 % Define new matrix
142 z = [1 1; 2 2]
143
144 % Works:
145 y*z
146 z*x
147
148 % Doesn't work:
149 z*y
150 x*z
151
152 %% Make your own matrices
153
154 % Identity matrix
155 id = eye(3)
156
157 % Example:
158 x*id
159
160 id*x'
161
162 % diagonal matrix
163 di = eye(3)
164 di(1,1) = 1
165 di(2,2) = 2
166 di(3,3) = 3
167
168 % Multiplies columns by a factor:
169 x*di
170
171 % Multiplies rows by a factor
172 di*y
173
174 %% Some useful functions
175
176 % get the diagonal of a (square) matrix
177 diag(di)
178
179 % create a matrix/vector with ones
180 ones(10)   % creates 10x10 matrix
181 ones(10,1) % creates 10x1 column vector
182
183 % create a matrix/vector with zeros
184 zeros(10)   % creates 10x10 matrix
185 zeros(1,10) % creates 1x10 row vector
186
187 % create matrix/vector with standard uniform random numbers in interval 0-1
188 rand(3)
189
190 % create matrix/vector with standard normal random numbers in interval 0-1
191 randn(3)
192
193 % "reshaping" a matrix or a vector
194 x = 1:10
195 reshape(x,5,2)
196 reshape(x,2,5)
197
198 % Kronecker product ("concatenates" matrices/vectors)
199 kron(id,y)
```

## Attached Files

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• [get | view] (2013-03-15 17:25:09, 262.2 KB) [[attachment:EMA_syllabus_060313.pdf]]
• [get | view] (2013-03-19 10:19:59, 3.0 KB) [[attachment:Example Scripts 26Feb13.m]]
• [get | view] (2013-03-19 10:18:51, 1.3 KB) [[attachment:Example Scripts GLM 27Feb13.m]]
• [get | view] (2013-03-19 10:15:39, 642.6 KB) [[attachment:IntroGLM_27Feb13.pdf]]
• [get | view] (2013-03-19 10:23:10, 823.8 KB) [[attachment:IntroMatrixAlgebra]]
• [get | view] (2013-03-19 10:15:50, 823.8 KB) [[attachment:IntroMatrixAlgebra_Matlab_26Feb13.pdf]]
• [get | view] (2013-03-15 17:35:59, 1567.6 KB) [[attachment:MEGforward_Stenroos_EMA13.pdf]]
• [get | view] (2013-03-15 17:36:07, 1514.0 KB) [[attachment:MRPhysics.ppt]]
• [get | view] (2013-03-15 17:36:13, 4907.5 KB) [[attachment:MRPhysicsII.ppt]]
• [get | view] (2013-03-19 10:21:14, 3.0 KB) [[attachment:example_algebra]]
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