軟體實作與計算實驗 1

SummationSymbolic differentiationCounting ATCG

Lecture 5 FOR Looping

軟體實作與計算實驗 2

Summation

x = 1.5

floor(x)

1

x = 1.5

ceil(x)

2

軟體實作與計算實驗 3

Flow chart

sn=floor(n^2)+ceil(2*n/3) S=S+sn

S=0

for n=1:N

軟體實作與計算實驗 4

Symbolic Differentiation

>> x=sym('x');>> diff(tanh(x)) ans = 1-tanh(x)^2

軟體實作與計算實驗 5

Symbolic differentiation

>> x=sym('x');>> diff(x.^3+2*x) ans = 3*x^2+2

軟體實作與計算實驗 6

Symbolic Differentiation

demo_diff.m

• Input a string, fstr• Plot the function specified by fstr• Plot the derivative of the given function

軟體實作與計算實驗 7

Example

-5 -4 -3 -2 -1 0 1 2 3 4 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

function of x:tanh(x)

fx1 =

Inline function: fx1(x) = 1-tanh(x).^2

軟體實作與計算實驗 8

Histogram

Sample space of a die: {1,2,3,4,5,6}Count occurrences of outcomes

軟體實作與計算實驗 9

Create a sample

n=1000;s=ceil(rand(1,1000)*6);h=hist(s,[1 2 3 4 5 6]);

軟體實作與計算實驗 10

hist(s,[1 2 3 4 5 6])

軟體實作與計算實驗 11

c=s(i); count(c) = count(c) +1;

軟體實作與計算實驗 12

Flow chart :

c = s (i); count(c) = count(c)+1;

n=length(s);count=zeros(1,6);

for i=1:n

軟體實作與計算實驗 13

n=length(s);count=zeros(1,6);for i=1:n c = s (i); count(c) = count(c)+1;end

軟體實作與計算實驗 14

Flow chart :

ind = find(s==i); count(i) = length(ind);

n=length(s);count=zeros(1,6);

for i=1:6

軟體實作與計算實驗 15

n=length(s);count=zeros(1,6);for i=1:6 ind = find(s==i); count(i) = length(ind);end

軟體實作與計算實驗 16

DNA sequence

ATCG sequence

load mitochondriamitochondria(1:200)

軟體實作與計算實驗 17

mitochondria(1:200)

gatcacaggtctatcaccctattaaccactcacgggagctctccatgcatttggtattttcgtctggggggtgtgcacgcgatagcattgcgagacgctggagccggagcaccctatgtcgcagtatctgtctttgattcctgcctcattctattatttatcgcacctacgttcaatattacaggcgaacatacctacta

軟體實作與計算實驗 18

ATCG

Calculate probabilities of a,t,c,g occurring in a given ATCG sequence.

?)''Pr(

?)''Pr(

?)''Pr(

?)''Pr(

gx

cx

tx

ax

軟體實作與計算實驗 19

Switch

cc=mitochondria(i); switch cc case 'a' count(1)=count(1)+1; case 't' count(2)=count(2)+1; case 'c' count(3)=count(3)+1; case 'g' count(4)=count(4)+1; end

軟體實作與計算實驗 20

Flow chart

cc=mitochondria(i); switch cc

. . . end

load mitochondrian=length(mitochondria);count=zeros(4);

for i =1:n

軟體實作與計算實驗 21

load mitochondrian=length(mitochondria);count=zeros(1,4);for i =1:n cc=mitochondria(i); switch cc case 'a' count(1)=count(1)+1; case 't' count(2)=count(2)+1; case 'c' count(3)=count(3)+1; case 'g' count(4)=count(4)+1; endend