Matlabの基本的操作 - 東京大学

1 Matlab . 2015 .. Web .. Google . HP class/Summer/2015 . Matlab . MathWorks .. >> .. a 2 + b2 = c2 a = 3.. b = 4. c = 5.. Matlab .. n = ' Pythagoras'. c = ' Greece'.. = . = = .. ans .. -2 2 1 (1,2) .. 1 .. 2 . 2 .. a . 2 . index . b . end .. 2 a .. length(x) x . 2 . size(A) A .. aa 0 . k . k k=1,2, ,10.. aa .. x=1 . x=-2 .. [-5,5] . 100 .. 2 .. >help plot .. *.m .. edit . M .. exp(x) x = 1 . Matlab .. upper(x) x = Euclid' EUCLID' .. function end .. save . save .. save . * .. >> @( x ) x^2. ans =.. @( [ 1, 2, ] ) . >> ans( 2 ). ans =. y=x2 @( x ) x^2 . 4.. >> sqr = @( x ) x^2. sqr =.. sqr >> sqr( 2 ). ans =. 4.. Ordinary Differential Equation .. dx 1. = x . dt t . x(t ) = x0 e .. ODE .. ( x) 2. y ( x + x) = y ( x) + x y ( x) + y ( x) + . 2! .. n n . (Euler's method). 1.

2 ( x) 2. y ( x + x) = y ( x) + x y ( x) + y ( x) + . 2! y ( x + x) = y ( x) + x y ( x). 1 .. ODE .. f'(x). f'(0). x O. x MATLAB ODE . ode45 (Dormand-Prince 5(4)). 4 5 .. ode15s ( ).. ODE 2 .. ODE solver .. @ . ODE .. ODE Solver t . '@' .. ODE solver .. @ .. @(t,x) ode_eq(x,t,tau). ODE 3 . ODE .. ODE Solver t .. @(t,x) ode_eq(x,t,tau) ode_eq t,x .. function [ x_ans , y_ans ] = odeEuler( f , x_range, y0 ). dx = ; % . ODE x = x_range(1);. y = y0;. % x . % y . solution = [ x , y ]; % ODE . while x <= x_range(end). dy = f( x ) * ; % . x = x + dx; % x . y= ; % y . f : ODE solution = [ solution ; x , y ];% . end x_ans = solution(:,1); % solution 1 x y_ans = solution(:,2); % solution 2 y end y'=x2 . >> [x,y] = odeEuler(@(x) x^2 , [0:1], 0);. >> plot(x,y).. >help ** ** . >help ode15s >lookfor **.

3 ** >lookfor ode Web . : 1/2.. dbquit .. 10 ? .. 2/2. F10 .. NaN. NaN Not a Number .. >> 0/0 , 1/0 . Matlab Inf . NaN warning . Matlab .. max, min . sum . while . xlabel, ylabel, title, legend .. help .. Google . HP class/Summer/2015 .. ERK .. PC .. 1. 2.. kf [A] + [B] [A B]. kb kb Kd = Kd: dissociation constant kf d[A]. = kb[A B] kf [A][B]. dt Ligand and receptor G proteins and effectors .. k1 k3. [E] + [S] [E S] [E] + [P]. k2. d[E S]. = k1 [S] [E] - k2 [ES] - k3 [ES]. dt .. 1. 2.. kf k1 k3. [A] + [B] [A B] [E] + [S] [E S] [E] + [P]. kb k2. d[AB] d[ES]. = kf [A] [B] kb [AB] = k1 [S] [E] - k2 [ES] - k3 [ES]. dt dt . A Kf = AB. Kb = 0. B. 1 Kd =Kb / Kf .. [A], [B], [AB] Kf, Kb d[A]. = Kf [A] [B] + Kb [AB]. dt d[B]. = Kf [A] [B] + Kb [AB]. dt d[AB]. = Kf [A] [B] Kb [AB].

4 Dt . : . ODE . ode15s ODE(t, y, param) . time , y0 .. X t, Y time_course .. Figure . Matlab % .. t, time_course 100 .. 1, . 2, MI . 3, MI . ).. figure window . x, y .. 1 . Kd [Kf, Kb] A. A . B Kb C . A B D .. Kd =Kb / Kf . for loop . Kf . 1 . for loop Kd . Kf, Kb.