I have a code and a function which multiplies matrix and print. However, I need to create a multiplication table with them. I only know how to print my output, not formating as table
my code is:
o4 = [0 1;-1 0]';
o2 = o4**2;
o4m = o4**3;
o1 = eye(2,2);
om_x = [-1 0;0 1]';
om_xbx = o4 * om_x;
om_y = o2 * om_x;
om_xx = o4m * om_x;
ops = {o1,o4,o2,o4m,om_xx,om_xbx,om_x,om_y};
labels = {"o1","o4","o2","o4m","om_xx","om_xbx","om_x","om_y"};
for j=1:8
for i=1:8
printf("%s * %s = %s\n",labels{j},labels{i},whichop(ops{j}*ops{i},ops,labels));
endfor
endfor
and the function is:
for i = 1:numel(labels)
current_op = ops{i};
if(norm(m - current_op)<1E-8)
f = labels{i};
break;
endif
endfor
endfunction
But the output must be like:
Related
I am trying to find three parameters (a, b, c) to fit my experimental data using ODE solver and optimization by least squares using Scilab in-built functions.
However, I keep having the message "submatrix incorrectly defined" at line "y_exp(:,1) = [0.135 ..."
When I try another series of data (t, yexp) such as the one used in the original template I get no error messages. The template I use was found here: https://wiki.scilab.org/Non%20linear%20optimization%20for%20parameter%20fitting%20example
function dy = myModel ( t , y , a , b, c )
// The right-hand side of the Ordinary Differential Equation.
dy(1) = -a*y(1) - b*y(1)*y(2)
dy(2) = a*y(1) - b*y(1)*y(2) - c*y(2)
endfunction
function f = myDifferences ( k )
// Returns the difference between the simulated differential
// equation and the experimental data.
global MYDATA
t = MYDATA.t
y_exp = MYDATA.y_exp
a = k(1)
b = k(2)
c = k(3)
y0 = y_exp(1,:)
t0 = 0
y_calc=ode(y0',t0,t,list(myModel,a,b,c))
diffmat = y_calc' - y_exp
// Make a column vector
f = diffmat(:)
MYDATA.funeval = MYDATA.funeval+ 1
endfunction
// Experimental data
t = [0,20,30,45,75,105,135,180,240]';
y_exp(:,1) =
[0.135,0.0924,0.067,0.0527,0.0363,0.02445,0.01668,0.012,0.009]';
y_exp(:,2) =
[0,0.00918,0.0132,0.01835,0.0261,0.03215,0.0366,0.0393,0.0401]';
// Store data for future use
global MYDATA;
MYDATA.t = t;
MYDATA.y_exp = y_exp;
MYDATA.funeval = 0;
function val = L_Squares ( k )
// Computes the sum of squares of the differences.
f = myDifferences ( k )
val = sum(f.^2)
endfunction
// Initial guess
a = 0;
b = 0;
c = 0;
x0 = [a;b;c];
[fopt ,xopt]=leastsq(myDifferences, x0)
Does anyone know how to approach this problem?
Just rewrite lines 28,29 as
y_exp = [0.135,0.0924,0.067,0.0527,0.0363,0.02445,0.01668,0.012,0.009
0,0.00918,0.0132,0.01835,0.0261,0.03215,0.0366,0.0393,0.0401]';
or insert a clear at line 1 (you may have defined y_exp before with a different size).
I have found many times a solution for my problems from here, but this time I am totally baffled. I don't know what's wrong at my code.
I made a code to create a box with charged particles inside with Vpython. As I launch the program, I get only a grey screen and the program crash. No error message, nothing.
from visual import *
from random import *
def electronizer(num):
list = []
electron_charge = -1.60217662e-19
electron_mass = 9.10938356e-31
for i in range(num):
another_list = []
e = sphere(pos=(random(), random(),random()), radius=2.818e-15,
color=color.cyan)
e.v = vector(random(), random(), random())
another_list.append(e)
another_list.append(e.v)
another_list.append(electron_charge)
another_list.append(electron_mass)
list.append(another_list)
return list
def protonizer(num):
list = []
proton_charge = 1.60217662e-19
proton_mass = 1.6726219e-27
for i in range(num):
another_list = []
p = sphere(pos=(random(), random(),random()), radius=0.8408739e-15, color=color.red)
p.v = vector(random(), random(), random())
another_list.append(p)
another_list.append(p.v)
another_list.append(proton_charge)
another_list.append(proton_mass)
list.append(another_list)
return list
def cross(a, b):
c = vector(a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0])
return c
def positioner(work_list):
k = 8.9875517873681764e3 #Nm2/C2
G = 6.674e-11 # Nm2/kg2
vac_perm = 1.2566370614e-6 # H/m
pi = 3.14159265
dt = 0.1e-3
constant = 1
force = vector(0,0,0)
for i in range(len(work_list)):
for j in range(len(work_list)):
if i != j:
r = work_list[i][0].pos - work_list[j][0].pos
r_mag = mag(r)
r_norm = norm(r)
F = k * ((work_list[i][2] * work_list[j][2]) / (r_mag**2)) * r_norm
force += F
B = constant*(vac_perm / 4*pi) * (cross(work_list[j][2] * work_list[j][1], norm(r)))/r_mag**2
F = cross(work_list[i][2] * work_list[i][1], B)
force += F
F = -(G * work_list[i][3] * work_list[j][3]) / r_mag**2 * r_norm
force += F
acceleration = force / work_list[i][3]
difference_in_velocity = acceleration * dt
work_list[i][1] += difference_in_velocity
difference_in_position = work_list[i][1] * dt
work_list[i][0].pos += difference_in_position
if abs(work_list[i][0].pos[0]) > 2.5e-6:
work_list[i][1][0] = -work_list[i][1][0]
elif abs(work_list[i][0][1]) > 2.5e-6:
work_list[i][1][1] = -work_list[i][1][1]
elif abs(work_list[i][0][2]) > 2.5e-6:
work_list[i][1][2] = -work_list[i][1][2]
return work_list
box = box(pos=(0, 0, 0), length = 5e-6, width = 5e-6, height = 5e-6, opacity = 0.5)
protons_num = raw_input("number of protons: ")
electrons_num = raw_input("number of electrons: ")
list_of_electrons = electronizer(int(electrons_num))
list_of_protons = protonizer(int(protons_num))
work_list = list_of_electrons + list_of_protons
while True:
work_list = positioner(work_list)
You should ask your question on the VPython.org forum where the VPython experts hang out and will be able to answer your question. You should mention which operating system you are using and which version of python you are using. From your code I see that you are using classic VPython. There is a newer version of VPython 7 that just came out but the VPython syntax has changed.
Suppose x,y,z are int variables and A is a matrix, I want to express a constraint like:
z == A[x][y]
However this leads to an error:
TypeError: object cannot be interpreted as an index
What would be the correct way to do this?
=======================
A specific example:
I want to select 2 items with the best combination score,
where the score is given by the value of each item and a bonus on the selection pair.
For example,
for 3 items: a, b, c with related value [1,2,1], and the bonus on pairs (a,b) = 2, (a,c)=5, (b,c) = 3, the best selection is (a,c), because it has the highest score: 1 + 1 + 5 = 7.
My question is how to represent the constraint of selection bonus.
Suppose CHOICE[0] and CHOICE[1] are the selection variables and B is the bonus variable.
The ideal constraint should be:
B = bonus[CHOICE[0]][CHOICE[1]]
but it results in TypeError: object cannot be interpreted as an index
I know another way is to use a nested for to instantiate first the CHOICE, then represent B, but this is really inefficient for large quantity of data.
Could any expert suggest me a better solution please?
If someone wants to play a toy example, here's the code:
from z3 import *
items = [0,1,2]
value = [1,2,1]
bonus = [[1,2,5],
[2,1,3],
[5,3,1]]
choices = [0,1]
# selection score
SCORE = [ Int('SCORE_%s' % i) for i in choices ]
# bonus
B = Int('B')
# final score
metric = Int('metric')
# selection variable
CHOICE = [ Int('CHOICE_%s' % i) for i in choices ]
# variable domain
domain_choice = [ And(0 <= CHOICE[i], CHOICE[i] < len(items)) for i in choices ]
# selection implication
constraint_sel = []
for c in choices:
for i in items:
constraint_sel += [Implies(CHOICE[c] == i, SCORE[c] == value[i])]
# choice not the same
constraint_neq = [CHOICE[0] != CHOICE[1]]
# bonus constraint. uncomment it to see the issue
# constraint_b = [B == bonus[val(CHOICE[0])][val(CHOICE[1])]]
# metric definition
constraint_sumscore = [metric == sum([SCORE[i] for i in choices ]) + B]
constraints = constraint_sumscore + constraint_sel + domain_choice + constraint_neq + constraint_b
opt = Optimize()
opt.add(constraints)
opt.maximize(metric)
s = []
if opt.check() == sat:
m = opt.model()
print [ m.evaluate(CHOICE[i]) for i in choices ]
print m.evaluate(metric)
else:
print "failed to solve"
Turns out the best way to deal with this problem is to actually not use arrays at all, but simply create integer variables. With this method, the 317x317 item problem originally posted actually gets solved in about 40 seconds on my relatively old computer:
[ 0.01s] Data loaded
[ 2.06s] Variables defined
[37.90s] Constraints added
[38.95s] Solved:
c0 = 19
c1 = 99
maxVal = 27
Note that the actual "solution" is found in about a second! But adding all the required constraints takes the bulk of the 40 seconds spent. Here's the encoding:
from z3 import *
import sys
import json
import sys
import time
start = time.time()
def tprint(s):
global start
now = time.time()
etime = now - start
print "[%ss] %s" % ('{0:5.2f}'.format(etime), s)
# load data
with open('data.json') as data_file:
dic = json.load(data_file)
tprint("Data loaded")
items = dic['items']
valueVals = dic['value']
bonusVals = dic['bonusVals']
vals = [[Int("val_%d_%d" % (i, j)) for j in items if j > i] for i in items]
tprint("Variables defined")
opt = Optimize()
for i in items:
for j in items:
if j > i:
opt.add(vals[i][j-i-1] == valueVals[i] + valueVals[j] + bonusVals[i][j])
c0, c1 = Ints('c0 c1')
maxVal = Int('maxVal')
opt.add(Or([Or([And(c0 == i, c1 == j, maxVal == vals[i][j-i-1]) for j in items if j > i]) for i in items]))
tprint("Constraints added")
opt.maximize(maxVal)
r = opt.check ()
if r == unsat or r == unknown:
raise Z3Exception("Failed")
tprint("Solved:")
m = opt.model()
print " c0 = %s" % m[c0]
print " c1 = %s" % m[c1]
print " maxVal = %s" % m[maxVal]
I think this is as fast as it'll get with Z3 for this problem. Of course, if you want to maximize multiple metrics, then you can probably structure the code so that you can reuse most of the constraints, thus amortizing the cost of constructing the model just once, and incrementally optimizing afterwards for optimal performance.
I want to set values depends on the selected radio button and to use that values in other function.
Whatever i try, i always get the same answer
NameError: global name 'tX' is not defined #
import maya.cmds as cmds
from functools import partial
winID='MSDKID'
def init(*args):
print tX
print tY
print tZ
print rX
print rY
print rZ
return
def prozor():
if cmds.window(winID, exists = True):
cmds.deleteUI(winID);
cmds.window()
cmds.columnLayout( adjustableColumn=True, rowSpacing=10 )
cmds.button(label = "Init")
cmds.button(label = "MirrorSDK",command=init)
cmds.setParent( '..' )
cmds.setParent( '..' )
cmds.frameLayout( label='Position' )
cmds.columnLayout()
collection2 = cmds.radioCollection()
RButton0 = cmds.radioButton( label='Behavior' )
RButton1 = cmds.radioButton( label='Orientation' )
cmds.button(l='Apply', command = partial(script,RButton0,RButton1,))
cmds.setParent( '..' )
cmds.setParent( '..' )
print script(RButton0,RButton1)
cmds.showWindow()
def script(RButton0,RButton1,*_cb_val):
X = 0
rb0 = cmds.radioButton(RButton0, q = True, sl = True)
rb1 = cmds.radioButton(RButton1,q = True, sl = True)
if (rb0 == True):
tX = -1
tY = -1
tZ = -1
rX = 1
rY = 1
rZ = 1
if (rb1 == True):
tX = -1
tY = 1
tZ = 1
rX = 1
rY = -1
rZ = -1
return tX,tY,tZ,rX,rY,rZ
prozor()
The variables you are defining in script() are local to that function. The other functions don't see them.
If you need multiple UI elements to share data, you'll probably need to create a class to let them share variables. Some reference here and here
Till now x has two colomns and there was no problems, but now x have got various num of colomns, and I don't know how to write analog code but with dynamic number of colomns in x?
min_x = min(x);
max_x = max(x);
step = (max_x - min_x)/50;
[X, Y] = ndgrid(min_x(1):step(1):max_x(1), min_x(2):step(2):max_x(2));
You can use cellarrays to generate a comma separated list:
%# sample data
x = rand(10,3); %# you can change the column numbers here
%# calculate step sizes
mn = min(x);
mx = max(x);
step = (mx-mn)/50;
%# vec{i} = mn(i):s(i):mx(i)
vec = arrayfun(#(a,s,b)a:s:b, mn,step,mx, 'UniformOutput',false);
%# [X,Y,...] = ndgrid(vec{1},vec{2},...)
C = cell(1,numel(vec));
[C{:}] = ndgrid( vec{:} );
%# result = [X(:),Y(:),...]
result = cell2mat( cellfun(#(v)v(:), C, 'UniformOutput',false) );