I've written this function to calculate sin(x) using Taylor series to any specified degree of accuracy, 'N terms', my problem is the results aren't being returned as expected and I can't figure out why, any help would be appreciated.
What is am expecting is:
1 6.28318530718
2 -35.0585169332
3 46.5467323429
4 -30.1591274102
5 11.8995665347
6 -3.19507604213
7 0.624876542716
8 -0.0932457590621
9 0.0109834031461
What I am getting is:
1 None
2 6.28318530718
3 -35.0585169332
4 46.5467323429
5 -30.1591274102
6 11.8995665347
7 -3.19507604213
8 0.624876542716
9 -0.0932457590621
Thanks in advance.
def factorial(x):
if x <= 1:
return 1
else:
return x * factorial(x-1)
def sinNterms(x, N):
x = float(x)
while N >1:
result = x
for i in range(2, N):
power = ((2 * i)-1)
sign = 1
if i % 2 == 0:
sign = -1
else:
sign = 1
result = result + (((x ** power)*sign) / factorial(power))
return result
pi = 3.141592653589793
for i in range(1,10):
print i, sinNterms(2*pi, i)
I see that you are putting the return under the for which will break it out of the while loop. You should explain if this is what you mean to do. However, given the for i in range(1,10): means that you will ignore the first entry and return None when the input argument i is 1. Is this really what you wanted? Also, since you always exit after the calculation, you should not do a while N > 1 but use if N > 1 to avoid infinite recursion.
The reason why your results are off is because you are using range incorrectly. range(2, N) gives you a list of numbers from 2 to N-1. Thus range(2, 2) gives you an empty list.
You should calculate the range(2, N+1)
def sinNterms(x, N):
x = float(x)
while N >1:
result = x
for i in range(2, N):
Your comment explains that you have the lines of code in the wrong order. You should have
def sinNterms(x, N):
x = float(x)
result = x
# replace the while with an if since you do not need a loop
# Otherwise you would get an infinite recursion
if N > 1:
for i in range(2, N+1):
power = ((2 * i)-1)
sign = 1
if i % 2 == 0:
sign = -1
# The else is not needed as this is the default
# else:
# sign = 1
# use += operator for the calculation
result += (((x ** power)*sign) / factorial(power))
# Now return the value with the indentation under the if N > 1
return result
Note that in order to handle things set factorial to return a float not an int.
An alternative method that saves some calculations is
def sinNterms(x, N):
x = float(x)
lim = 1e-12
result = 0
sign = 1
# This range gives the odd numbers, saves calculation.
for i in range(1, 2*(N+1), 2):
# use += operator for the calculation
temp = ((x ** i)*sign) / factorial(i)
if fabs(temp) < lim:
break
result += temp
sign *= -1
return result
Related
from random import randrange
a = randrange(1, 9)
print (a)
if (a % 2) == 0:
y = a / 2
while True:
if (y % 2) == 0:
y = y / 2
print (y)
else:
b = (a * 3) + 1
while True:
if (b % 2) == 0:
b = b / 2
else:
b = (a * 3) + 1
print (b)
"I want to make a math problem solver in python that can find a random number
between 1 and 9. Then if it is odd so it multiply it with 3 and add 1 in it and if it
is even so it divide it by two and this process keep repeating. For example a number
computer choose is 7 so :
7*3 + 1 = 22
22/2 = 11
11*3 = 33
and so on.
It shouldn't stop until the answer is 0.Here is my code in which I tried but not sure where should I make it right?"
You have too many lines in there. You need to loop to stop repeating when the number becomes 1 (it will never become 0):
from random import randrange
a = randrange(1, 9)
while a != 1:
print(a)
if a % 2 == 0:
a = a // 2
else:
a = (a * 3) + 1
print(a)
You can use the following code to check for any number or any range of numbers. This code is created by using the recursive function approach.
def f(x): #creating a function
if x!=4:
a.append(x)
if x%2==0:
while x%2==0:
x=x/2
a.append(x)
x=3*x+1
f(x)
For checking a particular value, run this:
a=[]
f(2**100+1) #2 to the power 10, plus 1
a[-1]
For checking for a range of values, run this:
for i in range(1,100):
a=[]
f(i)
print(i, "gives output" ,a)
I call it impossible maths because never reaches zero, it just keeps on looping forever Collatz problem. But this function does that, it does not take any parameter.
import random as r
def impossible_math():
x = r.ran(1,9)
while x !=0:
if x%2 ==0:
x = x/2
print(x)
else:
x = (x*3)+1
print(x)
x = impossible_math()
Can you explain it what problems are here? To my mind, this code is like a heap of crap but with the right solving. I beg your pardon for my english.
the task of this kata:
Some numbers have funny properties. For example:
89 --> 8¹ + 9² = 89 * 1
695 --> 6² + 9³ + 5⁴= 1390 = 695 * 2
46288 --> 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51
Given a positive integer n written as abcd... (a, b, c, d... being digits) and a positive integer p we want to find a positive integer k, if it exists, such as the sum of the digits of n taken to the successive powers of p is equal to k * n. In other words:
Is there an integer k such as : (a ^ p + b ^ (p+1) + c ^(p+2) + d ^ (p+3) + ...) = n * k
If it is the case we will return k, if not return -1.
Note: n, p will always be given as strictly positive integers.
dig_pow(89, 1) should return 1 since 8¹ + 9² = 89 = 89 * 1
dig_pow(92, 1) should return -1 since there is no k such as 9¹ + 2² equals 92 * k
dig_pow(695, 2) should return 2 since 6² + 9³ + 5⁴= 1390 = 695 * 2
dig_pow(46288, 3) should return 51 since 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51
def dig_pow(n, p):
if n > 0 and p > 0:
b = []
a = str(n)
result = []
for i in a:
b.append(int(i))
for x in b:
if p != 1:
result.append(x ** p)
p += 1
else:
result.append(x ** (p + 1))
if int((sum(result)) / n) < 1:
return -1
elif int((sum(result)) / n) < 2:
return 1
else:
return int((sum(result)) / n)
test results:
Test Passed
Test Passed
Test Passed
Test Passed
3263 should equal -1
I don't know what exact version of Python you're using. This following code are in Python 3. And if I get you correctly, the code can be as simple as
def dig_pow(n, p):
assert n > 0 and p > 0
digits = (int(i) for i in str(n)) # replaces your a,b part with generator
result = 0 # you don't use result as a list, so an int suffice
for x in digits: # why do you need if in the loop? (am I missing something?)
result += x ** p
p += 1
if result % n: # you just test for divisibility
return -1
else:
return result // n
The major problem is that, in your objective, you have only two option of returning, but you wrote if elif else, which is definitely unnecessary and leads to problems and bugs. The % is modulus operator.
Also, having an if and not returning anything in the other branch is often not a good idea (see the assert part). Of course, if you don't like it, just fall back to if.
I believe this could work as well and I find it a little easier to read, however it can definitely be improved:
def dig_pow(n, p):
value = 0
for digit in str(n):
value += int(digit)**p
p += 1
for k in range(1,value):
if value/k == n:
return k
return -1
this is some example simple example than using:
digits = (int(i) for i in str(n))
I'm opting to use this version since I am still a beginner which can be done with this alt way:
result = 0
for digits in str(n):
#iterate through each digit from n
# single of digits turn to int & power to p
for number in digits:
result += int(number) ** p
p += 1
as for the full solution, it goes like this:
def dig_pow(n, p):
# example n = 123 , change it to string = 1, 2, 3
# each string[] **p, and p iterate by 1
# if n % p not equal to p return - 1
result = 0
for digits in str(n):
#iterate through each digit from n
# single digit turn to int & power to p
for number in digits:
result += int(number) ** p
p += 1
if result % n:
return -1
else:
return result // n
I've implemented Miller-Rabin primality test and every function seems to be working properly in isolation. However, when I try to find a prime by generating random numbers of 70 bits my program generates in average more than 100000 numbers before finding a number that passes the Miller-Rabin test (10 steps). This is very strange, the probability of being prime for a random odd number of less than 70 bits should be very high (more than 1/50 according to Hadamard-de la Vallée Poussin Theorem). What could be wrong with my code? Would it be possible that the random number generator throws prime numbers with very low probability? I guess not... Any help is very welcome.
import random
def miller_rabin_rounds(n, t):
'''Runs miller-rabin primallity test t times for n'''
# First find the values r and s such that 2^s * r = n - 1
r = (n - 1) / 2
s = 1
while r % 2 == 0:
s += 1
r /= 2
# Run the test t times
for i in range(t):
a = random.randint(2, n - 1)
y = power_remainder(a, r, n)
if y != 1 and y != n - 1:
# check there is no j for which (a^r)^(2^j) = -1 (mod n)
j = 0
while j < s - 1 and y != n - 1:
y = (y * y) % n
if y == 1:
return False
j += 1
if y != n - 1:
return False
return True
def power_remainder(a, k, n):
'''Computes (a^k) mod n efficiently by decomposing k into binary'''
r = 1
while k > 0:
if k % 2 != 0:
r = (r * a) % n
a = (a * a) % n
k //= 2
return r
def random_odd(n):
'''Generates a random odd number of max n bits'''
a = random.getrandbits(n)
if a % 2 == 0:
a -= 1
return a
if __name__ == '__main__':
t = 10 # Number of Miller-Rabin tests per number
bits = 70 # Number of bits of the random number
a = random_odd(bits)
count = 0
while not miller_rabin_rounds(a, t):
count += 1
if count % 10000 == 0:
print(count)
a = random_odd(bits)
print(a)
The reason this works in python 2 and not python 3 is that the two handle integer division differently. In python 2, 3/2 = 1, whereas in python 3, 3/2=1.5.
It looks like you should be forcing integer division in python 3 (rather than float division). If you change the code to force integer division (//) as such:
# First find the values r and s such that 2^s * r = n - 1
r = (n - 1) // 2
s = 1
while r % 2 == 0:
s += 1
r //= 2
You should see the correct behaviour regardless of what python version you use.
I am learning python and I meet some troubles.
I want to write the script to reverse a negative integer " -1234 to 4321- " and non-integer " 1.234 to 432.1". please help me.
P.S. cannot use "str()" function
I just only can write the script to reverse positive integer 1234 to 4321
def reverse_int(n):
x = 0
while n > 0:
x *= 10
x += n % 10
n /= 10
return x
print reverse_int(1234)
def reve(x):
x=str(x)
if x[0]=='-':
a=x[::-1]
return f"{x[0]}{a[:-1]}"
else:
return x[::-1]
print(reve("abc"))
print(reve(123))
print(reve(-123))
#output
cba
321
-321
how about using your code, but just concatenate a - when n is negative?
rev_int.py:
def reverse_int(m):
x = 0
n = m
if m < 0 :
n *= -1
while n > 0 :
x *= 10
x += n % 10
n /= 10
if m < 0:
#concatenate a - sign at the end
return `x` + "-"
return x
print reverse_int(1234)
print reverse_int(-1234)
This produces:
$ python rev_int.py
4321
4321-
Using SLICING EASILY DONE IT
def uuu(num):
if num >= 0:
return int(str(num)[::-1])
else:
return int('-{val}'.format(val = str(num)[1:][::-1]))
Below code runs fine on Python-3 and handles positive and negative integer case. Below code takes STDIN and prints the output on STDOUT.
Note: below code handles only the integer case and doesn't handles the
non-integer case.
def reverseNumber(number):
x = 0
#Taking absolute of number for reversion logic
n = abs(number)
rev = 0
#Below logic is to reverse the integer
while(n > 0):
a = n % 10
rev = rev * 10 + a
n = n // 10
#Below case handles negative integer case
if(number < 0):
return (str(rev) + "-")
return (rev)
#Takes STDIN input from the user
number=int(input())
#Calls the reverseNumber function and prints the output to STDOUT
print(reverseNumber(number))
Using str convert method.
num = 123
print(str(num)[::-1])
Use this as a guide and make it work for floating point values as well:
import math
def reverse_int(n):
if abs(n) < 10:
v = chr(abs(n) + ord('0'))
if n < 0: v += '-'
return v
else:
x = abs(n) % 10
if n < 0: return chr(x + ord('0')) + reverse_int(math.ceil(n / 10))
else: return chr(x + ord('0')) + reverse_int(math.floor(n / 10))
print reverse_int(1234)
Why not just do the following?:
def reverse(num):
revNum = ''
for i in `num`:
revNum = i + revNum
return revNum
print reverse(1.12345)
print reverse(-12345)
These would print 54321.1 and 54321-.
I need to generate the result of the log.
I know that:
Then I made my code:
def log(x, base):
log_b = 2
while x != int(round(base ** log_b)):
log_b += 0.01
print(log_b)
return int(round(log_b))
But it works very slowly. Can I use other method?
One other thing you might want to consider is using the Taylor series of the natural logarithm:
Once you've approximated the natural log using a number of terms from this series, it is easy to change base:
EDIT: Here's another useful identity:
Using this, we could write something along the lines of
def ln(x):
n = 1000.0
return n * ((x ** (1/n)) - 1)
Testing it out, we have:
print ln(math.e), math.log(math.e)
print ln(0.5), math.log(0.5)
print ln(100.0), math.log(100.0)
Output:
1.00050016671 1.0
-0.692907009547 -0.69314718056
4.6157902784 4.60517018599
This shows our value compared to the math.log value (separated by a space) and, as you can see, we're pretty accurate. You'll probably start to lose some accuracy as you get very large (e.g. ln(10000) will be about 0.4 greater than it should), but you can always increase n if you need to.
I used recursion:
def myLog(x, b):
if x < b:
return 0
return 1 + myLog(x/b, b)
You can use binary search for that.
You can get more information on binary search on Wikipedia:
Binary search;
Doubling search.
# search for log_base(x) in range [mn, mx] using binary search
def log_in_range(x, base, mn, mx):
if (mn <= mx):
med = (mn + mx) / 2.0
y = base ** med
if abs(y - x) < 0.00001: # or if math.isclose(x, y): https://docs.python.org/3/library/math.html#math.isclose
return med
elif x > y:
return log_in_range(x, base, med, mx)
elif x < y:
return log_in_range(x, base, mn, med)
return 0
# determine range using doubling search, then call log_in_range
def log(x, base):
if base <= 0 or base == 1 or x <= 0:
raise ValueError('math domain error')
elif 0 < base < 1:
return -log(x, 1/base)
elif 1 <= x and 1 < base:
mx = 1
y = base
while y < x:
y *= y
mx *= 2
return log_in_range(x, base, 0, mx)
elif 0 <= x < 1 and 1 < base:
mn = -1
y = 1/base
while y > x:
y = y ** 0.5
mn *= 2
return log_in_range(x, base, mn, 0)
import math
try :
number_and_base = input() ##input the values for number and base
##assigning those values for the variables
number = int(number_and_base.split()[0])
base = int(number_and_base.split()[1])
##exception handling
except ValueError :
print ("Invalid input...!")
##program
else:
n1 = 1 ##taking an initial value to iterate
while(number >= int(round(base**(n1),0))) : ##finding the most similer value to the number given, varying the vlaue of the power
n1 += 0.000001 ##increasing the initial value bit by bit
n2 = n1-0.0001
if abs(number-base**(n2)) < abs(base**(n1)-number) :
n = n2
else :
n = n1
print(math.floor(n)) ##output value
Comparison:-
This is how your log works:-
def your_log(x, base):
log_b = 2
while x != int(round(base ** log_b)):
log_b += 0.01
#print log_b
return int(round(log_b))
print your_log(16, 2)
# %timeit %run your_log.py
# 1000 loops, best of 3: 579 us per loop
This is my proposed improvement:-
def my_log(x, base):
count = -1
while x > 0:
x /= base
count += 1
if x == 0:
return count
print my_log(16, 2)
# %timeit %run my_log.py
# 1000 loops, best of 3: 321 us per loop
which is faster, using the %timeit magic function in iPython to time the execution for comparison.
It will be long process since it goes in a loop. Therefore,
def log(x,base):
result = ln(x)/ln(base)
return result
def ln(x):
val = x
return 99999999*(x**(1/99999999)-1)
log(8,3)
Values are nearly equal but not exact.