Utilizing Quadratic Equation to Output Roots or Message saying Undefinable - string

Finding quadratic roots:
import math
def main():
print "Hello! This program finds the real solutions to a quadratic"
print
a, b, c = input("Please enter the coefficients (a, b, c): ")
d = (b**2) - (4*a*c) # finding the discriminant
if d < 0:
d = -d
else:
print "This quadratic equation does not have imaginary roots"
return
dRoot = math.sqrt(d)
root1r = (-b) / (2 * a)
root1i = dRoot / (2 * a)
root2r = root1r
root2i = -root1i
print "%s+%si , %s+%si" % (root1r, root1i, root2r, root2i)
print
main()
sample:::
a, b, c
0.0, 0.0, 0.0
0.0, 0.0, 1.0
0.0, 2.0, 4.0
1.0, 2.0, 1.0
1.0, -5.0, 6.0
1.0, 2.0, 3.0,
Need help making a quadratic equation that can help me find the square root(s) or outputing a message saying that the root cannot be found/ or it is undefinable. Using the given a, b, c as examples to finding root(s) or prompting a message. That is what i have,

Related

How to convert floating point number to ratio of integers in python with high accuracy? [duplicate]

This question already has answers here:
How to convert a decimal number into fraction?
(6 answers)
Is there a way to return a fully reduced ratio when calling .as_integer_ratio()?
(2 answers)
Is there an alternative to the: as_integer_ratio(), for getting "cleaner" fractions?
(2 answers)
Closed 1 year ago.
QUESTION:
I would like to convert floats into a ratio of integers in simplest form. (Not a duplicate of this question, see "EDIT" below). For example, 0.1 = 1, 10, 0.66666... = 2, 3, etc. In the code snippet below, I try doing this for x = 0.1, 0.2, ..., 1.0 using this default function; the method only works successfully for x = 0.5 and x = 1.0. Why does this algorithm fail for other values of x and what is a better method to do this? In case it is relevant, my use-case will be for dx ~ 0.0005 = x[1] - x[0] for 0.0005 < x 10.0.
CODE:
import numpy as np
f = np.vectorize(lambda x : x.as_integer_ratio())
x = np.arange(0.1, 1.1, 0.1)
nums, dens = f(x)
for xi, numerator, denominator in zip(x, nums, dens):
print("\n .. {} = {} / {}\n".format(xi, numerator, denominator))
OUTPUT:
.. 0.1 = 3602879701896397 / 36028797018963968
.. 0.2 = 3602879701896397 / 18014398509481984
.. 0.30000000000000004 = 1351079888211149 / 4503599627370496
.. 0.4 = 3602879701896397 / 9007199254740992
.. 0.5 = 1 / 2
.. 0.6 = 5404319552844595 / 9007199254740992
.. 0.7000000000000001 = 6305039478318695 / 9007199254740992
.. 0.8 = 3602879701896397 / 4503599627370496
.. 0.9 = 8106479329266893 / 9007199254740992
.. 1.0 = 1 / 1
EDIT:
This is not really a duplicate. Both methods of the accepted answer in the original question fail a basic use-case from my MWE. To show that the Fraction module gives the same error:
import numpy as np
from fractions import Fraction
f = np.vectorize(lambda x : Fraction(x))
x = np.arange(0.1, 1.1, 0.1)
y = f(x)
print(y)
## OUTPUT
[Fraction(3602879701896397, 36028797018963968)
Fraction(3602879701896397, 18014398509481984)
Fraction(1351079888211149, 4503599627370496)
Fraction(3602879701896397, 9007199254740992) Fraction(1, 2)
Fraction(5404319552844595, 9007199254740992)
Fraction(6305039478318695, 9007199254740992)
Fraction(3602879701896397, 4503599627370496)
Fraction(8106479329266893, 9007199254740992) Fraction(1, 1)]

Automatically round arithmetic operations to eight decimals

I am doing some numerical analysis exercise where I need calculate solution of linear system using a specific algorithm. My answer differs from the answer of the book by some decimal places which I believe is due to rounding errors. Is there a way where I can automatically set arithmetic to round eight decimal places after each arithmetic operation? The following is my python code.
import numpy as np
A1 = [4, -1, 0, 0, -1, 4, -1, 0,\
0, -1, 4, -1, 0, 0, -1, 4]
A1 = np.array(A1).reshape([4,4])
I = -np.identity(4)
O = np.zeros([4,4])
A = np.block([[A1, I, O, O],
[I, A1, I, O],
[O, I, A1, I],
[O, O, I, A1]])
b = np.array([1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6])
def conj_solve(A, b, pre=False):
n = len(A)
C = np.identity(n)
if pre == True:
for i in range(n):
C[i, i] = np.sqrt(A[i, i])
Ci = np.linalg.inv(C)
Ct = np.transpose(Ci)
x = np.zeros(n)
r = b - np.matmul(A, x)
w = np.matmul(Ci, r)
v = np.matmul(Ct, w)
alpha = np.dot(w, w)
for i in range(MAX_ITER):
if np.linalg.norm(v, np.infty) < TOL:
print(i+1, "steps")
print(x)
print(r)
return
u = np.matmul(A, v)
t = alpha/np.dot(v, u)
x = x + t*v
r = r - t*u
w = np.matmul(Ci, r)
beta = np.dot(w, w)
if np.abs(beta) < TOL:
if np.linalg.norm(r, np.infty) < TOL:
print(i+1, "steps")
print(x)
print(r)
return
s = beta/alpha
v = np.matmul(Ct, w) + s*v
alpha = beta
print("Max iteration exceeded")
return x
MAX_ITER = 1000
TOL = 0.05
sol = conj_solve(A, b, pre=True)
Using this, I get 2.55516527 as first element of array which should be 2.55613420.
OR, is there a language/program where I can specify the precision of arithmetic?
Precision/rounding during the calculation is unlikely to be the issue.
To test this I ran the calculation with precisions that bracket the precision you are aiming for: once with np.float64, and once with np.float32. Here is a table of the printed results, their approximate decimal precision, and the result of the calculation (ie, the first printed array value).
numpy type decimal places result
-------------------------------------------------
np.float64 15 2.55516527
np.float32 6 2.5551653
Given that these are so much in agreement, I doubt an intermediate precision of 8 decimal places is going to give an answer that's not between these two results (ie, 2.55613420 that's off in the 4th digit).
This isn't part isn't part of my answer, but is a comment on using mpmath. The questioner suggested it in the comments, and it was my first thought too, so I ran a quick test to see if it behaved how I expected with low precision calculations. It didn't, so I abandoned it (but I'm not an expert with it).
Here's my test function, basically multiplying 1/N by N and 1/N repeatedly to emphasise the error in 1/N.
def precision_test(dps=100, N=19, t=mpmath.mpf):
with mpmath.workdps(dps):
x = t(1)/t(N)
print(x)
y = x
for i in range(10000):
y *= x
y *= N
print(y)
This works as expected with, eg, np.float32:
precision_test(dps=2, N=3, t=np.float32)
# 0.33333334
# 0.3334327041164994
Note that the error has propagated into more significant digits, as expected.
But with mpmath, I could never get that to happen (testing with a range of dps and a various prime N values):
precision_test(dps=2, N=3)
# 0.33
# 0.33
Because of this test, I decided mpmath is not going to give normal results for low precision calculations.
TL;DR:
mpmath didn't behave how I expected at low precision so I abandoned it.

Find all root of an equation between a given range

I am trying to find all the root between a range of an equation as:
def f(x):
return np.tan(x) - 3*x
from scipy.optimize import fsolve
In [14]: fsolve(f,0)
Out[14]: array([ 0.]) # one of the root of the eqn
But for any other initial guess, it gives 0 unless the initial guess is very close to the root.
In [15]: fsolve(f, 2)
Out[15]: array([ 0.]) # expected ouptut 1.32419445
In [16]: fsolve(f,[1.32])
Out[16]: array([ 1.32419445])
In [17]: fsolve(f, 5)
Out[17]: array([ 0.]) # expected ouptut 4.64068363
In [18]: fsolve(f,[4.64])
Out[18]: array([ 4.64068363])
Is there any way to find all the root between a given range?
Every function, like a piece of wood, has its own "grain" that can present problems when working with it. One of my favorite methods is to rearrange the expression to get rid of the variable in the denominator. In your case, solving as sin(x)-3*x*cos(x) has a much better behavior:
>>> [nsolve(sin(x)-3*x*cos(x),i).n(2) for i in range(10)]
[0, 1.3, 1.3, -1.3, 4.6, 4.6, 1.3, 7.8, 7.8, 7.8]
Continuation is also a useful method for ill behaved functions. In this case, using a parameter to slowly turn on the ill-behaved part of the function can be useful. In your case, the x in 3*x*cos(x) makes things more difficult. But if you divide by the approximate value you are seeking and slowly change that divisor to 1 you can follow the approximate root to the desired root. Here is an example:
>>> a = 0.
>>> for j in range(5):
... for i in range(10):
... a = nsolve(sin(x)-3*x*cos(x)/(a + i*(1-a)/9),a)
... print(a)
... a += pi.n()+0.1
...
0
4.64068363077555
7.81133447513087
10.9651844009289
14.1135533715145
If a simple binary search suits you, and you can provide x's for which f has different signs, the following might help:
from math import *
eps = 1e-20
def test_func(x):
return tan(x) - 3*x
def find_root(f, a, b):
for i in range(20):
x = i / 10.0
print(x, f(x))
fa = f(a)
fb = f(b)
if fa*fb > 0:
raise ("f(a) and f(b) need to have different signs")
while True:
if fabs(fa) < eps:
return a
elif fabs(fb) < eps:
return b
else:
m = (a + b) / 2
fm = f(m)
if m == a or m == b:
return m
if fa*fm > 0:
a, fa = m, fm
else:
b, fb = m, fm
r = find_root(test_func, 1.0, 1.5)
print (r, test_func(r)) # 1.324194449575503 3.1086244689504383e-15

How can I set a random seed using the jags() function?

Each time I run my JAGS model using the jags() function, I get very different values of fitted parameters. However, I want other people to reproduce my results.
I tried to add set.seed(123), but it didn't help. This link describes how to achieve my goal using the run.jags() function. I wonder how I can do similar things using jags(). Thank you!
Below is my model in R:
##------------- read data -------------##
m <- 6
l <- 3
node <- read.csv("answer.csv", header = F)
n <- nrow(node)
# values of nodes
## IG
IG <- c(c(0.0, 1.0, 0.0), c(0.0, 0.0, 1.0), c(1.0, 0.0, 0.0), c(1.0, 0.0, 0.0), c(0.0, 1.0, 0.0), c(0.0, 0.0, 1.0))
IG <- matrix(IG, nrow=6, ncol=3, byrow=T)
V_IG <- array(0, dim=c(n, m, l))
for (i in 1:n){
for (j in 1:m){
for (k in 1:l)
{
V_IG[i,j,k] <- IG[j,k] # alternatively, V[i,j,k] <- PTS[j,k]
}
}
}
## PTS
PTS <- c(c(1.0, 0.5, 0.0), c(1.0, 0.0, 0.5), c(1.0, 1.0, 0.0), c(1.0, 0.0, 1.0), c(0.0, 0.5, 1.0), c(0.0, 1.0, 0.5))
PTS <- matrix(PTS, nrow=m, ncol=3, byrow=T)
V_PTS <- array(0, dim=c(n, m, l))
for (i in 1:n){
for (j in 1:m){
for (k in 1:l)
{
V_PTS[i,j,k] <- PTS[j,k]
}
}
}
##------------- fit model -------------##
set.seed(123)
data <- list("n", "m", "V_IG", "V_PTS", "node")
myinits <- list(list(tau = rep(1,n), theta = rep(0.5,n)))
parameters <- c("tau", "theta")
samples <- jags(data, inits=myinits, parameters,
model.file ="model.txt", n.chains=1, n.iter=10000,
n.burnin=1, n.thin=1, DIC=T)
And my model file model.txt:
model{
# data: which node (1, 2, 3) was chosen by each child in each puzzle
for(i in 1:n) # for each child
{
for (j in 1:m) # for each problem
{
# node chosen
node[i,j] ~ dcat(mu[i,j,1:3])
mu[i,j,1:3] <- exp_v[i,j,1:3] / sum(exp_v[i,j,1:3])
for (k in 1:3) {
exp_v[i,j,k] <- exp((V_IG[i,j,k]*theta[i] + V_PTS[i,j,k]*(1-theta[i]))/tau[i])
}
}
}
# priors on tau and theta
for (i in 1:n)
{
tau[i] ~ dgamma(0.001,0.001)
theta[i] ~ dbeta(1,1)
}
}
I know this is an older question, but for anyone using the jagsUI package, the jags() function has an argument for setting the seed, 'seed = ####'. So for example, a JAGS call could be;
np.sim1 <- jags(data = data1, parameters.to.save = params1, model.file = "mod1_all.txt",
n.chains = nc, n.iter = ni, n.burnin = nb, n.thin = nt, seed = 4879)
summary(np.sim1)
Here is a toy example for linear regression. First the model:
model{
a0 ~ dnorm(0, 0.0001)
a1 ~ dnorm(0, 0.0001)
tau ~ dgamma(0.001,0.001)
for (i in 1:100) {
y[i] ~ dnorm(mu[i], tau)
mu[i] <- a0 + a1 * x[i]
}
}
Now we generate some data and you the set.seed function to generate identical results from multiple calls to the jags function.
# make the data and prepare what we need to fit the model
x <- rnorm(100)
y <- 1 + 1.2 * x + rnorm(100)
data <- list("x", "y")
parameters <- c("a0", "a1", "tau")
inits = list(list(a0 = 1, a1=0.5, tau = 1))
# First fit
set.seed(121)
samples <- jags(data, inits,
parameters,model.file = "./sov/lin_reg.R",
n.chains = 1, n.iter = 5000, n.burnin = 1, n.thin = 1)
# second fit
set.seed(121) # with set.seed at same value
samples2 <- jags(data, inits,
parameters,model.file = "./sov/lin_reg.R",
n.chains = 1, n.iter = 5000, n.burnin = 1, n.thin = 1)
If we pull out the draws for one of the parameters from samples and samples2 we can see that they have generated the same values.
a0_1 <- samples$BUGSoutput$sims.list$a0
a0_2 <- samples2$BUGSoutput$sims.list$a0
head(cbind(a0_1, a0_2))
[,1] [,2]
[1,] 1.0392019 1.0392019
[2,] 0.9155636 0.9155636
[3,] 0.9497509 0.9497509
[4,] 1.0706620 1.0706620
[5,] 0.9901852 0.9901852
[6,] 0.9307072 0.9307072

Python-3.x range() with step in float format [duplicate]

How do I iterate between 0 and 1 by a step of 0.1?
This says that the step argument cannot be zero:
for i in range(0, 1, 0.1):
print(i)
Rather than using a decimal step directly, it's much safer to express this in terms of how many points you want. Otherwise, floating-point rounding error is likely to give you a wrong result.
Use the linspace function from the NumPy library (which isn't part of the standard library but is relatively easy to obtain). linspace takes a number of points to return, and also lets you specify whether or not to include the right endpoint:
>>> np.linspace(0,1,11)
array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])
>>> np.linspace(0,1,10,endpoint=False)
array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
If you really want to use a floating-point step value, use numpy.arange:
>>> import numpy as np
>>> np.arange(0.0, 1.0, 0.1)
array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
Floating-point rounding error will cause problems, though. Here's a simple case where rounding error causes arange to produce a length-4 array when it should only produce 3 numbers:
>>> numpy.arange(1, 1.3, 0.1)
array([1. , 1.1, 1.2, 1.3])
range() can only do integers, not floating point.
Use a list comprehension instead to obtain a list of steps:
[x * 0.1 for x in range(0, 10)]
More generally, a generator comprehension minimizes memory allocations:
xs = (x * 0.1 for x in range(0, 10))
for x in xs:
print(x)
Building on 'xrange([start], stop[, step])', you can define a generator that accepts and produces any type you choose (stick to types supporting + and <):
>>> def drange(start, stop, step):
... r = start
... while r < stop:
... yield r
... r += step
...
>>> i0=drange(0.0, 1.0, 0.1)
>>> ["%g" % x for x in i0]
['0', '0.1', '0.2', '0.3', '0.4', '0.5', '0.6', '0.7', '0.8', '0.9', '1']
>>>
Increase the magnitude of i for the loop and then reduce it when you need it.
for i * 100 in range(0, 100, 10):
print i / 100.0
EDIT: I honestly cannot remember why I thought that would work syntactically
for i in range(0, 11, 1):
print i / 10.0
That should have the desired output.
NumPy is a bit overkill, I think.
[p/10 for p in range(0, 10)]
[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]
Generally speaking, to do a step-by-1/x up to y you would do
x=100
y=2
[p/x for p in range(0, int(x*y))]
[0.0, 0.01, 0.02, 0.03, ..., 1.97, 1.98, 1.99]
(1/x produced less rounding noise when I tested).
scipy has a built in function arange which generalizes Python's range() constructor to satisfy your requirement of float handling.
from scipy import arange
Similar to R's seq function, this one returns a sequence in any order given the correct step value. The last value is equal to the stop value.
def seq(start, stop, step=1):
n = int(round((stop - start)/float(step)))
if n > 1:
return([start + step*i for i in range(n+1)])
elif n == 1:
return([start])
else:
return([])
Results
seq(1, 5, 0.5)
[1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0]
seq(10, 0, -1)
[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
seq(10, 0, -2)
[10, 8, 6, 4, 2, 0]
seq(1, 1)
[ 1 ]
The range() built-in function returns a sequence of integer values, I'm afraid, so you can't use it to do a decimal step.
I'd say just use a while loop:
i = 0.0
while i <= 1.0:
print i
i += 0.1
If you're curious, Python is converting your 0.1 to 0, which is why it's telling you the argument can't be zero.
Here's a solution using itertools:
import itertools
def seq(start, end, step):
if step == 0:
raise ValueError("step must not be 0")
sample_count = int(abs(end - start) / step)
return itertools.islice(itertools.count(start, step), sample_count)
Usage Example:
for i in seq(0, 1, 0.1):
print(i)
[x * 0.1 for x in range(0, 10)]
in Python 2.7x gives you the result of:
[0.0, 0.1, 0.2, 0.30000000000000004, 0.4, 0.5, 0.6000000000000001, 0.7000000000000001, 0.8, 0.9]
but if you use:
[ round(x * 0.1, 1) for x in range(0, 10)]
gives you the desired:
[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]
import numpy as np
for i in np.arange(0, 1, 0.1):
print i
Best Solution: no rounding error
>>> step = .1
>>> N = 10 # number of data points
>>> [ x / pow(step, -1) for x in range(0, N + 1) ]
[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
Or, for a set range instead of set data points (e.g. continuous function), use:
>>> step = .1
>>> rnge = 1 # NOTE range = 1, i.e. span of data points
>>> N = int(rnge / step
>>> [ x / pow(step,-1) for x in range(0, N + 1) ]
[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
To implement a function: replace x / pow(step, -1) with f( x / pow(step, -1) ), and define f.
For example:
>>> import math
>>> def f(x):
return math.sin(x)
>>> step = .1
>>> rnge = 1 # NOTE range = 1, i.e. span of data points
>>> N = int(rnge / step)
>>> [ f( x / pow(step,-1) ) for x in range(0, N + 1) ]
[0.0, 0.09983341664682815, 0.19866933079506122, 0.29552020666133955, 0.3894183423086505,
0.479425538604203, 0.5646424733950354, 0.644217687237691, 0.7173560908995228,
0.7833269096274834, 0.8414709848078965]
And if you do this often, you might want to save the generated list r
r=map(lambda x: x/10.0,range(0,10))
for i in r:
print i
more_itertools is a third-party library that implements a numeric_range tool:
import more_itertools as mit
for x in mit.numeric_range(0, 1, 0.1):
print("{:.1f}".format(x))
Output
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
This tool also works for Decimal and Fraction.
My versions use the original range function to create multiplicative indices for the shift. This allows same syntax to the original range function.
I have made two versions, one using float, and one using Decimal, because I found that in some cases I wanted to avoid the roundoff drift introduced by the floating point arithmetic.
It is consistent with empty set results as in range/xrange.
Passing only a single numeric value to either function will return the standard range output to the integer ceiling value of the input parameter (so if you gave it 5.5, it would return range(6).)
Edit: the code below is now available as package on pypi: Franges
## frange.py
from math import ceil
# find best range function available to version (2.7.x / 3.x.x)
try:
_xrange = xrange
except NameError:
_xrange = range
def frange(start, stop = None, step = 1):
"""frange generates a set of floating point values over the
range [start, stop) with step size step
frange([start,] stop [, step ])"""
if stop is None:
for x in _xrange(int(ceil(start))):
yield x
else:
# create a generator expression for the index values
indices = (i for i in _xrange(0, int((stop-start)/step)))
# yield results
for i in indices:
yield start + step*i
## drange.py
import decimal
from math import ceil
# find best range function available to version (2.7.x / 3.x.x)
try:
_xrange = xrange
except NameError:
_xrange = range
def drange(start, stop = None, step = 1, precision = None):
"""drange generates a set of Decimal values over the
range [start, stop) with step size step
drange([start,] stop, [step [,precision]])"""
if stop is None:
for x in _xrange(int(ceil(start))):
yield x
else:
# find precision
if precision is not None:
decimal.getcontext().prec = precision
# convert values to decimals
start = decimal.Decimal(start)
stop = decimal.Decimal(stop)
step = decimal.Decimal(step)
# create a generator expression for the index values
indices = (
i for i in _xrange(
0,
((stop-start)/step).to_integral_value()
)
)
# yield results
for i in indices:
yield float(start + step*i)
## testranges.py
import frange
import drange
list(frange.frange(0, 2, 0.5)) # [0.0, 0.5, 1.0, 1.5]
list(drange.drange(0, 2, 0.5, precision = 6)) # [0.0, 0.5, 1.0, 1.5]
list(frange.frange(3)) # [0, 1, 2]
list(frange.frange(3.5)) # [0, 1, 2, 3]
list(frange.frange(0,10, -1)) # []
Lots of the solutions here still had floating point errors in Python 3.6 and didnt do exactly what I personally needed.
Function below takes integers or floats, doesnt require imports and doesnt return floating point errors.
def frange(x, y, step):
if int(x + y + step) == (x + y + step):
r = list(range(int(x), int(y), int(step)))
else:
f = 10 ** (len(str(step)) - str(step).find('.') - 1)
rf = list(range(int(x * f), int(y * f), int(step * f)))
r = [i / f for i in rf]
return r
Suprised no-one has yet mentioned the recommended solution in the Python 3 docs:
See also:
The linspace recipe shows how to implement a lazy version of range that suitable for floating point applications.
Once defined, the recipe is easy to use and does not require numpy or any other external libraries, but functions like numpy.linspace(). Note that rather than a step argument, the third num argument specifies the number of desired values, for example:
print(linspace(0, 10, 5))
# linspace(0, 10, 5)
print(list(linspace(0, 10, 5)))
# [0.0, 2.5, 5.0, 7.5, 10]
I quote a modified version of the full Python 3 recipe from Andrew Barnert below:
import collections.abc
import numbers
class linspace(collections.abc.Sequence):
"""linspace(start, stop, num) -> linspace object
Return a virtual sequence of num numbers from start to stop (inclusive).
If you need a half-open range, use linspace(start, stop, num+1)[:-1].
"""
def __init__(self, start, stop, num):
if not isinstance(num, numbers.Integral) or num <= 1:
raise ValueError('num must be an integer > 1')
self.start, self.stop, self.num = start, stop, num
self.step = (stop-start)/(num-1)
def __len__(self):
return self.num
def __getitem__(self, i):
if isinstance(i, slice):
return [self[x] for x in range(*i.indices(len(self)))]
if i < 0:
i = self.num + i
if i >= self.num:
raise IndexError('linspace object index out of range')
if i == self.num-1:
return self.stop
return self.start + i*self.step
def __repr__(self):
return '{}({}, {}, {})'.format(type(self).__name__,
self.start, self.stop, self.num)
def __eq__(self, other):
if not isinstance(other, linspace):
return False
return ((self.start, self.stop, self.num) ==
(other.start, other.stop, other.num))
def __ne__(self, other):
return not self==other
def __hash__(self):
return hash((type(self), self.start, self.stop, self.num))
This is my solution to get ranges with float steps.
Using this function it's not necessary to import numpy, nor install it.
I'm pretty sure that it could be improved and optimized. Feel free to do it and post it here.
from __future__ import division
from math import log
def xfrange(start, stop, step):
old_start = start #backup this value
digits = int(round(log(10000, 10)))+1 #get number of digits
magnitude = 10**digits
stop = int(magnitude * stop) #convert from
step = int(magnitude * step) #0.1 to 10 (e.g.)
if start == 0:
start = 10**(digits-1)
else:
start = 10**(digits)*start
data = [] #create array
#calc number of iterations
end_loop = int((stop-start)//step)
if old_start == 0:
end_loop += 1
acc = start
for i in xrange(0, end_loop):
data.append(acc/magnitude)
acc += step
return data
print xfrange(1, 2.1, 0.1)
print xfrange(0, 1.1, 0.1)
print xfrange(-1, 0.1, 0.1)
The output is:
[1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0]
[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1]
[-1.0, -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.0]
For completeness of boutique, a functional solution:
def frange(a,b,s):
return [] if s > 0 and a > b or s < 0 and a < b or s==0 else [a]+frange(a+s,b,s)
You can use this function:
def frange(start,end,step):
return map(lambda x: x*step, range(int(start*1./step),int(end*1./step)))
It can be done using Numpy library. arange() function allows steps in float. But, it returns a numpy array which can be converted to list using tolist() for our convenience.
for i in np.arange(0, 1, 0.1).tolist():
print i
start and stop are inclusive rather than one or the other (usually stop is excluded) and without imports, and using generators
def rangef(start, stop, step, fround=5):
"""
Yields sequence of numbers from start (inclusive) to stop (inclusive)
by step (increment) with rounding set to n digits.
:param start: start of sequence
:param stop: end of sequence
:param step: int or float increment (e.g. 1 or 0.001)
:param fround: float rounding, n decimal places
:return:
"""
try:
i = 0
while stop >= start and step > 0:
if i==0:
yield start
elif start >= stop:
yield stop
elif start < stop:
if start == 0:
yield 0
if start != 0:
yield start
i += 1
start += step
start = round(start, fround)
else:
pass
except TypeError as e:
yield "type-error({})".format(e)
else:
pass
# passing
print(list(rangef(-100.0,10.0,1)))
print(list(rangef(-100,0,0.5)))
print(list(rangef(-1,1,0.2)))
print(list(rangef(-1,1,0.1)))
print(list(rangef(-1,1,0.05)))
print(list(rangef(-1,1,0.02)))
print(list(rangef(-1,1,0.01)))
print(list(rangef(-1,1,0.005)))
# failing: type-error:
print(list(rangef("1","10","1")))
print(list(rangef(1,10,"1")))
Python 3.6.2 (v3.6.2:5fd33b5, Jul 8 2017, 04:57:36) [MSC v.1900 64
bit (AMD64)]
I know I'm late to the party here, but here's a trivial generator solution that's working in 3.6:
def floatRange(*args):
start, step = 0, 1
if len(args) == 1:
stop = args[0]
elif len(args) == 2:
start, stop = args[0], args[1]
elif len(args) == 3:
start, stop, step = args[0], args[1], args[2]
else:
raise TypeError("floatRange accepts 1, 2, or 3 arguments. ({0} given)".format(len(args)))
for num in start, step, stop:
if not isinstance(num, (int, float)):
raise TypeError("floatRange only accepts float and integer arguments. ({0} : {1} given)".format(type(num), str(num)))
for x in range(int((stop-start)/step)):
yield start + (x * step)
return
then you can call it just like the original range()... there's no error handling, but let me know if there is an error that can be reasonably caught, and I'll update. or you can update it. this is StackOverflow.
To counter the float precision issues, you could use the Decimal module.
This demands an extra effort of converting to Decimal from int or float while writing the code, but you can instead pass str and modify the function if that sort of convenience is indeed necessary.
from decimal import Decimal
def decimal_range(*args):
zero, one = Decimal('0'), Decimal('1')
if len(args) == 1:
start, stop, step = zero, args[0], one
elif len(args) == 2:
start, stop, step = args + (one,)
elif len(args) == 3:
start, stop, step = args
else:
raise ValueError('Expected 1 or 2 arguments, got %s' % len(args))
if not all([type(arg) == Decimal for arg in (start, stop, step)]):
raise ValueError('Arguments must be passed as <type: Decimal>')
# neglect bad cases
if (start == stop) or (start > stop and step >= zero) or \
(start < stop and step <= zero):
return []
current = start
while abs(current) < abs(stop):
yield current
current += step
Sample outputs -
from decimal import Decimal as D
list(decimal_range(D('2')))
# [Decimal('0'), Decimal('1')]
list(decimal_range(D('2'), D('4.5')))
# [Decimal('2'), Decimal('3'), Decimal('4')]
list(decimal_range(D('2'), D('4.5'), D('0.5')))
# [Decimal('2'), Decimal('2.5'), Decimal('3.0'), Decimal('3.5'), Decimal('4.0')]
list(decimal_range(D('2'), D('4.5'), D('-0.5')))
# []
list(decimal_range(D('2'), D('-4.5'), D('-0.5')))
# [Decimal('2'),
# Decimal('1.5'),
# Decimal('1.0'),
# Decimal('0.5'),
# Decimal('0.0'),
# Decimal('-0.5'),
# Decimal('-1.0'),
# Decimal('-1.5'),
# Decimal('-2.0'),
# Decimal('-2.5'),
# Decimal('-3.0'),
# Decimal('-3.5'),
# Decimal('-4.0')]
Add auto-correction for the possibility of an incorrect sign on step:
def frange(start,step,stop):
step *= 2*((stop>start)^(step<0))-1
return [start+i*step for i in range(int((stop-start)/step))]
My solution:
def seq(start, stop, step=1, digit=0):
x = float(start)
v = []
while x <= stop:
v.append(round(x,digit))
x += step
return v
Here is my solution which works fine with float_range(-1, 0, 0.01) and works without floating point representation errors. It is not very fast, but works fine:
from decimal import Decimal
def get_multiplier(_from, _to, step):
digits = []
for number in [_from, _to, step]:
pre = Decimal(str(number)) % 1
digit = len(str(pre)) - 2
digits.append(digit)
max_digits = max(digits)
return float(10 ** (max_digits))
def float_range(_from, _to, step, include=False):
"""Generates a range list of floating point values over the Range [start, stop]
with step size step
include=True - allows to include right value to if possible
!! Works fine with floating point representation !!
"""
mult = get_multiplier(_from, _to, step)
# print mult
int_from = int(round(_from * mult))
int_to = int(round(_to * mult))
int_step = int(round(step * mult))
# print int_from,int_to,int_step
if include:
result = range(int_from, int_to + int_step, int_step)
result = [r for r in result if r <= int_to]
else:
result = range(int_from, int_to, int_step)
# print result
float_result = [r / mult for r in result]
return float_result
print float_range(-1, 0, 0.01,include=False)
assert float_range(1.01, 2.06, 5.05 % 1, True) ==\
[1.01, 1.06, 1.11, 1.16, 1.21, 1.26, 1.31, 1.36, 1.41, 1.46, 1.51, 1.56, 1.61, 1.66, 1.71, 1.76, 1.81, 1.86, 1.91, 1.96, 2.01, 2.06]
assert float_range(1.01, 2.06, 5.05 % 1, False)==\
[1.01, 1.06, 1.11, 1.16, 1.21, 1.26, 1.31, 1.36, 1.41, 1.46, 1.51, 1.56, 1.61, 1.66, 1.71, 1.76, 1.81, 1.86, 1.91, 1.96, 2.01]
I am only a beginner, but I had the same problem, when simulating some calculations. Here is how I attempted to work this out, which seems to be working with decimal steps.
I am also quite lazy and so I found it hard to write my own range function.
Basically what I did is changed my xrange(0.0, 1.0, 0.01) to xrange(0, 100, 1) and used the division by 100.0 inside the loop.
I was also concerned, if there will be rounding mistakes. So I decided to test, whether there are any. Now I heard, that if for example 0.01 from a calculation isn't exactly the float 0.01 comparing them should return False (if I am wrong, please let me know).
So I decided to test if my solution will work for my range by running a short test:
for d100 in xrange(0, 100, 1):
d = d100 / 100.0
fl = float("0.00"[:4 - len(str(d100))] + str(d100))
print d, "=", fl , d == fl
And it printed True for each.
Now, if I'm getting it totally wrong, please let me know.
The trick to avoid round-off problem is to use a separate number to move through the range, that starts and half the step ahead of start.
# floating point range
def frange(a, b, stp=1.0):
i = a+stp/2.0
while i<b:
yield a
a += stp
i += stp
Alternatively, numpy.arange can be used.
My answer is similar to others using map(), without need of NumPy, and without using lambda (though you could). To get a list of float values from 0.0 to t_max in steps of dt:
def xdt(n):
return dt*float(n)
tlist = map(xdt, range(int(t_max/dt)+1))

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