Gauss Quadrature in numerical methods
2
$begingroup$
In the following code I have implemented gauss quadrature. It is working correctly for my first function but for my second function I am getting an error.
So,
Is it possible to do this code without sing p_roots? and if not how do I fix it so my second function works?
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: sin(x),0,pi/2,100))
giving the output
291.6666666666665
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-22-b4248b816207> in <module>()
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
<ipython-input-22-b4248b816207> in gaussquad(f, a, b, n)
2 def gaussquad(f,a,b,n):
3 [x,w] = p_roots(n+1)
----> 4 G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
<ipython-input-22-b4248b816207> in <lambda>(x)
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
TypeError: only size-1 arrays can be converted to Python scalars
numerical-methods
asked Dec 4 '18 at 1:42
fr14fr14
38318
$endgroup$
add a comment |
2
$begingroup$
In the following code I have implemented gauss quadrature. It is working correctly for my first function but for my second function I am getting an error.
So,
Is it possible to do this code without sing p_roots? and if not how do I fix it so my second function works?
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: sin(x),0,pi/2,100))
giving the output
291.6666666666665
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-22-b4248b816207> in <module>()
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
<ipython-input-22-b4248b816207> in gaussquad(f, a, b, n)
2 def gaussquad(f,a,b,n):
3 [x,w] = p_roots(n+1)
----> 4 G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
<ipython-input-22-b4248b816207> in <lambda>(x)
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
TypeError: only size-1 arrays can be converted to Python scalars
numerical-methods
asked Dec 4 '18 at 1:42
fr14fr14
38318
$endgroup$
add a comment |
2
2
2
$begingroup$
In the following code I have implemented gauss quadrature. It is working correctly for my first function but for my second function I am getting an error.
So,
Is it possible to do this code without sing p_roots? and if not how do I fix it so my second function works?
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: sin(x),0,pi/2,100))
giving the output
291.6666666666665
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-22-b4248b816207> in <module>()
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
<ipython-input-22-b4248b816207> in gaussquad(f, a, b, n)
2 def gaussquad(f,a,b,n):
3 [x,w] = p_roots(n+1)
----> 4 G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
<ipython-input-22-b4248b816207> in <lambda>(x)
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
TypeError: only size-1 arrays can be converted to Python scalars
numerical-methods
asked Dec 4 '18 at 1:42
fr14fr14
38318
$endgroup$
In the following code I have implemented gauss quadrature. It is working correctly for my first function but for my second function I am getting an error.
So,
Is it possible to do this code without sing p_roots? and if not how do I fix it so my second function works?
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: sin(x),0,pi/2,100))
giving the output
291.6666666666665
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-22-b4248b816207> in <module>()
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
<ipython-input-22-b4248b816207> in gaussquad(f, a, b, n)
2 def gaussquad(f,a,b,n):
3 [x,w] = p_roots(n+1)
----> 4 G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
<ipython-input-22-b4248b816207> in <lambda>(x)
5 return G
6 print(gaussquad(lambda x: x**2,5,10,100))
----> 7 print(gaussquad(lambda x: sin(x),0,pi/2,100))
TypeError: only size-1 arrays can be converted to Python scalars
numerical-methods
numerical-methods
asked Dec 4 '18 at 1:42
fr14fr14
38318
asked Dec 4 '18 at 1:42
fr14fr14
38318
asked Dec 4 '18 at 1:42
fr14fr14
38318
asked Dec 4 '18 at 1:42
fr14fr14
38318
asked Dec 4 '18 at 1:42
fr14fr14
38318
38318
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
2
$begingroup$
Vectorization issues. Use numpy instead
import numpy
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: numpy.sin(x),0,numpy.pi/2,100))
Result is
1.000000000000001
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
$endgroup$
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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oldest
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2
$begingroup$
Vectorization issues. Use numpy instead
import numpy
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: numpy.sin(x),0,numpy.pi/2,100))
Result is
1.000000000000001
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
$endgroup$
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
add a comment |
2
$begingroup$
Vectorization issues. Use numpy instead
import numpy
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: numpy.sin(x),0,numpy.pi/2,100))
Result is
1.000000000000001
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
$endgroup$
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
add a comment |
2
2
2
$begingroup$
Vectorization issues. Use numpy instead
import numpy
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: numpy.sin(x),0,numpy.pi/2,100))
Result is
1.000000000000001
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
$endgroup$
Vectorization issues. Use numpy instead
import numpy
from scipy.special.orthogonal import p_roots
def gaussquad(f,a,b,n):
[x,w] = p_roots(n+1)
G = 0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
print(gaussquad(lambda x: x**2,5,10,100))
print(gaussquad(lambda x: numpy.sin(x),0,numpy.pi/2,100))
Result is
1.000000000000001
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
answered Dec 4 '18 at 1:51
caveraccaverac
14.5k31130
14.5k31130
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
add a comment |
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
thanks again!!!
$endgroup$
– fr14
Dec 4 '18 at 1:59
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
$begingroup$
I posted my final question, this one has to do with simpsons rule but I am running into an error again with my section function
$endgroup$
– fr14
Dec 4 '18 at 2:04
add a comment |
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