Revision history [back]

I plot an integral with quad() function in a Python file. I wanted to plot the same result with SageMath but the values returned are differents and I really don't understand why the two graphics are not the same ... Here is my sage code :

import scipy.integrate as sp_int

int1(a, j, k,L) =  piecewise([[[0,1/4],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[(1/4,3/4),2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[[3/4,1],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)]])


def int2(a, j, k,L):
    if a < 1 / 4 or a > 3 / 4:
        return cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)
    else:
        return 2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)


def integral1(j):
    k=2
    L = 0.5
    return numerical_integral(int1, 0, 1,max_points=10, params=[j, k,L])[0]


def integral2(j):
    k=2
    L = 0.5
    return sp_int.quad(int2, 0, 1, args=(j, k,L))[0]


i1 = plot(integral1, 0,10,rgbcolor=(0.8,0,0),legend_label='SageMath/numerical_integral')
i2 = plot(integral2, 0,10,rgbcolor=(0,0.8,0),legend_label='Python/Quad')
show(i2+i1)

I can't upload the png to show you the result because I'm a newby with less than 60 points :-) but you can just copy this code and run it in Sage to have a look by yourself. Thanks for any help.

I plot an integral with quad() function in a Python file. I wanted to plot the same result with SageMath but the values returned are differents and I really don't understand why the two graphics are not the same ... Here is my sage code :

import scipy.integrate as sp_int

int1(a, j, k,L) =  piecewise([[[0,1/4],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[(1/4,3/4),2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[[3/4,1],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)]])


def int2(a, j, k,L):
    if a < 1 / 4 or a > 3 / 4:
        return cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)
    else:
        return 2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)


def integral1(j):
    k=2
    L = 0.5
    return numerical_integral(int1, 0, 1,max_points=10, params=[j, k,L])[0]


def integral2(j):
    k=2
    L = 0.5
    return sp_int.quad(int2, 0, 1, args=(j, k,L))[0]


i1 = plot(integral1, 0,10,rgbcolor=(0.8,0,0),legend_label='SageMath/numerical_integral')
i2 = plot(integral2, 0,10,rgbcolor=(0,0.8,0),legend_label='Python/Quad')
show(i2+i1)

I can't upload the png to show you the result because I'm a newby with less than 60 points :-) :-( but you can just copy this code and run it in Sage to have a look by yourself. Thanks for any help.

I plot an integral with quad() function in a Python file. I wanted to plot the same result with SageMath but the values returned are differents and I really don't understand why the two graphics are not the same ... Here is my sage code :

import scipy.integrate as sp_int

int1(a, j, k,L) =  piecewise([[[0,1/4],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[(1/4,3/4),2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[[3/4,1],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)]])


def int2(a, j, k,L):
    if a < 1 / 4 or a > 3 / 4:
        return cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)
    else:
        return 2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)


def integral1(j):
    k=2
    L = 0.5
    return numerical_integral(int1, 0, 1,max_points=10, params=[j, k,L])[0]


def integral2(j):
    k=2
    L = 0.5
    return sp_int.quad(int2, 0, 1, args=(j, k,L))[0]


i1 = plot(integral1, 0,10,rgbcolor=(0.8,0,0),legend_label='SageMath/numerical_integral')
i2 = plot(integral2, 0,10,rgbcolor=(0,0.8,0),legend_label='Python/Quad')
show(i2+i1)

I can't upload the png to show you the result because I'm a newby with less than 60 points :-( but you can just copy this code and run it in Sage to have a look by yourself. Thanks for any help.

I plot an integral with quad() quad() function in a Python file. file.

I wanted to plot the same result with SageMath SageMath but the values returned are differents different and I really don't don't understand why the two graphics are not the same ... ...

Here is my sage Sage code :

import scipy.integrate as sp_int

int1(a, j, k,L) =  piecewise([[[0,1/4],1* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[(1/4,3/4),2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)],[[3/4,1],1* k, L) =  piecewise([[[0, 1/4], 1 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)], [(1/4, 3/4), 2 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)], [[3/4, 1], 1 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)]])
 
def int2(a, j, k,L):
k, L):
    if a < 1 / 4 or a > 3 / 4:
        return cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)
    else:
        return 2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)

 def integral1(j):
    k=2
k = 2
    L = 0.5
    return numerical_integral(int1, 0, 1,max_points=10, 1, max_points=10, params=[j, k,L])[0]

k, L])[0]

def integral2(j):
    k=2
k = 2
    L = 0.5
    return sp_int.quad(int2, 0, 1, args=(j, k,L))[0]

k, L))[0]

i1 = plot(integral1, 0,10,rgbcolor=(0.8,0,0),legend_label='SageMath/numerical_integral')
0, 10, rgbcolor=(0.8,0, 0),
          legend_label='SageMath/numerical_integral')
i2 = plot(integral2, 0,10,rgbcolor=(0,0.8,0),legend_label='Python/Quad')
show(i2+i1)
0, 10, rgbcolor=(0, 0.8, 0),
          legend_label='Python/Quad')
show(i2 + i1)

I can't upload the png to show you the result because I'm a newby with less than 60 points :-( but you can just copy this code and run it in Sage to have a look by yourself. Thanks for any help.