#  weibull function: p[0]=sigma-sat, p[1]=LET-thresh, p[2]=width, p[3]=exponent
# default display App
 @interact
#@interact   #https://doc.sagemath.org/html/en/prep/Quickstarts/Interact.html
#foo = ['bar' for _ in xrange(10000000)]
def plot_weibull(m=('sigma-sat', 1e-7), let0=('threshold', 0.001), w=('width', 100.0), s=('exponent', 1.0)):
    p = [1.77e-8, 0.584, 240.1, 0.812]#Note REW Fit of 7-Series data (DSLee REDW + two low LET points)
    f(x) = p[0] * (1 - 1/(exp(((x - p[1])/p[2]) ^ p[3])))

    f(x) = m * (1 - 1/(exp(((x - let0)/w) ^ s)))

  plot_semilogy(f(x), xmin=let0+0.001, xmax=120, thickness=2).show()   # alternative to xmin: ymin=m*0.00001
    plot_loglog(f, xmin=let0+0.001, xmax=120, thickness=2).show()
    plot(f(x), 0, 120, thickness=2).show()
    plot_semilogx(f, xmin=let0+0.001, xmax=120, thickness=2).show()
    return

#https://doc.sagemath.org/html/en/thematic_tutorials/numerical_sage/numpy.html

    #option 2: https://stackoverflow.com/questions/1316767/how-can-i-explicitly-free-memory-in-python
plot_weibull(1.77e-8, 0.584, 240.1, 0.812)
# plot_weibull()
#parametric_plot([cos(x) + 2*cos(x/4), sin(x) - 2*sin(x/4)], (x,0,8*pi), color='green', thickness=3, fill = True)

interactive(
plot_semilogy(f(x), xmin=p[1]+0.001, xmax=120, thickness=2).show())))
plot_loglog(f, xmin=p[1]+0.001, xmax=120, thickness=3)

plot_semilogx(f, xmin=p[1]+0.001, xmax=4
             20, thickness=3)

interact(plot(x^2, (x,0,5)).show()