TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

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Bertrand Cayzac

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Feb 16, 2020, 9:44:52 AM2/16/20
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Hello, 

The code below worked happlily each time I launched it in SageMathCell until recently. It now exits with the error below in a call to scipy.optimize.newton while I didn't make any change; 

I gathered that the casting rules have changed but it seems that ufunc doesn't take a "casting" argument in version 1.16 and I can't seem to fin a way to override
the safe rule. I don't know how to import or install a different version in a cell. 
Any idea?


Last lines of the trace : 
/home/sc_serv/sage/local/lib/python2.7/site-packages/numpy/core/numeric.pyc in isclose(a, b, rtol, atol, equal_nan)
   2519     y = array(y, dtype=dt, copy=False, subok=True)
   2520 
-> 2521     xfin = isfinite(x)
   2522     yfin = isfinite(y)
   2523     if all(xfin) and all(yfin):

TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''


The curent versions in SageMathCell are the following (I don't know what they used to be when the code was working)
Python : 2.7.15 (default, Oct  6 2019, 03:20:16) [GCC 7.4.0]
Numpy : 1.16.1
Scipy : 1.2.0

I gathered that the casting rules have changed but it seems that ufunc doesn't take a "casting" argument in version 1.16 and I can't seem to fin a way to override
the safe rule. I don't know how to import or install a different version in a cell. 
Any idea? 

Thanks and regards,
Bertrand Cayzac bnhmc...@gmail.com

Vincent Delecroix

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Feb 16, 2020, 2:51:24 PM2/16/20
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Dear Bertrand,

Where is "the code below"?

Vincent

Bertrand Cayzac

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Feb 16, 2020, 4:33:16 PM2/16/20
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Dear Vincent,

Sorry I did not paste it...Here it goes. You'll also find it in attachment. 

It is to be noted that I just ran the code again after a lo,g while and it now exits upon a "print" instruction instruction supposedly in line 33. 
My guess is that the code is more and more compatible with the SageMath celle interpreter version... I'll dig on that. If you have any idea they are welcome. 

KInd regards,
B



<html>
<head>
<meta name="description" content="Maria Gaetana Agnesi's Versiera (aka Witch) meets arcs.">
<meta name="description" content="A mathematical meditation on breast geometry.">
<meta name="version" content="9.05">
<meta name="keywords" content="HTML,JavaScript,Python,SageMathCell,Geometry,Breast">
<meta name="author" content="Floozman">
<meta name="credit" content="circle-cirlcle intersection by Xaedes (Github)">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width">
<title> VmA </title>
<script src="https://sagecell.sagemath.org/static/embedded_sagecell.js"></script>
<script>
// Make the div with id 'mycell' a Sage cell
sagecell.makeSagecell({inputLocation: '#mycell',
template: sagecell.templates.minimal,
evalButtonText: 'Let there be breasts !'});
</script>
</head>
<body>
<h2> Versiera meets arcs </h2>
Click the button below to make Maria Gaetana Agnesi's Versiera and arcs meet in beauty
<div id="mycell"><script type="text/x-sage">
from __future__ import division
import numpy as np
import scipy.optimize
"""
circle-circle intersection
credit: Xaedes (Github)
"""
#!/usr/bin/env python2
#-*- coding: utf-8 -*-
#from __future__ import division
#import numpy as np
from math import cos, sin, pi, sqrt, atan2
d2r = pi/180
class Geometry(object):
def circle_intersection(self, circle1, circle2):
'''
@summary: calculates intersection points of two circles
@param circle1: tuple(x,y,radius)
@param circle2: tuple(x,y,radius)
@result: tuple of intersection points (which are (x,y) tuple)
'''
# return self.circle_intersection_sympy(circle1,circle2)
x1,y1,r1 = circle1
x2,y2,r2 = circle2
# http://stackoverflow.com/a/3349134/798588
dx,dy = x2-x1,y2-y1
d = sqrt(dx*dx+dy*dy)
if d > r1+r2:
print "#1"
return None # no solutions, the circles are separate
if d < abs(r1-r2):
print "#2"
return None # no solutions because one circle is contained within the other
if d == 0 and r1 == r2:
print "#3"
return None # circles are coincident and there are an infinite number of solutions
a = (r1*r1-r2*r2+d*d)/(2*d)
h = sqrt(r1*r1-a*a)
xm = x1 + a*dx/d
ym = y1 + a*dy/d
xs1 = xm + h*dy/d
xs2 = xm - h*dy/d
ys1 = ym - h*dx/d
ys2 = ym + h*dx/d
return (xs1,ys1),(xs2,ys2)
def circle_intersection_sympy(self, circle1, circle2):
from sympy.geometry import Circle, Point
x1,y1,r1 = circle1
x2,y2,r2 = circle2
c1=Circle(Point(x1,y1),r1)
c2=Circle(Point(x2,y2),r2)
intersection = c1.intersection(c2)
if len(intersection) == 1:
intersection.append(intersection[0])
p1 = intersection[0]
p2 = intersection[1]
xs1,ys1 = p1.x,p1.y
xs2,ys2 = p2.x,p2.y
return (xs1,ys1),(xs2,ys2)
"""
Interaction in the sagemath cell
"""
@interact
def VmA(nipple_x=(1,1.7)):
# recommended values for r = 1 : x=(1, 1.5+)
var ('u,v,w,x,y,z')
var ('breastarc_x,nipple_x,nipple_y')
#presentation parameters
showmaths = True #print maths
showinvisible = True #Above and beyond breast, print curves in dotted line
thk = 2 # thickness of the visible
wi = 5 # width of the frame
#geometry parameters
r = 1 # Versiera radius
d=2*r # Versiera diameter
ptinf= (2*r)/sqrt(3) # Versiera positive point of inflexion
breastarc_r=0.9 # breast circle radius
areo_ratio=4.4 # ratio breast circle / areola circle
# Versiera curve
versiera = 8*(r^3)/((x^2) + 4*(r^2))
# Versiera curve (parametric)
t= var ('t')
xvp = d*t
yvp = d/(t^2+1)
#W=parametric_plot((xvp,yvp-r),(t,0,1))
# Find the y coordinate of the target intersection between versiera and breast arc when x = nipple_x
nipple_y = 8*(r^3)/((nipple_x^2) + 4*(r^2))
# Plot versiera from offset to nipple_x (heigth is shifted down 0.5 by subtracting the radius).
offset=r-breastarc_r
P=plot(versiera-r,offset+0.12,nipple_x,fill=0,rgbcolor="black",fillcolor='white',thickness=thk)
S=P
# Find the x coordinate of the center of a circle with radius breastarc_r to which belongs point (nipple_x, nipple_y)
eqdelta = (nipple_y-r)^2 + z^2 == breastarc_r^2
soldelta = solve([eqdelta],z,solution_dict=True)
breastarc_x=nipple_x-soldelta[1][z]
# Areola as a circle of center (areo_x,areo_y) and radius areo_r
areo_r = nipple_x/ areo_ratio
areo_x = nipple_x
areo_y = nipple_y-r
# Store the circles
tuplebreast= breastarc_x, 0, breastarc_r
tupleareo = areo_x, areo_y, areo_r
# Draw the breast arc
var('m,n')
arcbreast = (m-breastarc_x)^2 + (n-0) ^2 == breastarc_r^2
U=implicit_plot(arcbreast, (m, offset,r*2), (n,-r,nipple_y-r),color='black',linewidth=thk)
S=S+U
# Find areola low intersection point with circle
geom = Geometry()
getint = geom.circle_intersection(circle1=tuplebreast, circle2=tupleareo)
areoint_x = getint[0][0]
# Find areola intersection point with Versiera
function ('xt') (t)
function ('yt') (t)
function ('f') (t)
function ('df') (t)
xt(t) = 2*t
yt(t) = d/(t^2+1)-r
f(t)= (xt(x=t)-areo_x)^2 + (yt(x=t)-areo_y)^2 - areo_r^2
#st = solve([f(t) == 0],t)
df(t) = f(x=t).derivative()
# Use Newton-Raphson approximation
var ('xstart')
xstart=nipple_x/3.3
iter = 100
son = scipy.optimize.newton(f,xstart,df, maxiter= iter)
dyvp=(yt(son))
# Draw the areola circle between intersection points
var ('o,p')
arcareo = (o-areo_x)^2 + (p-areo_y)^2 == areo_r^2
V=implicit_plot(arcareo, (o,0,areoint_x), (p,-r,dyvp),color='black',linewidth=thk)
S=S+V
# Draw the vertical line perpendicular to x axis at Versiera's positive point of inflexion
L=line( [ (ptinf , -r), (ptinf, r) ], color="purple", thickness=1, linestyle="-.")
S=S+L
# Plot the whole shebang
if showinvisible :
IPV=plot(versiera-r,nipple_x,wi,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV
IPV2 = plot(versiera-r,-wi, offset+0.12,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV2
IPC = implicit_plot(arcbreast, (m, -r,r*2), (n,-r,r),color='black', linestyle='dotted')
S=S+IPC
IPA = implicit_plot(arcareo, (o,0,wi), (p,-0.5,1),color='black', linestyle='dotted')
S=S+IPA
S.show (axes=true,aspect_ratio=1)
if showmaths :
show ('nipple coordinates : x = ', nipple_x, ' y = ', nipple_y-r)
show ('areola / breast circle intersection coordinates : x = ', areoint_x, ' y = ', nipple_y-r)
show ('areola / Versiera intersection coordinates : x = ', xt(son), ' y = ', dyvp)
show ('numerical resolution : ')
show (' f(t) : ', f(t))
show (' dérivée df(t) : ', df)
show (' t approximation for f(t) = 0 (Newton-Raphson method) : ', son)
#show ('df(t) = 0 : ', st)
return
</script>
</div>
</body>
</html>


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Vincent Delecroix

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Feb 16, 2020, 4:59:21 PM2/16/20
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As a start you can notice that SageMath cell has switch to Python 3. To
see that, run the following two lines in a cell

import sys
print(sys.version)

In particular you need to modify the print statements from

print whatever

to

print(whatever)

The change from Python 2 to Python 3 impacts more than just the print
statements, see http://python-future.org/compatible_idioms.html

After making the appropriate change, I can at least reproduce the
error

TypeError: ufunc 'isfinite' not supported for the input types, and
the inputs could not be safely coerced to any supported types
according to the casting rule ''safe''

... which is a good start: the bug is reproducible!

Vincent

Vincent Delecroix

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Feb 16, 2020, 5:11:33 PM2/16/20
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It seems that sympy is picky about the input. You can use the following
workaround. Replace

son = scipy.optimize.newton(f, xstart, df, maxiter= iter)

By

f2 = lambda s: float(f(s))
xstart2 = float(xstart)
df2 = lambda s: float(df(s))
son = scipy.optimize.newton(f2, xstart2, df2, maxiter= iter)

I open https://trac.sagemath.org/ticket/29210 to track the issue.

Vincent

Bertrand Cayzac

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Feb 18, 2020, 3:11:22 AM2/18/20
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Dear Vincent,

Thanks for your quick reply and all the wealth of info in it ! I’ll test this asap that is aside of my daily job which doesn’t leave me much time...

Kind regard
Bertrand 

Bertrand Cayzac

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Feb 21, 2020, 6:11:55 PM2/21/20
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Hi Vincent,

Splendid ! It works just fine :-) 

Many thanks for your help,
Bertrand

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