numeric_test.sj

ClearAll(approxeq, f, f1, x)

# Check that someone does not pick up the global (Symata) binding
# upgrade 0.7 . Why did the following happen ?
#x = 1.0

# Use Function compiled from Julia code
# FIXME: method too new
#   f1 = J( x -> x^2)
#   codefile = J( joinpath(Symata.SYMATA_LANG_TEST_PATH, "numeric_code.sj"))
#   Get(codefile)
# T approxeq(NIntegrate(f1, [0,2])[1], 8.0/3)

approxeq(x_, y_) := Abs(x-y) < 1.0*10^(-8)

# Different ways to give integrand to NIntegrate

# Issue #71
T approxeq( NIntegrate(x, [0,3])[1], 4.5)
T approxeq( NIntegrate(x, [x,0,3])[1], 4.5)

# Explicitly compile Symata to Julia function
# FIXME: Method is too new. This will happen with
#        every function created in Symata code.
# T approxeq(NIntegrate(Compile([x], x^2), [0,2])[1], 8.0/3)
## FIXME: method too new
# ex = Compile([x], x^2)
# T  approxeq( NIntegrate(ex, [0,2])[1], 8.0/3)

# Wrap Symata expression
   f(x_) := x^2
T approxeq(NIntegrate(f(x), [x,0,2])[1], 8.0/3)

# Wrap Symata expression
T approxeq(NIntegrate(x^2, [x,0,2])[1], 8.0/3)

# Test evaluation succeeds with deep expression.
# We forgot Attribute HoldAll
T (NIntegrate( (Exp(-x)^2 + x/(1+x))^2 + x , [x,0.0,2]), True)
T (NIntegrate( Exp(-x), [x,0.0,2]), True)
a = 2.0
T approxeq(NIntegrate(Exp(-x)*x^(a-1), [x,0,Infinity])[1], 1)
mygamma(a_) := NIntegrate(Exp(-x)*x^(a-1), [x,0,Infinity])[1]
T approxeq(mygamma(3.0), Gamma(3.0))
T approxeq(mygamma(4.0), Gamma(4.0))
T approxeq(mygamma(5.0), Gamma(5.0))

ClearAll(ex, f, f1, x)

f = Compile([x], E^x)
T approxeq(f(1), N(E))
f = Compile([x], Cos(Pi*x))
T approxeq(f(1), -1)

ClearAll(x)

T ToJuliaString( x^2 + Cos(x), NoSymata => False) == "mplus(mpow(x, 2), Cos(x))"
T ToJuliaString( x^2 + Cos(x), NoSymata => True) == "x ^ 2 + cos(x)"

ClearAll(approxeq, f, f1, x, a, mygamma)
ClearTemporary()