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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Numerical-integration/Yabasic/numerical-integration.basic Normal file
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// Rosetta Code problem: https://rosettacode.org/wiki/Numerical_integration
// by Jjuanhdez, 06/2022
print "function range steps leftrect midrect rightrect trap simpson "
frmt$ = "%1.10f"
print "f(x) = x^3 0 - 1 100 ";
Integrate(0.0, 1.0, 1, 100)
print "f(x) = 1/x 1 - 100 1000 ";
Integrate(1.0, 100.0, 2, 1000)
frmt$ = "%8.3f"
print "f(x) = x 0 - 5000 5000000 ";
Integrate(0.0, 5000.0, 3, 5000000)
print "f(x) = x 0 - 6000 6000000 ";
Integrate(0.0, 6000.0, 3, 6000000)
end
sub Func(FN, X) //Return F(X) for function number FN
switch FN
case 1
return X ^ 3
case 2
return 1.0 / X
case 3
return X
default
return 0.0
end switch
end sub
sub Integrate(A, B, FN, N) //Display area under curve for function FN
// A, B, FN limits A, B, and number of slices N
DX = (B-A)/N
X = A
Area = 0.0 //rectangular left
for i = 1 to N
Area = Area + Func(FN,X)*DX
X = X + DX
next i
print str$(Area, frmt$);
X = A
Area = 0.0 //rectangular right
for i = 1 to N
X = X + DX
Area = Area + Func(FN,X)*DX
next i
print " ";
print str$(Area, frmt$);
X = A + DX / 2.0
Area = 0.0 //rectangular mid point
for i = 1 to N
Area = Area + Func(FN,X)*DX
X = X + DX
next i
print " ";
print str$(Area, frmt$);
X = A
Area = 0.0 //trapezium
for i = 1 to N
Area = Area + (Func(FN,X)+Func(FN,X + DX))/2.0*DX
X = X + DX
next i
print " ";
print str$(Area, frmt$);
X = A
Area = 0.0 //Simpson's rule
for i = 1 to N
Area = Area + DX/6.0*(Func(FN,X) + 4.0*Func(FN,(X+X + DX)/2.0) + Func(FN,X + DX))
X = X + DX
next i
print " ";
print str$(Area, frmt$)
end sub