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GeezerVison is showing github.com — smallbasic.github.io/samples/node/120.bas at master · smallbasic/smallbasic.github.io

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'''This program will display the real and imaginary roots for a polynomial of the form f(x)=A0 + A1*x + A2*x^2 +...
''spagetti code in http://www3.sympatico.ca/ltoms/html/bairstow_s_method.html modified by:
''Adolfo Leon Sepulveda
''Aug-01-2004
''Version 1.0
''Test case:
''real and imaginary roots of polynomials
''using bairstow''s method
''form is y = A0 + A1*x + A2*x^2 + A3*x^3 +....
''degree of polynomial: 4
''coefficent of A(0)= 12
''coefficent of A(1)= -19
''coefficent of A(2)= 12
''coefficent of A(3)= -6
''coefficent of A(4)= 1
''Roots:
''0.5 + 1.6583124 i
''0.5 - 1.6583124 i
''4.0
''1.0
rem roots of polynomials - bairstow''s method
cls
print
print "real and imaginary roots of polynomials"
print "using bairstow''s method"
print "form is y = A0 + A1*x + A2*x^2 + A3*x^3 +...."
print
dim a(22)
Const err=.0001
Const cero=1e-19
Const iter=100
InputData a,n
print
print "Roots:"
Bairstow a,n,err,iter
End
sub InputData( ByRef a(), ByRef n)
local i,xa
input "degree of polynomial: ";n
print
for i=0 to n
print "coefficent of A(";i;")= ";
input " ";xa
rem stored in array a in reverse order
a(n-i+1)=xa
next i
end
Sub Bairstow(a,n,err,iter)
dim b(22)
dim e(22)
local p, q, p1, q1, r0, r1, v0, v1, s0, s1, d0, d1, d2, s, t
local m1, n1, k, i, h, j
local const cero = 1e-19
rem branch for special treatment of 1st and 2nd degree equations
if n<=2 then
OrderLessThan2 a, n
Exit Sub
endif
a(n+2)=0
n1=2*int((n+1)/2)
m1 = 1
While true
If m1 >= n1 / 2 Then Exit loop
p=1
q=1
For k=1 to iter
while true
rem store coefficients in array b
for i=1 to n1+1
b(i)=a(i)
next i
for j=n1-2 to n1-4 step -2
for i=1 to j+1
b(i+1) = b(i+1) - p*b(i)
b(i+2) = b(i+2) - q*b(i)
next i
next j
r0 = b(n1+1)
r1 = b(n1)
s0 = b(n1-1)
s1 = b(n1-2)
v0 = -q*s1
v1 = s0 - s1*p
d0 = v1*s0 - v0*s1
if abs(d0) >= cero then Exit loop
p=p+5
q=q+5
wend
d1 = s0*r1 - s1*r0
d2 = r0*v1 - v0*r1
p1=d1/d0
q1=d2/d0
p=p+p1
q=q+q1
if !(Abs(r0)>=err or abs(r1)>=err) then
e(m1)=1
Exit For
endif
if !(abs(p1)>=err or abs(q1)>=err) then
e(m1)=2
Exit For
endif
if p=0 then
if !(q=0) Then
if !(abs(q1/q)>=err) Then
e(m1)=3
Exit For
endif
endif
Else
if !(abs(p1/p)>=err) Then
if !(q=0) Then
if !(abs(q1/q)>=err) Then
e(m1)=3
Exit For
endif
endif
endif
endif
Next k
If k > iter Then
e(m1) = 4 ''Is Order 2
endif
While true
s = -p/2
t = s^2 - q
if !(t<0) then
t=Sqr(t)
PrintReal s,t
Else
t=Sqr(-1*t)
PrintImag s,t
endif
If e(m1) = 4 then Exit Sub
for j=1 to n1-1
a(j+1) = a(j+1) - p*a(j)
a(j+2) = a(j+2) - q*a(j)
next j
n1 = n1 - 2
if !(n1>1) Then Exit Sub
if n1>3 then Exit loop
m1 = m1 + 1
e(m1)=1
p=a(2)/a(1)
q=a(3)/a(1)
Wend
Wend ''m1
end
Sub OrderLessThan2(a(),n)
If n = 2 Then
Order2 a
Else
print -a(2)/a(1)
Endif
End
sub order2(a())
local s,t
a(3) = a(2)*a(2) - 4*a(1)*a(3)
s = -a(2) / (2*a(1))
t=Sqr(abs(a(3))) / (2*a(1))
if sgn(a(3))<0 then
PrintImag s,t
Else
PrintReal s,t
endif
End
Sub PrintImag(s,t)
Print
If Abs(s) > cero
print s;" + ";t;" i"
print s;" - ";t;" i"
Else
Print 0;" + ";t;" i"
print 0;" - ";t;" i"
endif
End
Sub PrintReal(s,t)
print
If Abs(s+t) > cero
print s+t
endif
If Abs(s-t) > cero
print s-t
endif
End
'
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