Thiele's interpolation formula: Difference between revisions

=={{header|Sidef}}==

{{trans|Python}}

<lang ruby>func thiele(x, y) {

var ρ = y.range.map {|i| [y[i]]*(y.len-i) }

for i in ^(ρ.end) {

ρ[i][1] = ((x[i] - x[i+1]) / (ρ[i][0] - ρ[i+1][0]))

}

for i in range(2, ρ.end) {

for j in range(0, ρ.end - i) {

ρ[j][i] = (((x[j]-x[j+i]) / (ρ[j][i-1]-ρ[j+1][i-1])) + ρ[j+1][i-2])

}

}

var ρ0 = ρ[0]

func t(xin) {

var a = 0

for i in range(ρ0.end, 2, -1) {

a = ((xin - x[i-1]) / (ρ0[i] - ρ0[i-2] + a))

}

y[0] + ((xin-x[0]) / (ρ0[1]+a))

}

return t

}

# task 1: build 32 row trig table

var xVal = range(32).map { |k| k * 0.05 }

var tSin = xVal.map { .sin }

var tCos = xVal.map { .cos }

var tTan = xVal.map { .tan }

# task 2: define inverses

var iSin = thiele(tSin, xVal)

var iCos = thiele(tCos, xVal)

var iTan = thiele(tTan, xVal)

# task 3: demonstrate identities

say 6*iSin(0.5)

say 3*iCos(0.5)

say 4*iTan(1)</lang>

{{out}}

<pre>

3.14159265358979323846438729976819

3.14159265358979323846157620314931

3.14159265358979323846264318595256

</pre>