L = 8
f <- function(x) {
	return(exp(1)^(-(x^2)))
}

a <- function(n) {
	g <- function(x) {
		return(cos(n * 2 * pi / L * x) * f(x))
	}
	return(2/L * integrate(g, -L/2, L/2)$val)
}

b <- function(n) {
	g <- function(x) {
		return(sin(n * 2 * pi / L * x) * f(x))
	}
	return(2/L * integrate(g, -L/2, L/2)$val)
}

a0 = 1/L * integrate(f, -L/2, L/2)$val
M = 2
H <- function(x) {
	val <- a0
	for (n in 1:M) {
		val = val + a(n) * cos(n * 2 * pi / L * x) + b(n) * sin(n * 2 * pi / L * x)
	}
	return(val)
}
cat(c("a 0: ", a0, "\n"))
for (i in 1:10) {
	cat(c("a", i, ": ", a(i), "\n"))
}
for (i in 1:10) {
	cat(c("b", i, ": ", b(i), "\n"))
}
vals = c(2, 6, 10)
for (v in vals) {
	M = v
	png(paste('m', v, '.png', sep=''))
	curve(H, -L/2, L/2)
}
png('minf.png')
curve(f, -L/2, L/2)
png('m6diff.png')
M = 6
diff <- function(x) {
	f(x) - H(x)
}
curve(diff, -L/2, L/2)
png('m10diff.png')
M = 10
curve(diff, -L/2, L/2)

av <- c(a(1))
bv <- c(b(1))
nv <- c(1)
for (i in 2:10) {
	av <- append(av, a(i))
	bv <- append(bv, b(i))
	nv <- append(nv, i)
}

png('abplot.png')
plot(nv, av, col="red")
points(nv, bv, col="green")

f <- function(x) {
	return((exp(1)^(-x^2)) * (1/2 * sin(4 * pi / L * x) + 1/2  * cos(6 * pi / L * x)))
}
a <- function(n) {
	g <- function(x) {
		return(cos(n * 2 * pi / L * x) * f(x))
	}
	return(2/L * integrate(g, -L/2, L/2)$val)
}

b <- function(n) {
	g <- function(x) {
		return(sin(n * 2 * pi / L * x) * f(x))
	}
	return(2/L * integrate(g, -L/2, L/2)$val)
}

a0 = 1/L * integrate(f, -L/2, L/2)$val
M = 2
H <- function(x) {
	val <- a0
	for (n in 1:M) {
		val = val + a(n) * cos(n * 2 * pi / L * x) + b(n) * sin(n * 2 * pi / L * x)
	}
	return(val)
}

cat(c("a 0: ", a0, "\n"))
for (i in 1:10) {
	cat(c("a", i, ": ", a(i), "\n"))
}
for (i in 1:10) {
	cat(c("b", i, ": ", b(i), "\n"))
}
vals = c(2, 6, 10)
for (v in vals) {
	M = v
	png(paste('m2', v, '.png', sep=''))
	curve(H, -L/2, L/2)
}
png('m2inf.png')
curve(f, -L/2, L/2)


curve(f, -L/2, L/2)
png('m26diff.png')
M = 6
diff <- function(x) {
	f(x) - H(x)
}
curve(diff, -L/2, L/2)
png('m210diff.png')
M = 10
curve(diff, -L/2, L/2)

av <- c(a(1))
bv <- c(b(1))
nv <- c(1)
for (i in 2:10) {
	av <- append(av, a(i))
	bv <- append(bv, b(i))
	nv <- append(nv, i)
}

png('abplot2.png')
plot(nv, av, col="red")
points(nv, bv, col="green")