Playin' around with complex matrices...

cplx_mat.js

# Computes conjugate transpose of M
let conjTransp = function conjTransp(M) {
	return map(range(sizeof M[0]), function(row) {
		return map(range(sizeof M), function(col) {
			return cplx_conj(M[col][row]);
		});
	});
};

# Helper for cplxMatMul
let cplxVecScalarMul = function cplxVecScalarMul(A, B, row, col) {
	var M = { "re": 0.0, "im": 0.0 };
	let N = sizeof A;
	for (var i = 0; i < N; i++) {
		let P = cplx_mul(A[row][i], B[i][col]);
		M = cplx_add(M, P);
	}
	return M;
};

# Multiplies matrices A and B
# A and B are assumed to be square and of the same size,
# this condition is not checked.
let cplxMatMul = function cplxMatMul(A, B) {
	var R = {};
	let N = sizeof A;
	for (var row = 0; row < N; row++) {
		R[row] = {};
		for (var col = 0; col < N; col++) {
			R[row][col] = cplxVecScalarMul(A, B, row, col);
		}
	}
	return R;
};

# Helper for creating an array representing a complex number
# given its textual representation
let _ = function makeComplex(str) {
	let sep = indexof(str, "+", 1);
	if sep < 0 {
		sep = indexof(str, "-", 1);
	}
	let reStr = substrto(str, sep);
	let imStr = substrfrom(str, sep);
	return { "re": tofloat(reStr), "im": tofloat(imStr) };
};

# Formats a complex matrix
let printCplxMat = function printCplxMat(M) {
	foreach(M, function(i, row) {
		foreach(row, function(j, elem) {
			printf("    %.2f%+.2fi", elem.re, elem.im);
		});
		print();
	});
};

# A Hermitian matrix
let H = {
	{ _("3+0i"), _("2+1i") },
	{ _("2-1i"), _("0+0i") }
};

# A normal matrix
let N = {
	{ _("1+0i"), _("1+0i"), _("0+0i") },
	{ _("0+0i"), _("1+0i"), _("1+0i") },
	{ _("1+0i"), _("0+0i"), _("1+0i") }
};

# A unitary matrix
let U = {
	{ _("0.70710678118+0i"), _("0.70710678118+0i"), _("0+0i") },
	{ _("0-0.70710678118i"), _("0+0.70710678118i"), _("0+0i") },
	{ _("0+0i"),             _("0+0i"),             _("0+1i") }
};


print("Hermitian matrix:\nH = ");
printCplxMat(H);
print("H* = ");
printCplxMat(conjTransp(H));
print();

print("Normal matrix:\nN = ");
printCplxMat(N);
print("N* = ");
printCplxMat(conjTransp(N));
print("N* x N = ");
printCplxMat(cplxMatMul(conjTransp(N), N));
print("N x N* = ");
printCplxMat(cplxMatMul(N, conjTransp(N)));
print();

print("Unitary matrix:\nU = ");
printCplxMat(U);
print("U* = ");
printCplxMat(conjTransp(U));
print("U x U* = ");
printCplxMat(cplxMatMul(U, conjTransp(U)));
print();