test('simple case with four points, 8 segments', function (t) {
var result = zeroes( [ 8 + 1, 3 ] ); // n + 1 points define n segments
bezier(result, input, 8);
var expected = [ [ 0, 0, 0 ],
[ 0.001953125, 0.04296875, 0.330078125 ],
[ 0.015625, 0.15625, 0.578125 ],
[ 0.052734375, 0.31640625, 0.755859375 ],
[ 0.125, 0.5, 0.875 ],
[ 0.244140625, 0.68359375, 0.947265625 ],
[ 0.421875, 0.84375, 0.984375 ],
[ 0.669921875, 0.95703125, 0.998046875 ],
[ 1, 1, 1 ] ];
t.deepEqual(result, expected);
t.end();
});
test('simple case on 2D plane z = 1', function (t) {
var input2d = [ [ 0, 0, 1 ],
[ 0, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 0, 1 ] ];
var result = zeroes( [ 8 + 1, 3 ] ); // n + 1 points define n segments
bezier(result, input2d, 8);
var expected = [ [ 0, 0, 1 ],
[ 0.04296875, 0.328125, 1 ],
[ 0.15625, 0.5625, 1 ],
[ 0.31640625, 0.703125, 1 ],
[ 0.5, 0.75, 1 ],
[ 0.68359375, 0.703125, 1 ],
[ 0.84375, 0.5625, 1 ],
[ 0.95703125, 0.328125, 1 ],
[ 1, 0, 1 ] ];
t.deepEqual(result, expected);
t.end();
})
test('simple case with four points, 12 segments', function (t) {
var result = zeroes( [ 12 + 1, 3 ] ); // n + 1 points define n segments
bezier(result, input, 12);
var expected = [ [ 0, 0, 0 ],
[ 0.0005787037037037037, 0.019675925925925923, 0.22974537037037038 ],
[ 0.004629629629629629, 0.07407407407407407, 0.4212962962962963 ],
[ 0.015625, 0.15625, 0.578125 ],
[ 0.037037037037037035, 0.2592592592592593, 0.7037037037037037 ],
[ 0.07233796296296297, 0.37615740740740744, 0.8015046296296297 ],
[ 0.125, 0.5, 0.875 ],
[ 0.19849537037037038, 0.6238425925925926, 0.9276620370370371 ],
[ 0.2962962962962963, 0.7407407407407407, 0.962962962962963 ],
[ 0.421875, 0.84375, 0.9843750000000001 ],
[ 0.5787037037037037, 0.9259259259259259, 0.9953703703703706 ],
[ 0.7702546296296297, 0.9803240740740741, 0.9994212962962966 ],
[ 1, 1, 1 ] ];
t.deepEqual(result, expected);
t.end();
});
function zeroes (dimensions, initialValue) {
var array;
if (dimensions.length === 1) dimensions = dimensions[0];
if (initialValue === undefined) initialValue = 0;
// if it's a number, create a flat array of zeroes
if (typeof dimensions === 'number') {
array = new Array(dimensions);
for (var i = 0; i < dimensions; i += 1) {
array[i] = initialValue;
}
}
// else create an array of one-dimension-less arrays full of zeroes
else {
array = new Array(dimensions[0]);
for (var j = 0; j < dimensions[0]; j += 1) {
array[j] = zeroes(dimensions.slice(1));
}
}
return array;
}
chainProfile : function (isotope, charge) {
// First need to convert mass in kg to number of atoms
each(keys(charge), function (isotope) {
charge[isotope] /= isotopeData[isotope].molarMass;
});
var chain = this.chain(isotope);
var C = new Array(chain.length);
var molarMasses = [];
// calculate lambda coefficients
var lambda = map(chain, function (isotope) {
return ( Math.log(2) / isotopeData[isotope].halflife );
});
// coefficients for the first row
C[0] = zeroes(chain.length);
C[0][0] = charge[isotope] || 0;
charge[isotope] = 0;
molarMasses[0] = isotopeData[isotope].molarMass;
// coefficients for the remaining rows
for (var i = 1; i < chain.length; i++) {
// initialize array to zeroes
C[i] = zeroes(chain.length);
molarMasses[i] = isotopeData[chain[i]].molarMass;
var sum = 0;
for (var k = 0; k < i; k++) {
C[i][k] = lambda[k] * C[i-1][k] / (lambda[i] - lambda[k]);
sum += C[i][k];
}
// the last coefficient (on the diagonal)
var Ni0 = charge[chain[i]] || 0;
C[i][i] = Ni0 - sum;
charge[chain[i]] = 0;
}
// return function that can evaluate the profile for any time
var massProfile = function (years) {
var N = {};
N.total = 0;
for (var i = 0; i < C.length; i++) {
var Ni = 0;
for (var k = 0; k < C[i].length; k++) {
Ni += molarMasses[i] * C[i][k] * Math.exp(-lambda[k] * years);
}
N[chain[i]] = Math.max(0, Ni);
N.total += N[chain[i]];
}
return N;
};
var radioactivityProfile = function (years) {
var Bq = {};
Bq.total = 0;
for (var i = 0; i < C.length; i++) {
var Ni = 0;
for (var k = 0; k < C[i].length; k++) {
Ni += C[i][k] * Math.exp(-lambda[k] * years);
}
Bq[chain[i]] = convert.moles(lambda[i] * Math.max(0, Ni)) / (365.25 * 24 * 60 * 60);
Bq.total += Bq[chain[i]];
}
return Bq;
};
return {
mass : massProfile,
radioactivity : radioactivityProfile
};
},