JA_test_pinv_coeffs.scd

/*
compare a decoder matrix to the pseudoinverse of an encoder matrix
of the same dimensions.
*/

~cart = [
	[1, 1, 1],
	[-1, 1, 1],
	[-1, -1, 1],
	[1, -1, 1],
	[1, 1, -1],
	[-1, 1, -1],
	[-1, -1, -1],
	[1, -1, -1],
];

// dirs of a cube - in degrees
~dirs = ~cart.collect({ arg arr;
	arr.asCartesian.asSpherical
}).collect({ arg sph;
	[sph.theta, sph.phi].raddeg
});

~dirs.do(_.postln)



// newPeri
~d1 = FoaDecoderMatrix.newPeri(k: \velocity)
// newDiam - use this
~d2 = FoaDecoderMatrix.newDiametric(~dirs[0..3].degrad, \velocity)


~d1.dirChannels.raddeg.do(_.postln)
~d2.dirChannels.raddeg.do(_.postln)

~d1.matrix
~d2.matrix


// pseudo-inverse of newDiam
~e1 = FoaEncoderMatrix.newDirections(~d2.dirChannels)
~e1.dirChannels.raddeg.do(_.postln)
~e1.matrix;
~pinv = ~e1.matrix.pseudoInverse;

// compare to ~d2 matrix
~d2.matrix




// pseudo-inverse of newDirections
~e2 = FoaEncoderMatrix.newDirections(~dirs.degrad)
~e2.dirInputs.raddeg.do(_.postln)
~e2.matrix;
~pinv = ~e2.matrix.pseudoInverse;

// compare to ~d2 matrix
~d2.matrix


(// for every row, find a matching row in the other matrix
var results = [];
// var comparToD1 = ~d2.matrix;
var comparToD1 = ~pinv;

~d1rows = ~d1.matrix.rows.collect{|i| ~d1.matrix.getRow(i)};

comparToD1.rows.do{|i|
	var thisRow, result;
	thisRow = comparToD1.getRow(i);
	result=false;

	~d1rows.do{|testRow, j|
		result.not.if{ // skip if match found
			result = testRow.size.collect({ |k|
				thisRow[k].equalWithPrecision(testRow[k], 1e-16)
			}).includes(false).not;
		}
	};
	results = results.add(result)

};
postf( "Matrices Match??   %\n", results.includes(false).not );
nil;
)