WarpX 1D
========

.. code-block:: none

	opts := SpiralDefaults;

	ni:= 4;
	n := 8;
	no := 6;

	## 1D case -- getting started
	padg := fAdd(n, no, (n-no)/2);
	pads := fAdd(n, ni, (n-ni)/2);

	scat := Scat(pads);
	gath := Gath(padg);
	dft := DFT(n, 1);
	idft := DFT(n, -1);
	krn := Diag(List([0..n-1], i->i+1));

	op := gath * idft * krn * dft * scat;

	## pruned DFT
	sl := [(n-ni)/2 .. n - (n-ni)/2 - 1];
	gl := [(n-no)/2 .. n - (n-no)/2 - 1];

	pdft := PrunedDFT(n, 1, 1, sl);
	pidft := PrunedIDFT(n, -1, 1, gl);
	InfinityNormMat(MatSPL(gath * idft) - MatSPL(pidft));
	InfinityNormMat(MatSPL(dft * scat) - MatSPL(pdft));

	krn := Diag(List([0..n-1], i->i+1));
	pop := pidft * krn * pdft;

	InfinityNormMat(MatSPL(op) - MatSPL(pop));

	## constant vector field
	vi := 3;
	vo := 2;

	vpdft := Tensor(pdft, I(vi));
	vpidft := Tensor(pidft, I(vo));

	cmat := Mat([[1,2,3], [4,5,6]]);
	vkrn := Tensor(I(n), cmat);

	vpop := vpidft * vkrn * vpdft;

	## location dependent vector field
	nnz := 4;
	mf := FData(List([0..nnz * n-1], i-> Complex(i+E(4))));
	i := Ind(n);
	cimat := Mat([[mf.at(nnz*i),0,mf.at(nnz*i+1)], [0,mf.at(nnz*i+2),mf.at(nnz*i+3)]]);

	vikrn := IterDirectSum(i, cimat);
	vipop := vpidft * vikrn * vpdft;

	## real arithmetic
	rvipop := RC(vipop); 
	rvipopm := List(MatSPL(rvipop), r->List(r, ReComplex));

	# SPL Matrix
	rt := RandomRuleTree(rvipop, opts);
	spl := SPLRuleTree(rt);
	splm := List(MatSPL(spl), r->List(r, ReComplex));
	InfinityNormMat(rvipopm - splm);

	# CMatrix
	tvpdft := TTensorI(pdft, vi, AVec, AVec);
	tvpidft := TTensorI(pidft, vo, AVec, AVec);
	tvikrn := TTensorInd(cimat,i, APar, APar);
	tvipop := TRC(TCompose([tvpidft, tvikrn, tvpdft]));

	rt := RandomRuleTree(tvipop, opts);
	c := CodeRuleTree(rt, opts);

	cm := CMatrix(c, opts);
	InfinityNormMat(rvipopm - cm);