sbplib: diracPrimDiscrTest.m annotate

author	Martin Almquist <malmquist@stanford.edu>
date	Tue, 21 May 2019 18:44:01 -0700
parents
children	ea225a4659fe

rev	line source
1130 99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 function tests = diracPrimDiscrTest()
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 tests = functiontests(localfunctions);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 function testLeftGP(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 % Test left boundary grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 x0s = xl + [0, h, 2*h];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 function testLeftRandom(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Test random points near left boundary
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 x0s = xl + 2hrand(1,10);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 function testRightGP(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 % Test right boundary grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 x0s = xr-[0, h, 2*h];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 function testRightRandom(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 % Test random points near right boundary
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 x0s = xr - 2hrand(1,10);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 function testInteriorGP(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 % Test interior grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 m_half = round(m/2);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 x0s = xl + (m_half-1:m_half+1)*h;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 function testInteriorRandom(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 % Test random points in interior
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 x0s = (xl+2h) + (xr-xl-4h)*rand(1,20);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 % x0 outside grid should yield 0 integral!
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 function testX0OutsideGrid(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 % Test points outisde grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 x0s = [xl-1.1h, xr+1.1h];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 err = abs(integral - 0);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 function testAllGP(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 % Test all grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 x0s = x;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 function testHalfGP(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 % Test halfway between all grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 x0s = 1/2*( x(2:end)+x(1:end-1) );
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 fp = fps{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 fx = f(x);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 x0 = x0s(i);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 integral = delta'Hfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 err = abs(integral + fp(x0));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 %=============== 2D tests ==============================
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 % function testAllGP2D(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 % orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 % mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 % for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 % order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 % mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 % [xlims, ylims, m, x, X, ~, H, fs] = setup2D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 % H_global = kron(H{1}, H{2});
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 % % Test all grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 % x0s = X;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 % for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 % f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 % fx = f(X(:,1), X(:,2));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 % for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 % x0 = x0s(i,:);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 % delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 % integral = delta'H_globalfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 % err = abs(integral - f(x0(1), x0(2)));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 % testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 % function testAllRandom2D(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 % orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 % mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 % for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 % order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 % mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 % [xlims, ylims, m, x, X, h, H, fs] = setup2D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 % H_global = kron(H{1}, H{2});
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 % xl = xlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 % xr = xlims{2};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 % yl = ylims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 % yr = ylims{2};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 % % Test random points, even outside grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 % Npoints = 100;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 % x0s = [(xl-3h{1}) + (xr-xl+6h{1})*rand(Npoints,1), ...
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 % (yl-3h{2}) + (yr-yl+6h{2})*rand(Npoints,1) ];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310 % for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 % f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 % fx = f(X(:,1), X(:,2));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 % for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 % x0 = x0s(i,:);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 % delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 % integral = delta'H_globalfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 % % Integral should be 0 if point is outside grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 % if x0(1) < xl \|\| x0(1) > xr \|\| x0(2) < yl \|\| x0(2) > yr
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 % err = abs(integral - 0);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 % else
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 % err = abs(integral - f(x0(1), x0(2)));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 % testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 %=============== 3D tests ==============================
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 % function testAllGP3D(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 % orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 % mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 % for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 % order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 % mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 % [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 % H_global = kron(kron(H{1}, H{2}), H{3});
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 % % Test all grid points
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 % x0s = X;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 % for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 % fx = f(X(:,1), X(:,2), X(:,3));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 % for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 % x0 = x0s(i,:);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 % delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 % integral = delta'H_globalfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 % err = abs(integral - f(x0(1), x0(2), x0(3)));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 % testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 % function testAllRandom3D(testCase)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 % orders = [2, 4, 6];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 % mom_conds = orders;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 % for o = 1:length(orders)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 % order = orders(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 % mom_cond = mom_conds(o);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 % [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 % H_global = kron(kron(H{1}, H{2}), H{3});
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 % xl = xlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 % xr = xlims{2};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 % yl = ylims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 % yr = ylims{2};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 % zl = zlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 % zr = zlims{2};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 % % Test random points, even outside grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 % Npoints = 200;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 % x0s = [(xl-3h{1}) + (xr-xl+6h{1})*rand(Npoints,1), ...
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 % (yl-3h{2}) + (yr-yl+6h{2})*rand(Npoints,1), ...
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 % (zl-3h{3}) + (zr-zl+6h{3})*rand(Npoints,1) ];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 % for j = 1:length(fs)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 % f = fs{j};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 % fx = f(X(:,1), X(:,2), X(:,3));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 % for i = 1:length(x0s)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 % x0 = x0s(i,:);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 % delta = diracPrimDiscr(x0, x, mom_cond, 0, H);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 % integral = delta'H_globalfx;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 % % Integral should be 0 if point is outside grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 % if x0(1) < xl \|\| x0(1) > xr \|\| x0(2) < yl \|\| x0(2) > yr \|\| x0(3) < zl \|\| x0(3) > zr
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 % err = abs(integral - 0);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 % else
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 % err = abs(integral - f(x0(1), x0(2), x0(3)));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 % testCase.verifyLessThan(err, 1e-12);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 % ======================================================
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 % ============== Setup functions =======================
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 % ======================================================
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 function [xl, xr, m, h, x, H, fs, fps] = setup1D(order, mom_cond)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 % Grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 xl = -3;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 xr = 900;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 L = xr-xl;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 m = 101;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 h = (xr-xl)/(m-1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 g = grid.equidistant(m, {xl, xr});
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 x = g.points();
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 % Quadrature
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 ops = sbp.D2Standard(m, {xl, xr}, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 H = ops.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 % Moment conditions
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 fs = cell(mom_cond+1,1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 fps = cell(mom_cond+1,1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 for p = 0:mom_cond
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 fs{p+1} = @(x) (x/L).^p;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 fps{1} = @(x) 0*x;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 for p = 1:mom_cond
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 fps{p+1} = @(x) p/L*(x/L).^(p-1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435 end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 % function [xlims, ylims, m, x, X, h, H, fs] = setup2D(order, mom_cond)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 % % Grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440 % xlims = {-3, 20};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 % ylims = {-11,5};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442 % Lx = xlims{2} - xlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 % Ly = ylims{2} - ylims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 % m = [15, 16];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 % g = grid.equidistant(m, xlims, ylims);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 % X = g.points();
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 % x = g.x;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 % % Quadrature
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 % opsx = sbp.D2Standard(m(1), xlims, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 % opsy = sbp.D2Standard(m(2), ylims, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 % Hx = opsx.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 % Hy = opsy.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 % H = {Hx, Hy};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 % % Moment conditions
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 % fs = cell(mom_cond,1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 % for p = 0:mom_cond-1
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 % fs{p+1} = @(x,y) (x/Lx + y/Ly).^p;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 % % Grid spacing in interior
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 % mm = round(m/2);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 % hx = x{1}(mm(1)+1) - x{1}(mm(1));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 % hy = x{2}(mm(2)+1) - x{2}(mm(2));
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467 % h = {hx, hy};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 % function [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond)
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 % % Grid
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 % xlims = {-3, 20};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 % ylims = {-11,5};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476 % zlims = {2,4};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 % Lx = xlims{2} - xlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 % Ly = ylims{2} - ylims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 % Lz = zlims{2} - zlims{1};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 % m = [13, 14, 15];
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 % g = grid.equidistant(m, xlims, ylims, zlims);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 % X = g.points();
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 % x = g.x;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486 % % Quadrature
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 % opsx = sbp.D2Standard(m(1), xlims, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 % opsy = sbp.D2Standard(m(2), ylims, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489 % opsz = sbp.D2Standard(m(3), zlims, order);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490 % Hx = opsx.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 % Hy = opsy.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492 % Hz = opsz.H;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 % H = {Hx, Hy, Hz};
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495 % % Moment conditions
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496 % fs = cell(mom_cond,1);
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 % for p = 0:mom_cond-1
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 % fs{p+1} = @(x,y,z) (x/Lx + y/Ly + z/Lz).^p;
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 % end
99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500

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99fd66ffe714 Add derivative of delta functions and corresponding tests, tested for 1D.