public void rank1()
{
double[,] x = new double[3, 3] {
{ 1, 2, 3 },
{ 2, 4, 6 },
{ 3, 6, 9 }
};
QRDecomposition qr = new QRDecomposition(x);
Assert.False(qr.hasFullRank());
var v = new double[] { 3.741657, 7.483315, 11.22497 };
double t = 0;
for (int i = 0; i < 3; i++)
{
t += Math.Abs(v[i]) - Math.Abs(qr.getR()[0, i]);
}
Assert.AreEqual(0, t, 1.0e-5); /*(new DenseVector().aggregate(qr.getR().viewRow(0), Functions.PLUS, new DoubleDoubleFunction() {
* public double apply(double arg1, double arg2) {
* return Math.abs(arg1) - Math.abs(arg2);
* }
* })(*/
}
public void randomMatrix()
{
var a = new double[60, 60];
var rnd = RandomUtils.getRandom();
MatrixUtil.assign(a, (x) => { return(rnd.nextDouble()); });
QRDecomposition qr = new QRDecomposition(a);
// how close is Q to actually being orthornormal?
var tmp = MatrixUtil.times(MatrixUtil.transpose(qr.getQ()), qr.getQ());
var tmpDiag = MatrixUtil.viewDiagonal(tmp);
MatrixUtil.assign(tmpDiag, (x) => x - 1);
double maxIdent = MatrixUtil.norm1(tmpDiag);
Assert.AreEqual(0, maxIdent, 1.0e-13);
// how close is Q R to the original value of A?
var z = MatrixUtil.times(qr.getQ(), qr.getR());
var maxError = Double.MaxValue;
for (int i = 0; i < z.GetLength(0); i++)
{
for (int j = 0; j < z.GetLength(1); j++)
{
maxError = Math.Min(maxError, Math.Abs(z[i, j] - a[i, j]));
}
}
//.minus(a);
// double maxError = z.aggregate(Functions.MIN, Functions.ABS);
Assert.AreEqual(0, maxError, 1.0e-13);
}
public void fullRankTall()
{
var x = matrix();
QRDecomposition qr = new QRDecomposition(x);
Assert.True(qr.hasFullRank());
var rRef = reshape(new double[]{
-2.99129686445138, 0, 0, 0, 0,
-0.0282260628674372, -2.38850244769059, 0, 0, 0,
0.733739310355871, 1.48042000631646, 2.29051263117895, 0, 0,
-0.0394082168269326, 0.282829484207801, -0.00438521041803086, -2.90823198084203, 0,
0.923669647838536, 1.76679276072492, 0.637690104222683, -0.225890909498753, -1.35732293800944},
5, 5);
var r = qr.getR();
// check identity down to sign
double deltaRSum = 0;
for (int i=0; i<r.GetLength(0);i++)
for (int j=0; j<r.GetLength(1);j++) {
deltaRSum += Math.Abs( r[i,j] ) - Math.Abs( rRef[i,j] );
}
//r.clone().assign(Functions.ABS).minus(rRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaRSum, 1.0e-12);
var qRef = reshape(new double[]{
-0.165178287646573, 0.0510035857637869, 0.13985915987379, -0.120173729496501,
-0.453198314345324, 0.644400679630493, -0.503117990820608, 0.24968739845381,
0.323968339146224, -0.465266080134262, 0.276508948773268, -0.687909700644343,
0.0544048888907195, -0.0166677718378263, 0.171309755790717, 0.310339001630029,
0.674790532821663, 0.0058166082200493, -0.381707516461884, 0.300504956413142,
-0.105751091334003, 0.410450870871096, 0.31113446615821, 0.179338172684956,
0.361951807617901, 0.763921725548796, 0.380327892605634, -0.287274944594054,
0.0311604042556675, 0.0386096858143961, 0.0387156960650472, -0.232975755728917,
0.0358178276684149, 0.173105775703199, 0.327321867815603, 0.328671945345279,
-0.36015879836344, -0.444261660176044, 0.09438499563253, 0.646216148583769
}, 8, 5);
//printMatrix("qRef", qRef);
var q = qr.getQ();
//printMatrix("q", q);
double deltaQSum = 0;
for (int i=0; i<r.GetLength(0);i++)
for (int j=0; j<r.GetLength(1);j++) {
deltaQSum += Math.Abs( q[i,j] ) - Math.Abs( qRef[i,j] );
}
//q.clone().assign(Functions.ABS).minus(qRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaQSum, 1.0e-12);
var x1 = qr.solve(reshape(new double[]{
-0.0178247686747641, 0.68631714634098, -0.335464858468858, 1.50249941751569,
-0.669901640772149, -0.977025038942455, -1.18857546169856, -1.24792900492054
}, 8, 1));
var xref = reshape(new double[]{
-0.0127440093664874, 0.655825940180799, -0.100755415991702, -0.0349559562697406,
-0.190744297762028
}, 5, 1);
//printMatrix("x1", x1);
//printMatrix("xref", xref);
assertEquals(xref, x1, 1.0e-8);
}
public void rank1()
{
double[,] x = new double[3, 3] {
{1, 2, 3},
{2, 4, 6},
{3, 6, 9}
};
QRDecomposition qr = new QRDecomposition(x);
Assert.False(qr.hasFullRank());
var v = new double[]{3.741657, 7.483315, 11.22497};
double t = 0;
for (int i=0; i<3; i++) {
t += Math.Abs( v[i] ) - Math.Abs( qr.getR()[0, i] );
}
Assert.AreEqual(0, t, 1.0e-5); /*(new DenseVector().aggregate(qr.getR().viewRow(0), Functions.PLUS, new DoubleDoubleFunction() {
public double apply(double arg1, double arg2) {
return Math.abs(arg1) - Math.abs(arg2);
}
})(*/
}
public void randomMatrix()
{
var a = new double[60, 60];
var rnd = RandomUtils.getRandom();
MatrixUtil.assign( a, (x) => { return rnd.nextDouble(); });
QRDecomposition qr = new QRDecomposition(a);
// how close is Q to actually being orthornormal?
var tmp = MatrixUtil.times( MatrixUtil.transpose( qr.getQ() ), qr.getQ());
var tmpDiag = MatrixUtil.viewDiagonal( tmp );
MatrixUtil.assign(tmpDiag, (x) => x-1 );
double maxIdent = MatrixUtil.norm1(tmpDiag);
Assert.AreEqual(0, maxIdent, 1.0e-13);
// how close is Q R to the original value of A?
var z = MatrixUtil.times( qr.getQ(), qr.getR());
var maxError = Double.MaxValue;
for (int i=0; i<z.GetLength(0);i++)
for (int j=0; j<z.GetLength(1);j++) {
maxError = Math.Min(maxError, Math.Abs( z[i,j]-a[i,j] ) );
}
//.minus(a);
// double maxError = z.aggregate(Functions.MIN, Functions.ABS);
Assert.AreEqual(0, maxError, 1.0e-13);
}
public void fullRankWide()
{
var x = MatrixUtil.transpose( matrix() );
QRDecomposition qr = new QRDecomposition(x);
Assert.True(qr.hasFullRank());
var rActual = qr.getR();
var rRef = reshape(new double[]{
-2.42812464965842, 0, 0, 0, 0,
0.303587286111356, -2.91663643494775, 0, 0, 0,
-0.201812474153156, -0.765485720168378, 1.09989373598954, 0, 0,
1.47980701097885, -0.637545820524326, -1.55519859337935, 0.844655127991726, 0,
0.0248883129453161, 0.00115010570270549, -0.236340588891252, -0.092924118200147, 1.42910099545547,
-1.1678472412429, 0.531245845248056, 0.351978196071514, -1.03241474816555, -2.20223861735426,
-0.887809959067632, 0.189731251982918, -0.504321849233586, 0.490484123999836, 1.21266692336743,
-0.633888169775463, 1.04738559065986, 0.284041239547031, 0.578183510077156, -0.942314870832456
}, 5, 8);
//printMatrix("rRef", rRef);
//printMatrix("rActual", rActual);
double deltaRActualSum = 0;
for (int i=0; i<rActual.GetLength(0);i++)
for (int j=0; j<rActual.GetLength(1);j++) {
deltaRActualSum += Math.Abs( rActual[i,j] ) - Math.Abs( rRef[i,j] );
}
//rActual.clone().assign(Functions.ABS).minus(rRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaRActualSum, 1.0e-12);
// assertEquals(rRef, rActual, 1.0e-8);
var qRef = reshape(new double[]{
-0.203489262374627, 0.316761677948356, -0.784155643293468, 0.394321494579, -0.29641971170211,
0.0311283614803723, -0.34755265020736, 0.137138511478328, 0.848579887681972, 0.373287266507375,
-0.39603700561249, -0.787812566647329, -0.377864833067864, -0.275080943427399, 0.0636764674878229,
0.0763976893309043, -0.318551137554327, 0.286407036668598, 0.206004127289883, -0.876482672226889,
0.89159476695423, -0.238213616975551, -0.376141107880836, -0.0794701657055114, 0.0227025098210165
}, 5, 5);
var q = qr.getQ();
//printMatrix("qRef", qRef);
//printMatrix("q", q);
double deltaQSum = 0;
for (int i = 0; i < q.GetLength(0); i++)
for (int j = 0; j < q.GetLength(1); j++) {
deltaQSum += Math.Abs(q[i, j]) - Math.Abs(qRef[i, j]);
}
//q.clone().assign(Functions.ABS).minus(qRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaQSum, 1.0e-12);
// assertEquals(qRef, q, 1.0e-8);
var x1 = qr.solve(b());
var xRef = reshape(new double[]{
-0.182580239668147, -0.437233627652114, 0.138787653097464, 0.672934739896228, -0.131420217069083, 0, 0, 0
}, 8, 1);
//printMatrix("xRef", xRef);
//printMatrix("x", x1);
assertEquals(xRef, x1, 1.0e-8);
assertEquals(x, MatrixUtil.times( qr.getQ(), qr.getR()), 1.0e-15);
}
public void fullRankWide()
{
var x = MatrixUtil.transpose(matrix());
QRDecomposition qr = new QRDecomposition(x);
Assert.True(qr.hasFullRank());
var rActual = qr.getR();
var rRef = reshape(new double[] {
-2.42812464965842, 0, 0, 0, 0,
0.303587286111356, -2.91663643494775, 0, 0, 0,
-0.201812474153156, -0.765485720168378, 1.09989373598954, 0, 0,
1.47980701097885, -0.637545820524326, -1.55519859337935, 0.844655127991726, 0,
0.0248883129453161, 0.00115010570270549, -0.236340588891252, -0.092924118200147, 1.42910099545547,
-1.1678472412429, 0.531245845248056, 0.351978196071514, -1.03241474816555, -2.20223861735426,
-0.887809959067632, 0.189731251982918, -0.504321849233586, 0.490484123999836, 1.21266692336743,
-0.633888169775463, 1.04738559065986, 0.284041239547031, 0.578183510077156, -0.942314870832456
}, 5, 8);
//printMatrix("rRef", rRef);
//printMatrix("rActual", rActual);
double deltaRActualSum = 0;
for (int i = 0; i < rActual.GetLength(0); i++)
{
for (int j = 0; j < rActual.GetLength(1); j++)
{
deltaRActualSum += Math.Abs(rActual[i, j]) - Math.Abs(rRef[i, j]);
}
}
//rActual.clone().assign(Functions.ABS).minus(rRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaRActualSum, 1.0e-12);
// assertEquals(rRef, rActual, 1.0e-8);
var qRef = reshape(new double[] {
-0.203489262374627, 0.316761677948356, -0.784155643293468, 0.394321494579, -0.29641971170211,
0.0311283614803723, -0.34755265020736, 0.137138511478328, 0.848579887681972, 0.373287266507375,
-0.39603700561249, -0.787812566647329, -0.377864833067864, -0.275080943427399, 0.0636764674878229,
0.0763976893309043, -0.318551137554327, 0.286407036668598, 0.206004127289883, -0.876482672226889,
0.89159476695423, -0.238213616975551, -0.376141107880836, -0.0794701657055114, 0.0227025098210165
}, 5, 5);
var q = qr.getQ();
//printMatrix("qRef", qRef);
//printMatrix("q", q);
double deltaQSum = 0;
for (int i = 0; i < q.GetLength(0); i++)
{
for (int j = 0; j < q.GetLength(1); j++)
{
deltaQSum += Math.Abs(q[i, j]) - Math.Abs(qRef[i, j]);
}
}
//q.clone().assign(Functions.ABS).minus(qRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaQSum, 1.0e-12);
// assertEquals(qRef, q, 1.0e-8);
var x1 = qr.solve(b());
var xRef = reshape(new double[] {
-0.182580239668147, -0.437233627652114, 0.138787653097464, 0.672934739896228, -0.131420217069083, 0, 0, 0
}, 8, 1);
//printMatrix("xRef", xRef);
//printMatrix("x", x1);
assertEquals(xRef, x1, 1.0e-8);
assertEquals(x, MatrixUtil.times(qr.getQ(), qr.getR()), 1.0e-15);
}
public void fullRankTall()
{
var x = matrix();
QRDecomposition qr = new QRDecomposition(x);
Assert.True(qr.hasFullRank());
var rRef = reshape(new double[] {
-2.99129686445138, 0, 0, 0, 0,
-0.0282260628674372, -2.38850244769059, 0, 0, 0,
0.733739310355871, 1.48042000631646, 2.29051263117895, 0, 0,
-0.0394082168269326, 0.282829484207801, -0.00438521041803086, -2.90823198084203, 0,
0.923669647838536, 1.76679276072492, 0.637690104222683, -0.225890909498753, -1.35732293800944
},
5, 5);
var r = qr.getR();
// check identity down to sign
double deltaRSum = 0;
for (int i = 0; i < r.GetLength(0); i++)
{
for (int j = 0; j < r.GetLength(1); j++)
{
deltaRSum += Math.Abs(r[i, j]) - Math.Abs(rRef[i, j]);
}
}
//r.clone().assign(Functions.ABS).minus(rRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaRSum, 1.0e-12);
var qRef = reshape(new double[] {
-0.165178287646573, 0.0510035857637869, 0.13985915987379, -0.120173729496501,
-0.453198314345324, 0.644400679630493, -0.503117990820608, 0.24968739845381,
0.323968339146224, -0.465266080134262, 0.276508948773268, -0.687909700644343,
0.0544048888907195, -0.0166677718378263, 0.171309755790717, 0.310339001630029,
0.674790532821663, 0.0058166082200493, -0.381707516461884, 0.300504956413142,
-0.105751091334003, 0.410450870871096, 0.31113446615821, 0.179338172684956,
0.361951807617901, 0.763921725548796, 0.380327892605634, -0.287274944594054,
0.0311604042556675, 0.0386096858143961, 0.0387156960650472, -0.232975755728917,
0.0358178276684149, 0.173105775703199, 0.327321867815603, 0.328671945345279,
-0.36015879836344, -0.444261660176044, 0.09438499563253, 0.646216148583769
}, 8, 5);
//printMatrix("qRef", qRef);
var q = qr.getQ();
//printMatrix("q", q);
double deltaQSum = 0;
for (int i = 0; i < r.GetLength(0); i++)
{
for (int j = 0; j < r.GetLength(1); j++)
{
deltaQSum += Math.Abs(q[i, j]) - Math.Abs(qRef[i, j]);
}
}
//q.clone().assign(Functions.ABS).minus(qRef.clone().assign(Functions.ABS)).aggregate(Functions.PLUS, Functions.IDENTITY)
Assert.AreEqual(0, deltaQSum, 1.0e-12);
var x1 = qr.solve(reshape(new double[] {
-0.0178247686747641, 0.68631714634098, -0.335464858468858, 1.50249941751569,
-0.669901640772149, -0.977025038942455, -1.18857546169856, -1.24792900492054
}, 8, 1));
var xref = reshape(new double[] {
-0.0127440093664874, 0.655825940180799, -0.100755415991702, -0.0349559562697406,
-0.190744297762028
}, 5, 1);
//printMatrix("x1", x1);
//printMatrix("xref", xref);
assertEquals(xref, x1, 1.0e-8);
}