Skip to content

Commit

Permalink
Features:
Browse files Browse the repository at this point in the history 
	- Matrix Util Graham Schmidt #1 (1, 2, 3)
	- Matrix Util Graham Schmidt #2 (4, 5, 6)
	- Matrix Util Graham Schmidt #3 (7, 8, 9)
	- Matrix Util Modulus Internal Unchecked (10, 11, 12)
	- Matrix Util Graham Schmidt #4 (13, 14, 15)


Bug Fixes/Re-organization:

	- Matrix Graham Schmidt Process Run (16, 17)
	- Matrix Util QR Decomposition Fix (37, 38, 39)


Samples:

	- Bartels Stewart Sylvester Solver #1 (18, 19, 20)
	- Bartels Stewart Sylvester Solver #2 (21, 22)
	- Matrix Graham Schmidt Process #1 (23, 24)
	- Matrix Graham Schmidt Process #2 (25, 26)
	- Matrix Graham Schmidt Process #3 (27, 28)
	- Bartels Stewart Sylvester Solver #3 (29, 30)
	- Matrix Graham Schmidt Process #4 (31, 32)
	- Matrix Graham Schmidt Process #5 (33, 34)
	- Bartels Stewart Sylvester Solver #4 (35, 36)
	- Matrix Graham Schmidt Process #6 (40, 41, 42)
	- Matrix Graham Schmidt Process #7 (43, 44, 45)
	- Matrix Graham Schmidt Process #8 (46, 47, 48)
	- Matrix Graham Schmidt Process #9 (49, 50, 51)
	- Matrix Graham Schmidt Process #10 (52, 53, 54)
	- Matrix Graham Schmidt Process #11 (55, 56, 57)
	- Matrix Graham Schmidt Process #12 (58, 59, 60)
	- Matrix Graham Schmidt Process #13 (61, 62, 63)
	- Matrix Graham Schmidt Process #14 (64, 65, 66)
	- Matrix Graham Schmidt Process #15 (67, 68, 69)
	- Matrix Graham Schmidt Process #16 (70, 71, 72)
	- Matrix Graham Schmidt Process #17 (73, 74, 75)
	- Matrix Graham Schmidt Process #18 (76, 77, 78)
	- Matrix Graham Schmidt Process #19 (79, 80, 81)
	- Bartels Stewart Sylvester Solver #5 (85, 86, 87)
	- Bartels Stewart Sylvester Solver #6 (88, 89, 90)


IdeaDRIP:

	- Bartels-Stewart Algorithm (91-97)
	- Bartels-Stewart Algorithm The (98-117)
	- Bartels-Stewart Algorithm The - Computational Cost (118)
	- Bartels-Stewart Algorithm The - Simplifications and Special Cases (119, 120)
  • Loading branch information
@Lakshmik
Lakshmik committed Jul 9, 2024
1 parent 094488c commit ad64618
Show file tree
Hide file tree
Showing 3 changed files with 144 additions and 96 deletions.
51 changes: 51 additions & 0 deletions ReleaseNotes/02_13_2024.txt
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,51 @@

Features:

- Matrix Util Graham Schmidt #1 (1, 2, 3)
- Matrix Util Graham Schmidt #2 (4, 5, 6)
- Matrix Util Graham Schmidt #3 (7, 8, 9)
- Matrix Util Modulus Internal Unchecked (10, 11, 12)
- Matrix Util Graham Schmidt #4 (13, 14, 15)


Bug Fixes/Re-organization:

- Matrix Graham Schmidt Process Run (16, 17)
- Matrix Util QR Decomposition Fix (37, 38, 39)


Samples:

- Bartels Stewart Sylvester Solver #1 (18, 19, 20)
- Bartels Stewart Sylvester Solver #2 (21, 22)
- Matrix Graham Schmidt Process #1 (23, 24)
- Matrix Graham Schmidt Process #2 (25, 26)
- Matrix Graham Schmidt Process #3 (27, 28)
- Bartels Stewart Sylvester Solver #3 (29, 30)
- Matrix Graham Schmidt Process #4 (31, 32)
- Matrix Graham Schmidt Process #5 (33, 34)
- Bartels Stewart Sylvester Solver #4 (35, 36)
- Matrix Graham Schmidt Process #6 (40, 41, 42)
- Matrix Graham Schmidt Process #7 (43, 44, 45)
- Matrix Graham Schmidt Process #8 (46, 47, 48)
- Matrix Graham Schmidt Process #9 (49, 50, 51)
- Matrix Graham Schmidt Process #10 (52, 53, 54)
- Matrix Graham Schmidt Process #11 (55, 56, 57)
- Matrix Graham Schmidt Process #12 (58, 59, 60)
- Matrix Graham Schmidt Process #13 (61, 62, 63)
- Matrix Graham Schmidt Process #14 (64, 65, 66)
- Matrix Graham Schmidt Process #15 (67, 68, 69)
- Matrix Graham Schmidt Process #16 (70, 71, 72)
- Matrix Graham Schmidt Process #17 (73, 74, 75)
- Matrix Graham Schmidt Process #18 (76, 77, 78)
- Matrix Graham Schmidt Process #19 (79, 80, 81)
- Bartels Stewart Sylvester Solver #5 (85, 86, 87)
- Bartels Stewart Sylvester Solver #6 (88, 89, 90)


IdeaDRIP:

- Bartels-Stewart Algorithm (91-97)
- Bartels-Stewart Algorithm The (98-117)
- Bartels-Stewart Algorithm The - Computational Cost (118)
- Bartels-Stewart Algorithm The - Simplifications and Special Cases (119, 120)
162 changes: 66 additions & 96 deletions src/main/java/org/drip/numerical/linearalgebra/MatrixUtil.java
View file
Original file line number Diff line number Diff line change
Expand Up @@ -128,6 +128,33 @@ private static final double DotProductInternal (
return dotProductInternal;
}

private static final double[] ProjectVOnUInternal (
final double[] u,
final double[] v)
{
double vDotUOverUDotU = DotProductInternal (u, v) / DotProductInternal (u, u);

double[] projectVOnU = new double[u.length];

for (int i = 0; i < u.length; ++i) {
projectVOnU[i] = vDotUOverUDotU * u[i];
}

return projectVOnU;
}

private static final double ModulusInternal (
final double[] v)
{
double modulus = 0.;

for (int i = 0; i < v.length; ++i) {
modulus += v[i] * v[i];
}

return Math.sqrt (modulus);
}

/**
* Indicate if the Cell corresponds to Bottom Left Location in the Matrix
*
Expand Down Expand Up @@ -888,29 +915,22 @@ public static final double Sum (
/**
* Compute the Modulus of the Input Vector
*
* @param adbl The Input Vector
* @param v The Input Vector
*
* @return TRUE - The Modulus of the Input Vector
* @return The Modulus of the Input Vector
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
* @throws Exception Thrown if the Inputs are Invalid
*/

public static final double Modulus (
final double[] adbl)
throws java.lang.Exception
final double[] v)
throws Exception
{
if (null == adbl || !org.drip.numerical.common.NumberUtil.IsValid (adbl))
throw new java.lang.Exception ("MatrixUtil::Modulus => Invalid Inputs");

double dblModulus = 0.;
int iSize = adbl.length;

if (0 == iSize) throw new java.lang.Exception ("MatrixUtil::Modulus => Invalid Inputs");

for (int i = 0; i < iSize; ++i)
dblModulus += adbl[i] * adbl[i];
if (null == v || 0 == v.length || !NumberUtil.IsValid (v)) {
throw new Exception ("MatrixUtil::Modulus => Invalid Inputs");
}

return java.lang.Math.sqrt (dblModulus);
return ModulusInternal (v);
}

/**
Expand Down Expand Up @@ -1019,58 +1039,39 @@ public static final double[] Normalize (
/**
* Orthogonalize the Specified Matrix Using the Graham-Schmidt Method
*
* @param aadblV The Input Matrix
* @param v The Input Matrix
*
* @return The Orthogonalized Matrix
*/

public static final double[][] GrahamSchmidtOrthogonalization (
final double[][] aadblV)
final double[][] v)
{
if (null == aadblV) return null;
if (null == v || 0 == v.length || v.length != v[0].length) {
return null;
}

int iSize = aadblV.length;
double[][] aadblU = new double[iSize][iSize];
double[][] vTranspose = Transpose (v);

if (0 == iSize || null == aadblV[0] || iSize != aadblV[0].length) return null;
double[][] u = new double[vTranspose.length][vTranspose.length];

for (int i = 0; i < iSize; ++i) {
for (int j = 0; j < iSize; ++j)
aadblU[i][j] = aadblV[i][j];
for (int i = 0; i < vTranspose.length; ++i) {
for (int j = 0; j < vTranspose.length; ++j) {
u[i][j] = vTranspose[i][j];
}
}

for (int i = 1; i < vTranspose.length; ++i) {
for (int j = 0; j < i; ++j) {
double dblProjectionAmplitude = java.lang.Double.NaN;
double[] projectionTrimOff = ProjectVOnUInternal (u[j], vTranspose[i]);

try {
dblProjectionAmplitude = DotProduct (aadblV[i], aadblU[j]) / DotProduct (aadblU[j],
aadblU[j]);
} catch (java.lang.Exception e) {
e.printStackTrace();

return null;
for (int k = 0; k < projectionTrimOff.length; ++k) {
u[i][k] -= projectionTrimOff[k];
}

for (int k = 0; k < iSize; ++k)
aadblU[i][k] -= dblProjectionAmplitude * aadblU[j][k];
}
}

return aadblU;
}

private static final double[] ProjectVOnUInternal (
final double[] u,
final double[] v)
{
double vDotUOverUDotU = DotProductInternal (u, v) / DotProductInternal (u, u);

double[] projectVOnU = new double[u.length];

for (int i = 0; i < u.length; ++i) {
projectVOnU[i] = vDotUOverUDotU * u[i];
}

return projectVOnU;
return u;
}

/**
Expand All @@ -1084,30 +1085,17 @@ private static final double[] ProjectVOnUInternal (
public static final double[][] GrahamSchmidtOrthonormalization (
final double[][] v)
{
if (null == v || 0 == v.length || v.length != v[0].length) {
return null;
}

double[] uDotProduct = new double[v.length];
double[][] u = new double[v.length][v.length];

for (int i = 0; i < v.length; ++i) {
uDotProduct[0] += u[0][i] * u[0][i];
}
double[][] u = GrahamSchmidtOrthogonalization (v);

for (int i = 0; i < v.length; ++i) {
for (int j = 0; j < v.length; ++j) {
u[i][j] = v[i][j];
}
if (null == u) {
return null;
}

for (int i = 1; i < v.length; ++i) {
for (int j = 0; j < i; ++j) {
double[] projectionTrimOff = ProjectVOnUInternal (u[j], v[i]);
for (int i = 0; i < u.length; ++i) {
double modulusReciprocal = 1. / ModulusInternal (u[i]);

for (int k = 0; k < projectionTrimOff.length; ++k) {
u[i][j] -= projectionTrimOff[k];
}
for (int j = 0; j < u.length; ++j) {
u[i][j] *= modulusReciprocal;
}
}

Expand All @@ -1117,37 +1105,19 @@ public static final double[][] GrahamSchmidtOrthonormalization (
/**
* Perform a QR Decomposition on the Input Matrix
*
* @param aadblA The Input Matrix
* @param a The Input Matrix
*
* @return The Output of QR Decomposition
*/

public static final org.drip.numerical.linearalgebra.QR QRDecomposition (
final double[][] aadblA)
public static final QR QRDecomposition (
final double[][] a)
{
double[][] aadblQ = GrahamSchmidtOrthonormalization (aadblA);

if (null == aadblQ) return null;

for (int i = 0; i < aadblQ.length; ++i) {
System.out.println (
"\t| Matrix GSOQ => [" + NumberUtil.ArrayRow (aadblQ[i], 2, 4, false) + " ]||"
);
}

int iSize = aadblQ.length;
double[][] aadblR = new double[iSize][iSize];
double[][] q = GrahamSchmidtOrthonormalization (a);

try {
/* for (int i = 0; i < iSize; ++i) {
for (int j = 0; j < iSize; ++j)
aadblR[i][j] = i > j ? DotProduct (aadblQ[i], aadblA[j]) : 0.;
} */

aadblR = Product (Transpose (aadblQ), aadblA);

return new org.drip.numerical.linearalgebra.QR (aadblQ, aadblR);
} catch (java.lang.Exception e) {
return null == q ? null : new QR (q, Product (q, a));
} catch (Exception e) {
e.printStackTrace();
}

Expand Down
27 changes: 27 additions & 0 deletions src/main/java/org/drip/sample/matrix/GrahamSchmidtProcess.java
View file
Original file line number Diff line number Diff line change
Expand Up @@ -123,6 +123,12 @@ public static final void main (
{7, 0, 4, 5}
}; */

/* double[][] aadblV = new double[][] {
{ 12, 6, -4},
{-51, 167, 24},
{ 4, -68, -41}
}; */

double[][] aadblV = new double[][] {
{12, -51, 4},
{ 6, 167, -68},
Expand Down Expand Up @@ -165,6 +171,27 @@ public static final void main (
)
);

System.out.println();

double[][] uvTranspose = MatrixUtil.Product (aadblUOrthonormal, aadblV);

NumberUtil.PrintMatrix (
"R CHECK #1.1",
uvTranspose
);

System.out.println();

NumberUtil.PrintMatrix (
"R CHECK #1.2",
MatrixUtil.Product (MatrixUtil.Transpose (aadblUOrthonormal), uvTranspose)
);

/* NumberUtil.PrintMatrix (
"R CHECK #2",
MatrixUtil.Product (aadblV, MatrixUtil.Transpose (aadblUOrthonormal))
); */

EnvManager.TerminateEnv();
}
}

0 comments on commit ad64618

Please sign in to comment.