@@ -128,6 +128,33 @@ private static final double DotProductInternal (
128128 return dotProductInternal ;
129129 }
130130
131+ private static final double [] ProjectVOnUInternal (
132+ final double [] u ,
133+ final double [] v )
134+ {
135+ double vDotUOverUDotU = DotProductInternal (u , v ) / DotProductInternal (u , u );
136+
137+ double [] projectVOnU = new double [u .length ];
138+
139+ for (int i = 0 ; i < u .length ; ++i ) {
140+ projectVOnU [i ] = vDotUOverUDotU * u [i ];
141+ }
142+
143+ return projectVOnU ;
144+ }
145+
146+ private static final double ModulusInternal (
147+ final double [] v )
148+ {
149+ double modulus = 0. ;
150+
151+ for (int i = 0 ; i < v .length ; ++i ) {
152+ modulus += v [i ] * v [i ];
153+ }
154+
155+ return Math .sqrt (modulus );
156+ }
157+
131158 /**
132159 * Indicate if the Cell corresponds to Bottom Left Location in the Matrix
133160 *
@@ -888,29 +915,22 @@ public static final double Sum (
888915 /**
889916 * Compute the Modulus of the Input Vector
890917 *
891- * @param adbl The Input Vector
918+ * @param v The Input Vector
892919 *
893- * @return TRUE - The Modulus of the Input Vector
920+ * @return The Modulus of the Input Vector
894921 *
895- * @throws java.lang. Exception Thrown if the Inputs are Invalid
922+ * @throws Exception Thrown if the Inputs are Invalid
896923 */
897924
898925 public static final double Modulus (
899- final double [] adbl )
900- throws java . lang . Exception
926+ final double [] v )
927+ throws Exception
901928 {
902- if (null == adbl || !org .drip .numerical .common .NumberUtil .IsValid (adbl ))
903- throw new java .lang .Exception ("MatrixUtil::Modulus => Invalid Inputs" );
904-
905- double dblModulus = 0. ;
906- int iSize = adbl .length ;
907-
908- if (0 == iSize ) throw new java .lang .Exception ("MatrixUtil::Modulus => Invalid Inputs" );
909-
910- for (int i = 0 ; i < iSize ; ++i )
911- dblModulus += adbl [i ] * adbl [i ];
929+ if (null == v || 0 == v .length || !NumberUtil .IsValid (v )) {
930+ throw new Exception ("MatrixUtil::Modulus => Invalid Inputs" );
931+ }
912932
913- return java . lang . Math . sqrt ( dblModulus );
933+ return ModulusInternal ( v );
914934 }
915935
916936 /**
@@ -1019,58 +1039,39 @@ public static final double[] Normalize (
10191039 /**
10201040 * Orthogonalize the Specified Matrix Using the Graham-Schmidt Method
10211041 *
1022- * @param aadblV The Input Matrix
1042+ * @param v The Input Matrix
10231043 *
10241044 * @return The Orthogonalized Matrix
10251045 */
10261046
10271047 public static final double [][] GrahamSchmidtOrthogonalization (
1028- final double [][] aadblV )
1048+ final double [][] v )
10291049 {
1030- if (null == aadblV ) return null ;
1050+ if (null == v || 0 == v .length || v .length != v [0 ].length ) {
1051+ return null ;
1052+ }
10311053
1032- int iSize = aadblV .length ;
1033- double [][] aadblU = new double [iSize ][iSize ];
1054+ double [][] vTranspose = Transpose (v );
10341055
1035- if ( 0 == iSize || null == aadblV [ 0 ] || iSize != aadblV [ 0 ] .length ) return null ;
1056+ double [][] u = new double [ vTranspose . length ][ vTranspose .length ] ;
10361057
1037- for (int i = 0 ; i < iSize ; ++i ) {
1038- for (int j = 0 ; j < iSize ; ++j )
1039- aadblU [i ][j ] = aadblV [i ][j ];
1058+ for (int i = 0 ; i < vTranspose .length ; ++i ) {
1059+ for (int j = 0 ; j < vTranspose .length ; ++j ) {
1060+ u [i ][j ] = vTranspose [i ][j ];
1061+ }
1062+ }
10401063
1064+ for (int i = 1 ; i < vTranspose .length ; ++i ) {
10411065 for (int j = 0 ; j < i ; ++j ) {
1042- double dblProjectionAmplitude = java . lang . Double . NaN ;
1066+ double [] projectionTrimOff = ProjectVOnUInternal ( u [ j ], vTranspose [ i ]) ;
10431067
1044- try {
1045- dblProjectionAmplitude = DotProduct (aadblV [i ], aadblU [j ]) / DotProduct (aadblU [j ],
1046- aadblU [j ]);
1047- } catch (java .lang .Exception e ) {
1048- e .printStackTrace ();
1049-
1050- return null ;
1068+ for (int k = 0 ; k < projectionTrimOff .length ; ++k ) {
1069+ u [i ][k ] -= projectionTrimOff [k ];
10511070 }
1052-
1053- for (int k = 0 ; k < iSize ; ++k )
1054- aadblU [i ][k ] -= dblProjectionAmplitude * aadblU [j ][k ];
10551071 }
10561072 }
10571073
1058- return aadblU ;
1059- }
1060-
1061- private static final double [] ProjectVOnUInternal (
1062- final double [] u ,
1063- final double [] v )
1064- {
1065- double vDotUOverUDotU = DotProductInternal (u , v ) / DotProductInternal (u , u );
1066-
1067- double [] projectVOnU = new double [u .length ];
1068-
1069- for (int i = 0 ; i < u .length ; ++i ) {
1070- projectVOnU [i ] = vDotUOverUDotU * u [i ];
1071- }
1072-
1073- return projectVOnU ;
1074+ return u ;
10741075 }
10751076
10761077 /**
@@ -1084,30 +1085,17 @@ private static final double[] ProjectVOnUInternal (
10841085 public static final double [][] GrahamSchmidtOrthonormalization (
10851086 final double [][] v )
10861087 {
1087- if (null == v || 0 == v .length || v .length != v [0 ].length ) {
1088- return null ;
1089- }
1090-
1091- double [] uDotProduct = new double [v .length ];
1092- double [][] u = new double [v .length ][v .length ];
1093-
1094- for (int i = 0 ; i < v .length ; ++i ) {
1095- uDotProduct [0 ] += u [0 ][i ] * u [0 ][i ];
1096- }
1088+ double [][] u = GrahamSchmidtOrthogonalization (v );
10971089
1098- for (int i = 0 ; i < v .length ; ++i ) {
1099- for (int j = 0 ; j < v .length ; ++j ) {
1100- u [i ][j ] = v [i ][j ];
1101- }
1090+ if (null == u ) {
1091+ return null ;
11021092 }
11031093
1104- for (int i = 1 ; i < v .length ; ++i ) {
1105- for (int j = 0 ; j < i ; ++j ) {
1106- double [] projectionTrimOff = ProjectVOnUInternal (u [j ], v [i ]);
1094+ for (int i = 0 ; i < u .length ; ++i ) {
1095+ double modulusReciprocal = 1. / ModulusInternal (u [i ]);
11071096
1108- for (int k = 0 ; k < projectionTrimOff .length ; ++k ) {
1109- u [i ][j ] -= projectionTrimOff [k ];
1110- }
1097+ for (int j = 0 ; j < u .length ; ++j ) {
1098+ u [i ][j ] *= modulusReciprocal ;
11111099 }
11121100 }
11131101
@@ -1117,37 +1105,19 @@ public static final double[][] GrahamSchmidtOrthonormalization (
11171105 /**
11181106 * Perform a QR Decomposition on the Input Matrix
11191107 *
1120- * @param aadblA The Input Matrix
1108+ * @param a The Input Matrix
11211109 *
11221110 * @return The Output of QR Decomposition
11231111 */
11241112
1125- public static final org . drip . numerical . linearalgebra . QR QRDecomposition (
1126- final double [][] aadblA )
1113+ public static final QR QRDecomposition (
1114+ final double [][] a )
11271115 {
1128- double [][] aadblQ = GrahamSchmidtOrthonormalization (aadblA );
1129-
1130- if (null == aadblQ ) return null ;
1131-
1132- for (int i = 0 ; i < aadblQ .length ; ++i ) {
1133- System .out .println (
1134- "\t | Matrix GSOQ => [" + NumberUtil .ArrayRow (aadblQ [i ], 2 , 4 , false ) + " ]||"
1135- );
1136- }
1137-
1138- int iSize = aadblQ .length ;
1139- double [][] aadblR = new double [iSize ][iSize ];
1116+ double [][] q = GrahamSchmidtOrthonormalization (a );
11401117
11411118 try {
1142- /* for (int i = 0; i < iSize; ++i) {
1143- for (int j = 0; j < iSize; ++j)
1144- aadblR[i][j] = i > j ? DotProduct (aadblQ[i], aadblA[j]) : 0.;
1145- } */
1146-
1147- aadblR = Product (Transpose (aadblQ ), aadblA );
1148-
1149- return new org .drip .numerical .linearalgebra .QR (aadblQ , aadblR );
1150- } catch (java .lang .Exception e ) {
1119+ return null == q ? null : new QR (q , Product (q , a ));
1120+ } catch (Exception e ) {
11511121 e .printStackTrace ();
11521122 }
11531123
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