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gml_ElMat2.h Go to the documentation of this file. /** @file gml_ElMat2.h * * Basic operations on row-major 2x2 matrices and 2x1 vectors. * * Copyright (c) 1997-2004 The CLIPS-IMAG Laboratory * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * Created in March, 1997 (FB). * Updated to GML in February, 2004 (JL). */ #ifndef __GML_ELMAT2__ #define __GML_ELMAT2__ // system includes #include <math.h> // project includes #include "gml/base/gml_Errors.h" /// gml_EM2_Invert -- /// /// Invert the <source> matrix in <dest>. /// <source> and <dest> may be indentical. /// Return an error if <source> is not invertible. template <class T> inline static gml_TError gml_EM2_Invert (T* source, T* dest); /// gml_EM2_Det -- /// /// Return the determinant of <source> template <class T> inline static T gml_EM2_Det (T* source); /// gml_EM2_AddMat -- /// /// Add the two matrix <a> and <b> and put the result in <dest> /// <dest> may be <a> or <b> template <class T> inline static void gml_EM2_AddMat (T* a, T* b, T* dest); /// gml_EM2_AddVect -- /// /// Add the two vectors <a> and <b> and put the result in <dest> /// <dest> may be <a> or <b> template <class T> inline static void gml_EM2_AddVect (T* a, T* b, T* dest); /// gml_EM2_MultVect -- /// /// Multiply matrix <a> anv vector <b> and put the result in <dest> /// <dest> may be <a> or <b>. template <class T> inline static void gml_EM2_MultVect (T* a, T* b, T* dest); /// gml_EM2_EigenStuff -- /// /// Return in <e> the eigenvalues of matrix <a>. Largest value goes in /// first position. The corresponding eigenvectors are returned in /// <v>. <v> contains 2 values: v[0] is the 2nd component of eigenvector /// corresponding to eigenvalue e[0] (its first component is choosen as 1) /// v[1] corresponds to e[1]. template <class T> inline static gml_TError gml_EM2_EigenStuff (T* a, T* e, T* v); /// gml_EM2_EigenVal -- /// /// Return in <e> the eigenvalues of matrix <a>. Largest value goes in /// first position. template <class T> inline static gml_TError gml_EM2_EigenVal (T* a, T* e); /// gml_EM2_EigenVect -- /// /// Return in <v> the eigenvectors of matrix <a>. <v> contains 2 values: /// v[0] is the 2nd component of eigenvector corresponding to the largest /// eigenvalue (its first component is choosen as 1) /// v[1] corresponds to the smallest eigenvalue template <class T> inline static gml_TError gml_EM2_EigenVect (T* a, T* v); // Implementation follows. //////////////////////////////////////////////////////////////////////////////// // // gml_EM2_Invert // template <class T> inline static gml_TError gml_EM2_Invert (T* source, T* dest) { // gml_EM2Init (); T a = source[0]; T b = source[2]; T c = source[1]; T d = source[3]; T det = gml_EM2_Det (source); T invdet; if (det == 0) { return gml_gDivideByZero; } invdet = 1/det; dest[0] = d * invdet; dest[1] = -c * invdet; dest[2] = -b * invdet; dest[3] = a * invdet; return gml_cNoError; } // // gml_EM2_Det // template <class T> inline static T gml_EM2_Det (T* source) { T a = source[0]; T b = source[2]; T c = source[1]; T d = source[3]; return a*d - b*c; } // // gml_EM2_AddMat // template <class T> inline static void gml_EM2_AddMat (T* a, T* b, T* dest) { dest[0] = a[0]+b[0]; dest[1] = a[1]+b[1]; dest[2] = a[2]+b[2]; dest[3] = a[3]+b[3]; } // // gml_EM2_AddVect // template <class T> inline static void gml_EM2_AddVect (T* a, T* b, T* dest) { dest[0] = a[0]+b[0]; dest[1] = a[1]+b[1]; } // // gml_EM2_MultVect // template <class T> inline static void gml_EM2_MultVect (T* a, T* b, T* dest) { T tmp = b[0]; dest[0] = a[0]*tmp + a[2]*b[1]; dest[1] = a[1]*tmp + a[3]*b[1]; } // // gml_EM2_EigenStuff // template <class T> inline static gml_TError gml_EM2_EigenStuff (T* a, T* e, T* v) { if (gml_EM2_EigenVal (a, e) != gml_cNoError) return gml_gDivideByZero; v[0] = - (a[0] - e[0]) / a[1]; v[1] = - (a[0] - e[1]) / a[1]; return gml_cNoError; } // // gml_EM2_EigenVal // template <class T> inline static gml_TError gml_EM2_EigenVal (T* a, T* e) { T ad, bc, apd, sq, del, l1, l2; assert (a[1] == a[2]); ad = apd = a[0]; bc = a[1]; bc *= bc; ad *= a[3]; apd += a[3]; del = apd*apd - 4*(ad - bc); if (del < 0) return gml_gDivideByZero; sq = Sqrt (del); l1 = (apd + sq) / 2; l2 = (apd - sq) / 2; // l1 should be always greater (or equal) to l2 e[0] = l1; e[1] = l2; return gml_cNoError; } // // gml_EM2_EigenVect // template <class T> inline static gml_TError gml_EM2_EigenVect (T* a, T* v) { T e[2]; return gml_EM2_EigenStuff (a, e, v); } #endif /* __GML_ELMAT2__ */ Generated on Tue Jun 12 14:03:27 2007 for gml by Doxygen 1.5.2.

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