gauss elimination for vecmat3

This commit is contained in:
Jiri Pittner 2021-11-21 00:08:09 +01:00
parent 30f4d29d82
commit 0b3a6c5473
3 changed files with 117 additions and 3 deletions

37
t.cc
View File

@ -2321,7 +2321,7 @@ Polynomial<double> pp({1,2,3,4,5});
cout<<pp; cout<<pp;
} }
if(1) if(0)
{ {
//prepare random symmetric mat3 //prepare random symmetric mat3
int seed; int seed;
@ -2352,4 +2352,39 @@ cout<<"eival error = "<<(w-www).norm()<<endl;
cout<<"eivec error = "<<(m.diffabs(vvv)).norm()<<endl; //just ignore signs due to arb. phases (not full check) cout<<"eivec error = "<<(m.diffabs(vvv)).norm()<<endl; //just ignore signs due to arb. phases (not full check)
} }
if(1)
{
//prepare random mat3
int seed;
int f=open("/dev/random",O_RDONLY);
if(sizeof(int)!=read(f,&seed,sizeof(int))) laerror("cannot read /dev/random");
close(f);
srand(seed);
NRMat<double> tmp(3,3);
tmp.randomize(2.);
Mat3<double> mm(tmp);
NRMat<double> m(&mm[0][0],3,3);
cout <<m<<"3 3\n"<<mm<<endl;
double rr[2][3]={{1,2,3},{4,5,6}};
NRMat r(rr);
cout<<r;
double d;
linear_solve(m,&r,&d);
Mat3<double> mmi=mm.inverse();
double dd=simple_gaussj(mm.elements(),rr);
cout <<"det="<<dd<<endl;
cout <<"error of inverse = "<<(mmi-mm).norm()<<endl;
cout <<"3 3\n"<<mm<<NRMat<double>(rr);
cout<<"linear solve det="<<d<<endl;
cout <<r;
cout <<"det error="<<d-dd<<endl;
cout <<"solution error="<<(r-rr).norm()<<endl;
}
} }

View File

@ -522,7 +522,7 @@ q[2][1]=q[1][2]=tmp;
// //
//numeric_limits not available on some crosscompilers for small MCUs //numeric_limits not available on some crosscompilers for small MCUs
#ifdef ARM_SOURCE37 #ifdef QUAT_NO_DOUBLE
#define DBL_EPSILON 1.19209290e-07f #define DBL_EPSILON 1.19209290e-07f
#else #else
#define DBL_EPSILON std::numeric_limits<T>::epsilon() #define DBL_EPSILON std::numeric_limits<T>::epsilon()
@ -785,6 +785,19 @@ Mat3<T> A(*this); //scratch copy
//end eigensolver for 3x3 matrix //end eigensolver for 3x3 matrix
///////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////////
template<typename T>
T Mat3<T>::norm(const T scalar) const
{
T sum(0);
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) {
T tmp = q[i][j];
if(i == j) tmp -= scalar;
sum += tmp*tmp;
}
return sqrt(sum);
}
//force instantization //force instantization
#define INSTANTIZE(T) \ #define INSTANTIZE(T) \
template class Vec3<T>; \ template class Vec3<T>; \

View File

@ -1,6 +1,6 @@
/* /*
LA: linear algebra C++ interface library LA: linear algebra C++ interface library
Copyright (C) 2020 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com> Copyright (C) 2020-2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
This program is free software: you can redistribute it and/or modify This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by it under the terms of the GNU General Public License as published by
@ -46,6 +46,9 @@ class Vec3
public: public:
//just plain old data //just plain old data
T q[3]; T q[3];
T (&elements())[3] {return q;};
const T (&elements()const)[3] {return q;};
// //
Vec3(void) {}; Vec3(void) {};
Vec3(const T x, const T u=0, const T v=0) {q[0]=x; q[1]=u; q[2]=v;}; //Vec3 from real(s) Vec3(const T x, const T u=0, const T v=0) {q[0]=x; q[1]=u; q[2]=v;}; //Vec3 from real(s)
@ -98,6 +101,8 @@ public:
//just plain old data //just plain old data
T q[3][3]; T q[3][3];
// //
T (&elements())[3][3] {return q;};
const T (&elements()const)[3][3] {return q;};
Mat3(void) {}; Mat3(void) {};
Mat3(const T (&a)[3][3]) {memcpy(q,a,3*3*sizeof(T));} Mat3(const T (&a)[3][3]) {memcpy(q,a,3*3*sizeof(T));}
Mat3(const T x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x;}; //scalar matrix Mat3(const T x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x;}; //scalar matrix
@ -148,9 +153,70 @@ public:
void symmetrize(); //average offdiagonal elements void symmetrize(); //average offdiagonal elements
void eival_sym(Vec3<T> &w) const; //only for real symmetric matrix, symmetry is not checked void eival_sym(Vec3<T> &w) const; //only for real symmetric matrix, symmetry is not checked
void eivec_sym(Vec3<T> &w, Mat3 &v) const; //only for real symmetric matrix, symmetry is not checked void eivec_sym(Vec3<T> &w, Mat3 &v) const; //only for real symmetric matrix, symmetry is not checked
T norm(const T scalar = 0) const;
}; };
//a simple gauss elimination as a template also for larger-size matrices in form of C-style arrays
#define SWAP(a,b) {T temp=(a);(a)=(b);(b)=temp;}
template<typename T, int n, int m>
T simple_gaussj(T (&a)[n][n],T (&b)[m][n]) //returns determinant, m is number of rhs to solve
{
int indxc[n],indxr[n],ipiv[n];
int i,icol,irow,j,k,l,ll;
T det,big,dum,pivinv;
det=1;
for (j=0;j<n;j++) ipiv[j]=0;
for (i=0;i<n;i++) {
big=0.0;
for (j=0;j<n;j++)
if (ipiv[j] != 1)
for (k=0;k<n;k++) {
if (ipiv[k] == 0) {
if (abs(a[j][k]) >= big) {
big=abs(a[j][k]);
irow=j;
icol=k;
}
} else if (ipiv[k] > 1) {return 0;}
}
++(ipiv[icol]);
if (irow != icol) {
det = (-det);
for (l=0;l<n;l++) SWAP(a[irow][l],a[icol][l])
for (l=0;l<m;l++) SWAP(b[l][irow],b[l][icol])
}
indxr[i]=irow;
indxc[i]=icol;
if (a[icol][icol] == 0) {return 0;}
pivinv=1/a[icol][icol];
det *= a[icol][icol];
a[icol][icol]=1.0;
for (l=0;l<n;l++) a[icol][l] *= pivinv;
for (l=0;l<m;l++) b[l][icol] *= pivinv;
for (ll=0;ll<n;ll++)
if (ll != icol) {
dum=a[ll][icol];
a[ll][icol]=0.0;
for (l=0;l<n;l++) a[ll][l] -= a[icol][l]*dum;
for (l=0;l<m;l++) b[l][ll] -= b[l][icol]*dum;
}
}
for (l=n-1;l>=0;l--) {
if (indxr[l] != indxc[l])
for (k=0;k<n;k++)
SWAP(a[k][indxr[l]],a[k][indxc[l]]);
}
return det;
}
#undef SWAP
//stream I/O //stream I/O
#ifndef AVOID_STDSTREAM #ifndef AVOID_STDSTREAM