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gauss elimination for vecmat3

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Jiri Pittner
2021-11-21 00:08:09 +01:00
parent 30f4d29d82
commit 0b3a6c5473
3 changed files with 117 additions and 3 deletions
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68
vecmat3.h
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@@ -1,6 +1,6 @@
/*
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
it under the terms of the GNU General Public License as published by
@@ -46,6 +46,9 @@ class Vec3
public:
//just plain old data
T q[3];
T (&elements())[3] {return q;};
const T (&elements()const)[3] {return q;};
//
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)
@@ -98,6 +101,8 @@ public:
//just plain old data
T q[3][3];
//
T (&elements())[3][3] {return q;};
const T (&elements()const)[3][3] {return q;};
Mat3(void) {};
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
@@ -148,9 +153,70 @@ public:
void symmetrize(); //average offdiagonal elements
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
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
#ifndef AVOID_STDSTREAM