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geant4/source/analysis/g4tools/include/tools/lina/mat4
T
Gabriele Cosmo fc6af9e721 Import Geant4 10.4.0 source tree
2017-12-08 12:52:30 +01:00

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// Copyright (C) 2010, Guy Barrand. All rights reserved.
// See the file tools.license for terms.
#ifndef tools_mat4
#define tools_mat4
#include "mat"
//#include <cmath>
namespace tools {
template <class T>
class mat4 : public mat<T,4> {
typedef mat<T,4> parent;
typedef mat<T,4> pr;
public:
#ifdef TOOLS_MEM
mat4(bool a_inc = true):parent(a_inc) {}
#else
mat4():parent() {}
#endif
mat4(const mat<T,4>& a_from):parent(a_from){}
virtual ~mat4() {}
public:
mat4(const mat4& a_from):parent(a_from){}
mat4& operator=(const mat4& a_from){
parent::operator=(a_from);
return *this;
}
public:
mat4(const T& a_00,const T& a_01,const T& a_02,const T& a_03, //first row
const T& a_10,const T& a_11,const T& a_12,const T& a_13, //second row
const T& a_20,const T& a_21,const T& a_22,const T& a_23, //third row
const T& a_30,const T& a_31,const T& a_32,const T& a_33) //fourth row
{
set_matrix(a_00,a_01,a_02,a_03,
a_10,a_11,a_12,a_13,
a_20,a_21,a_22,a_23,
a_30,a_31,a_32,a_33);
}
public:
void set_matrix(const mat4<T>& a_m){
parent::set_matrix(a_m);
}
void set_matrix(
const T& a_00,const T& a_01,const T& a_02,const T& a_03, //1 row
const T& a_10,const T& a_11,const T& a_12,const T& a_13, //2 row
const T& a_20,const T& a_21,const T& a_22,const T& a_23, //3 row
const T& a_30,const T& a_31,const T& a_32,const T& a_33) //4 row
{
//a_<R><C>
//pr::m_vec[R + C * 4];
pr::m_vec[0] = a_00;pr::m_vec[4] = a_01;pr::m_vec[ 8] = a_02;pr::m_vec[12] = a_03;
pr::m_vec[1] = a_10;pr::m_vec[5] = a_11;pr::m_vec[ 9] = a_12;pr::m_vec[13] = a_13;
pr::m_vec[2] = a_20;pr::m_vec[6] = a_21;pr::m_vec[10] = a_22;pr::m_vec[14] = a_23;
pr::m_vec[3] = a_30;pr::m_vec[7] = a_31;pr::m_vec[11] = a_32;pr::m_vec[15] = a_33;
}
void set_scale(const T& a_s) {
_set_scale(a_s,a_s,a_s,pr::m_vec);
}
void set_scale(const T& a_1,const T& a_2,const T& a_3) {
_set_scale(a_1,a_2,a_3,pr::m_vec);
}
void set_translate(const T& a_x,const T& a_y,const T& a_z) {
_set_translate(a_x,a_y,a_z,pr::m_vec);
}
void set_rotate(const T& a_x,const T& a_y,const T& a_z,const T& a_angle,T(*a_sin)(T),T(*a_cos)(T)) {
_set_rotate(a_x,a_y,a_z,a_angle,pr::m_vec,a_sin,a_cos);
}
void set_ortho(const T& a_l,const T& a_r, //left,right
const T& a_b,const T& a_t, //bottom,top
const T& a_n,const T& a_f) { //znear,zfar
// from man glOrtho.
T tx = -(a_r+a_l)/(a_r-a_l);
T ty = -(a_t+a_b)/(a_t-a_b);
T tz = -(a_f+a_n)/(a_f-a_n);
T a_00,a_01,a_02,a_03;
T a_10,a_11,a_12,a_13;
T a_20,a_21,a_22,a_23;
T a_30,a_31,a_32,a_33;
a_00 = 2/(a_r-a_l);a_01 = 0;a_02 = 0;a_03 = tx;
a_10 = 0;a_11 = 2/(a_t-a_b);a_12 = 0;a_13 = ty;
a_20 = 0;a_21 = 0;a_22 = -2/(a_f-a_n);a_23 = tz;
a_30 = 0;a_31 = 0;a_32 = 0;a_33 = 1;
set_matrix(a_00,a_01,a_02,a_03, //1 row
a_10,a_11,a_12,a_13, //2 row
a_20,a_21,a_22,a_23, //3 row
a_30,a_31,a_32,a_33); //4 row
//NOTE : Z(x,y, z,1) = -2z/(f-n)+tz = [-2z-f-n]/(f-n)
// W(x,y, z,1) = 1 -> Z/W = Z
// Z(x,y,-n,1) = -1
// Z(x,y,-f,1) = 1
// Z(x,y,-(f+n)/2,1) = 0
// X(x,0, z,1) = 2x/(r-l)+tx = [2x-r-l]/(r-l)
// X(r,0, z,1) = 1
// the view direction is then (0,0,1) in the final projection.
}
void set_frustum(const T& a_l,const T& a_r, //left,right
const T& a_b,const T& a_t, //bottom,top
const T& a_n,const T& a_f) { //znear,zfar
// from man glFrustum.
T A = (a_r+a_l)/(a_r-a_l);
T B = (a_t+a_b)/(a_t-a_b);
T C = -(a_f+a_n)/(a_f-a_n);
T D = -(2*a_f*a_n)/(a_f-a_n);
T a_00,a_01,a_02,a_03;
T a_10,a_11,a_12,a_13;
T a_20,a_21,a_22,a_23;
T a_30,a_31,a_32,a_33;
a_00 = (2*a_n)/(a_r-a_l);a_01 = 0;a_02 = A;a_03 = 0;
a_10 = 0;a_11 = (2*a_n)/(a_t-a_b);a_12 = B;a_13 = 0;
a_20 = 0;a_21 = 0;a_22 = C;a_23 = D;
a_30 = 0;a_31 = 0;a_32 = -1;a_33 = 0;
set_matrix(a_00,a_01,a_02,a_03, //1 row
a_10,a_11,a_12,a_13, //2 row
a_20,a_21,a_22,a_23, //3 row
a_30,a_31,a_32,a_33); //4 row
//NOTE : Z(x,y, z,1) = C*z+D = -[(f+n)*z+2*f*n]/(f-n)
// Z(x,y,-n,1) = -[-fn-nn+2fn]/(f-n) = -[fn-nn]/(f-n) = -n
// W(x,y,-n,1) = n
// -> Z/W(x,y,-n,1) = -1
// Z(x,y,-2fn/(f+n),1) = 0
// -> Z/W = 0
// Z(x,y,-f,1) = -[-ff-fn+2fn]/(f-n) = -[fn-ff]/(f-n) = f
// W(x,y,-f,1) = f
// -> Z/W(x,y,-f,1) = 1
// X(x,0, z,1) = 2nx/(r-l)+z(r+l)/(r-l) = [2nx+zr+zl]/(r-l)
// X(r,0,-n,1) = [nr-nl]/(r-l) = n
// W(r,0,-n,1) = n
// -> X/W(r,0,-n,1) = 1
// X(l,0,-n,1) = (2nl-n(r+l))/(r-l) = -n
// W(l,0,-n,1) = n
// -> X/W(l,0,-n,1) = -1
// lrbt corners are in plane z=-1 at xy=+/-1.
// eye ?
// eye before ? (0,0,z,1) -> (zA,zB,zC+D,-z) /W -> (-A,-B,-(C+D/z),1)
// z=0 -> (0,0,D=-2fn(f-n),0)
}
void get_translate(T& a_x,T& a_y,T& a_z) const {
a_x = pr::m_vec[12];
a_y = pr::m_vec[13];
a_z = pr::m_vec[14];
}
//void set_translate_only(const T& a_x,const T& a_y,const T& a_z) {
// pr::m_vec[12] = a_x;
// pr::m_vec[13] = a_y;
// pr::m_vec[14] = a_z;
//}
public:
void mul_4(T& a_x,T& a_y,T& a_z,T& a_p) const {
// a_[x,y,z,p] = this * a_[x,y,z,p]
//pr::m_vec[R + C * 4];
//pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m_vec[ 8] = 02;pr::m_vec[12] = 03;
//pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m_vec[ 9] = 12;pr::m_vec[13] = 13;
//pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m_vec[10] = 22;pr::m_vec[14] = 23;
//pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m_vec[11] = 32;pr::m_vec[15] = 33;
T x= pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr::m_vec[ 8]*a_z+pr::m_vec[12]*a_p;
T y= pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr::m_vec[ 9]*a_z+pr::m_vec[13]*a_p;
T z= pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr::m_vec[10]*a_z+pr::m_vec[14]*a_p;
T p= pr::m_vec[3]*a_x+pr::m_vec[7]*a_y+pr::m_vec[11]*a_z+pr::m_vec[15]*a_p;
a_x = x;
a_y = y;
a_z = z;
a_p = p;
}
void mul_3(T& a_x,T& a_y,T& a_z) const {
// a_[x,y,z] = this * a_[x,y,z]
//pr::m_vec[R + C * 4];
//pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m_vec[ 8] = 02;pr::m_vec[12] = 03;
//pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m_vec[ 9] = 12;pr::m_vec[13] = 13;
//pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m_vec[10] = 22;pr::m_vec[14] = 23;
//pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m_vec[11] = 32;pr::m_vec[15] = 33;
T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr::m_vec[ 8]*a_z+pr::m_vec[12];
T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr::m_vec[ 9]*a_z+pr::m_vec[13];
T z = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr::m_vec[10]*a_z+pr::m_vec[14];
a_x = x;
a_y = y;
a_z = z;
}
void mul_2(T& a_x,T& a_y) const {
// a_[x,y] = this * a_[x,y]
//pr::m_vec[R + C * 4];
//pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m_vec[ 8] = 02;pr::m_vec[12] = 03;
//pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m_vec[ 9] = 12;pr::m_vec[13] = 13;
//pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m_vec[10] = 22;pr::m_vec[14] = 23;
//pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m_vec[11] = 32;pr::m_vec[15] = 33;
T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr::m_vec[12];
T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr::m_vec[13];
a_x = x;
a_y = y;
}
void mul_dir_3(T& a_x,T& a_y,T& a_z) const {
// used to multiply normals.
// a_[x,y,z] = rot_part(this) * a_[x,y,z]
T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr::m_vec[ 8]*a_z;
T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr::m_vec[ 9]*a_z;
T z = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr::m_vec[10]*a_z;
a_x = x;
a_y = y;
a_z = z;
}
void mul_trans_3(T& a_x,T& a_y,T& a_z) const {
// used in sg::healpix.
// a_[x,y,z] = trans_part(this) * a_[x,y,z]
a_x += pr::m_vec[12];
a_y += pr::m_vec[13];
a_z += pr::m_vec[14];
}
template <class VEC>
void mul_dir_3(VEC& a_dir) const {
mul_dir_3(a_dir[0],a_dir[1],a_dir[2]);
}
void mul_scale(const T& a_sx,const T& a_sy,const T& a_sz) {
// this = this * mat4_scale(a_s[x,y,z]
//pr::m_vec[R + C * 4];
//pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m_vec[ 8] = 02;pr::m_vec[12] = 03;
//pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m_vec[ 9] = 12;pr::m_vec[13] = 13;
//pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m_vec[10] = 22;pr::m_vec[14] = 23;
//pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m_vec[11] = 32;pr::m_vec[15] = 33;
pr::m_vec[0] *= a_sx;
pr::m_vec[1] *= a_sx;
pr::m_vec[2] *= a_sx;
pr::m_vec[3] *= a_sx;
pr::m_vec[4] *= a_sy;
pr::m_vec[5] *= a_sy;
pr::m_vec[6] *= a_sy;
pr::m_vec[7] *= a_sy;
pr::m_vec[ 8] *= a_sz;
pr::m_vec[ 9] *= a_sz;
pr::m_vec[10] *= a_sz;
pr::m_vec[11] *= a_sz;
}
void mul_scale(const T& a_s) {
pr::m_vec[0] *= a_s;
pr::m_vec[1] *= a_s;
pr::m_vec[2] *= a_s;
pr::m_vec[3] *= a_s;
pr::m_vec[4] *= a_s;
pr::m_vec[5] *= a_s;
pr::m_vec[6] *= a_s;
pr::m_vec[7] *= a_s;
pr::m_vec[ 8] *= a_s;
pr::m_vec[ 9] *= a_s;
pr::m_vec[10] *= a_s;
pr::m_vec[11] *= a_s;
}
void mul_translate(const T& a_x,const T& a_y,const T& a_z) {
pr::m_vec[12] = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr::m_vec[ 8]*a_z+pr::m_vec[12];
pr::m_vec[13] = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr::m_vec[ 9]*a_z+pr::m_vec[13];
pr::m_vec[14] = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr::m_vec[10]*a_z+pr::m_vec[14];
pr::m_vec[15] = pr::m_vec[3]*a_x+pr::m_vec[7]*a_y+pr::m_vec[11]*a_z+pr::m_vec[15];
}
void mul_rotate(const T& a_x,const T& a_y,const T& a_z,const T& a_angle,T(*a_sin)(T),T(*a_cos)(T)) {
T rot[16];
_set_rotate(a_x,a_y,a_z,a_angle,rot,a_sin,a_cos);
parent::_mul_mtx(rot);
}
void left_mul_rotate(const T& a_x,const T& a_y,const T& a_z,const T& a_angle,T(*a_sin)(T),T(*a_cos)(T)) {
T _m[16];
_set_rotate(a_x,a_y,a_z,a_angle,_m,a_sin,a_cos);
parent::_left_mul_mtx(_m);
}
void left_mul_scale(const T& a_x,const T& a_y,const T& a_z) {
T _m[16];
_set_scale(a_x,a_y,a_z,_m);
parent::_left_mul_mtx(_m);
}
void left_mul_translate(const T& a_x,const T& a_y,const T& a_z) {
T _m[16];
_set_translate(a_x,a_y,a_z,_m);
parent::_left_mul_mtx(_m);
}
void v00(const T& a_value){pr::m_vec[0+0*4] = a_value;}
void v10(const T& a_value){pr::m_vec[1+0*4] = a_value;}
void v20(const T& a_value){pr::m_vec[2+0*4] = a_value;}
void v30(const T& a_value){pr::m_vec[3+0*4] = a_value;}
void v01(const T& a_value){pr::m_vec[0+1*4] = a_value;}
void v11(const T& a_value){pr::m_vec[1+1*4] = a_value;}
void v21(const T& a_value){pr::m_vec[2+1*4] = a_value;}
void v31(const T& a_value){pr::m_vec[3+1*4] = a_value;}
void v02(const T& a_value){pr::m_vec[0+2*4] = a_value;}
void v12(const T& a_value){pr::m_vec[1+2*4] = a_value;}
void v22(const T& a_value){pr::m_vec[2+2*4] = a_value;}
void v32(const T& a_value){pr::m_vec[3+2*4] = a_value;}
void v03(const T& a_value){pr::m_vec[0+3*4] = a_value;}
void v13(const T& a_value){pr::m_vec[1+3*4] = a_value;}
void v23(const T& a_value){pr::m_vec[2+3*4] = a_value;}
void v33(const T& a_value){pr::m_vec[3+3*4] = a_value;}
const T& v00() const {return pr::m_vec[0+0*4];}
const T& v10() const {return pr::m_vec[1+0*4];}
const T& v20() const {return pr::m_vec[2+0*4];}
const T& v30() const {return pr::m_vec[3+0*4];}
const T& v01() const {return pr::m_vec[0+1*4];}
const T& v11() const {return pr::m_vec[1+1*4];}
const T& v21() const {return pr::m_vec[2+1*4];}
const T& v31() const {return pr::m_vec[3+1*4];}
const T& v02() const {return pr::m_vec[0+2*4];}
const T& v12() const {return pr::m_vec[1+2*4];}
const T& v22() const {return pr::m_vec[2+2*4];}
const T& v32() const {return pr::m_vec[3+2*4];}
const T& v03() const {return pr::m_vec[0+3*4];}
const T& v13() const {return pr::m_vec[1+3*4];}
const T& v23() const {return pr::m_vec[2+3*4];}
const T& v33() const {return pr::m_vec[3+3*4];}
protected:
static void _set_translate(const T& a_x,const T& a_y,const T& a_z,T v[]) {
v[0] = T(1);v[4] = 0;v[ 8] = 0;v[12] = a_x;
v[1] = 0;v[5] = T(1);v[ 9] = 0;v[13] = a_y;
v[2] = 0;v[6] = 0;v[10] = T(1);v[14] = a_z;
v[3] = 0;v[7] = 0;v[11] = 0;v[15] = T(1);
}
static void _set_scale(const T& a_1,const T& a_2,const T& a_3,T v[]) {
v[0] = a_1;v[4] = 0;v[ 8] = 0;v[12] = 0;
v[1] = 0;v[5] = a_2;v[ 9] = 0;v[13] = 0;
v[2] = 0;v[6] = 0;v[10] = a_3;v[14] = 0;
v[3] = 0;v[7] = 0;v[11] = 0;v[15] = T(1);
}
static void _set_rotate(const T& a_x,const T& a_y,const T& a_z,const T& a_angle,T v[],T(*a_sin)(T),T(*a_cos)(T)) {
//WARNING : (a_x,a_y,a_z) must be a normalized vector.
T si = a_sin(a_angle);
T co = a_cos(a_angle);
T x = a_x;
T y = a_y;
T z = a_z;
T x2 = x*x;
T y2 = y*y;
T z2 = z*z;
T xy = x*y;
T xz = x*z;
T yz = y*z;
v[0] = x2+(1-x2)*co;v[4] = xy*(1-co)-z*si;v[ 8] = xz*(1-co)+y*si;v[12] = 0;
v[1] = xy*(1-co)+z*si;v[5] = y2+(1-y2)*co;v[ 9] = yz*(1-co)-x*si;v[13] = 0;
v[2] = xz*(1-co)-y*si;v[6] = yz*(1-co)+x*si;v[10] = z2+(1-z2)*co;v[14] = 0;
v[3] = 0;v[7] = 0;v[11] = 0;v[15] = 1;
// If :
// n =(x,y,z)
// n2 = x2+y2+z2 = 1
// n.E = x*E1+y*E2+z*E3
// with :
// E1 E2 E3
// 0 0 0 0 0 -1 0 1 0
// 0 0 1 0 0 0 -1 0 0
// 0 -1 0 1 0 0 0 0 0
//
// R(r,c) = cos(theta)*Id(r,c)+(1-cos(theta))*nr*nc-sin(theta)*(n.E)(r,c)
//
// R = exp(-theta*(n.E))
}
public:
void mul_mtx_rot_root(const T& a_00,const T& a_01,const T& a_02, //1 row
const T& a_10,const T& a_11,const T& a_12, //2 row
const T& a_20,const T& a_21,const T& a_22) //3 row
{
T* tv = pr::m_vec;
//pr::m_vec[0] = 00;pr::m_vec[4] = 01;pr::m_vec[ 8] = 02;pr::m_vec[12] = 03;
//pr::m_vec[1] = 10;pr::m_vec[5] = 11;pr::m_vec[ 9] = 12;pr::m_vec[13] = 13;
//pr::m_vec[2] = 20;pr::m_vec[6] = 21;pr::m_vec[10] = 22;pr::m_vec[14] = 23;
//pr::m_vec[3] = 30;pr::m_vec[7] = 31;pr::m_vec[11] = 32;pr::m_vec[15] = 33;
T tv_0 = tv[0];
T tv_1 = tv[1];
T tv_2 = tv[2];
T tv_3 = tv[3];
T tv_4 = tv[4];
T tv_5 = tv[5];
T tv_6 = tv[6];
T tv_7 = tv[7];
T tv_8 = tv[8];
T tv_9 = tv[9];
T tv_10 = tv[10];
T tv_11 = tv[11];
T tv_12 = tv[12];
T tv_13 = tv[13];
T tv_14 = tv[14];
T tv_15 = tv[15];
T fv_0 = a_00;
T fv_1 = a_10;
T fv_2 = a_20;
//T fv_3 = 0;
T fv_4 = a_01;
T fv_5 = a_11;
T fv_6 = a_21;
//T fv_7 = 0;
T fv_8 = a_02;
T fv_9 = a_12;
T fv_10 = a_22;
//T fv_11 = 0;
//T fv_12 = 0;
//T fv_13 = 0;
//T fv_14 = 0;
//T fv_15 = 1;
tv[0] = tv_0*fv_0+tv_4*fv_1+ tv_8*fv_2;
tv[1] = tv_1*fv_0+tv_5*fv_1+ tv_9*fv_2;
tv[2] = tv_2*fv_0+tv_6*fv_1+tv_10*fv_2;
tv[3] = tv_3*fv_0+tv_7*fv_1+tv_11*fv_2;
tv[4] = tv_0*fv_4+tv_4*fv_5+ tv_8*fv_6;
tv[5] = tv_1*fv_4+tv_5*fv_5+ tv_9*fv_6;
tv[6] = tv_2*fv_4+tv_6*fv_5+tv_10*fv_6;
tv[7] = tv_3*fv_4+tv_7*fv_5+tv_11*fv_6;
tv[8] = tv_0*fv_8+tv_4*fv_9+ tv_8*fv_10;
tv[9] = tv_1*fv_8+tv_5*fv_9+ tv_9*fv_10;
tv[10] = tv_2*fv_8+tv_6*fv_9+tv_10*fv_10;
tv[11] = tv_3*fv_8+tv_7*fv_9+tv_11*fv_10;
tv[12] = tv_12;
tv[13] = tv_13;
tv[14] = tv_14;
tv[15] = tv_15;
}
private:static void check_instantiation() {mat4<float> dummy;}
};
////////////////////////////////////////////////
/// common matrices : //////////////////////////
////////////////////////////////////////////////
#ifdef TOOLS_MEM
template <class T> inline const mat4<T>& mat4_zero() {static const mat4<T> s_v(false);return s_v;}
#else
template <class T> inline const mat4<T>& mat4_zero() {static const mat4<T> s_v;return s_v;}
#endif
/*
template <class T>
inline const mat4<T>& mat4_identity() {
static mat4<T> s_v(false);
static bool s_first = true;
if(s_first) {s_v.set_identity();s_first=false;}
return s_v;
}
*/
//for sf, mf :
template <class T>
inline const T* get_data(const mat4<T>& a_v) {return a_v.data();}
}
#include <ostream>
namespace tools {
template <class T>
inline std::ostream& operator<<(std::ostream& a_out,const mat4<T>& a_mtx){
const T* v = a_mtx.data();
a_out << v[0] << "," << v[4] << "," << v[ 8] << "," << v[12]
<< std::endl
<< v[1] << "," << v[5] << "," << v[ 9] << "," << v[13]
<< std::endl
<< v[2] << "," << v[6] << "," << v[10] << "," << v[14]
<< std::endl
<< v[3] << "," << v[7] << "," << v[11] << "," << v[15]
<< std::endl;
return a_out;
}
}
#endif
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