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# Help Target
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help:
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|
||||
@echo "... all (the default if no target is provided)"
|
||||
@echo "... clean"
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||||
|
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#=============================================================================
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||||
|
||||
# Special rule to run CMake to check the build system integrity.
|
||||
# No rule that depends on this can have commands that come from listfiles
|
||||
# because they might be regenerated.
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cmake_check_build_system:
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||||
cd /home/harle/catkin_ws/src/BaxterInterface/ASIFT_tests/demo_ASIFT_src && $(CMAKE_COMMAND) -H$(CMAKE_SOURCE_DIR) -B$(CMAKE_BINARY_DIR) --check-build-system CMakeFiles/Makefile.cmake 0
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# Install script for directory: /home/harle/catkin_ws/src/BaxterInterface/ASIFT_tests/demo_ASIFT_src/libNumerics
|
||||
|
||||
# Set the install prefix
|
||||
IF(NOT DEFINED CMAKE_INSTALL_PREFIX)
|
||||
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|
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|
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STRING(REGEX REPLACE "/$" "" CMAKE_INSTALL_PREFIX "${CMAKE_INSTALL_PREFIX}")
|
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|
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|
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|
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STRING(REGEX REPLACE "^[^A-Za-z0-9_]+" ""
|
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|
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|
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|
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MESSAGE(STATUS "Install configuration: \"${CMAKE_INSTALL_CONFIG_NAME}\"")
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|
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|
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MESSAGE(STATUS "Install component: \"${COMPONENT}\"")
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|
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|
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|
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|
||||
651
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/computeH.cpp
Executable file
651
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/computeH.cpp
Executable file
|
|
@ -0,0 +1,651 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#include "homography.h"
|
||||
#include "numerics.h"
|
||||
|
||||
#include <algorithm>
|
||||
#include <math.h> /* For sqrt */
|
||||
#include <string.h>
|
||||
|
||||
static const float minEigenValue = 1e-3f; // For regular matrix
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// Constructor. Field `b' used only for error computation.
|
||||
ComputeH::ComputeH(Type type)
|
||||
: _type(type), n( size(type) ), b(0)
|
||||
{
|
||||
clear();
|
||||
}
|
||||
|
||||
// Destructor
|
||||
ComputeH::~ComputeH()
|
||||
{}
|
||||
|
||||
// Dimension of matrix w.r.t. type
|
||||
int ComputeH::size(Type type)
|
||||
{
|
||||
switch(type) {
|
||||
case Translation:
|
||||
return 2;
|
||||
case Zoom:
|
||||
return 3;
|
||||
case Rotation: // In fact 3, but nonlinear system
|
||||
case GeneralZoom:
|
||||
case Similarity:
|
||||
return 4;
|
||||
case Affine:
|
||||
return 6;
|
||||
case Projective:
|
||||
return 8;
|
||||
}
|
||||
return 8;
|
||||
}
|
||||
|
||||
// Return less general motion
|
||||
ComputeH::Type ComputeH::restrict(Type t)
|
||||
{
|
||||
switch(t) {
|
||||
case Translation:
|
||||
return Translation; // Should return identity
|
||||
case Rotation:
|
||||
case Zoom:
|
||||
return Translation;
|
||||
case Similarity:
|
||||
return Zoom; // Rotation also correct. Arbitrary choice.
|
||||
case GeneralZoom:
|
||||
return Zoom;
|
||||
case Affine:
|
||||
return Similarity;
|
||||
case Projective:
|
||||
return Affine;
|
||||
}
|
||||
return Affine;
|
||||
}
|
||||
|
||||
// Reinitialize
|
||||
void ComputeH::clear()
|
||||
{
|
||||
memset(Ann, 0, n*n*sizeof(double));
|
||||
memset(Bn, 0, n*sizeof(double));
|
||||
b = 0;
|
||||
}
|
||||
|
||||
// Add two corresponding points
|
||||
void ComputeH::add(float x, float y, float X, float Y, float w)
|
||||
{
|
||||
if(_type <= Similarity) { // Separate for readability
|
||||
add_4parameters(x, y, X, Y, w);
|
||||
return;
|
||||
}
|
||||
double x2 = x*x, y2 = y*y, xy = x*y;
|
||||
double xX = x*X, yX = y*X, xY = x*Y, yY = y*Y;
|
||||
double *A = Ann, *B = Bn;
|
||||
|
||||
*A++ += w* x2; // Equation 1
|
||||
*A++ += w* xy;
|
||||
A += 2;
|
||||
*A++ += w* x;
|
||||
A++;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* x*xX;
|
||||
*A++ -= w* x*yX;
|
||||
}
|
||||
*B++ += w* x*X;
|
||||
|
||||
A++; // Equation 2
|
||||
*A++ += w* y2;
|
||||
A += 2;
|
||||
*A++ += w* y;
|
||||
A++;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* y*xX;
|
||||
*A++ -= w* y*yX;
|
||||
}
|
||||
*B++ += w* y*X;
|
||||
|
||||
A +=2; // Equation 3
|
||||
*A++ += w* x2;
|
||||
*A++ += w* xy;
|
||||
A++;
|
||||
*A++ += w* x;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* x*xY;
|
||||
*A++ -= w* x*yY;
|
||||
}
|
||||
*B++ += w* x*Y;
|
||||
|
||||
A +=3; // Equation 4
|
||||
*A++ += w* y2;
|
||||
A++;
|
||||
*A++ += w* y;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* y*xY;
|
||||
*A++ -= w* y*yY;
|
||||
}
|
||||
*B++ += w* y*Y;
|
||||
|
||||
A+= 4; // Equation 5
|
||||
*A++ += w;
|
||||
A++;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xX;
|
||||
*A++ -= w* yX;
|
||||
}
|
||||
*B++ += w* X;
|
||||
|
||||
A += 5; // Equation 6
|
||||
*A++ += w;
|
||||
*B++ += w* Y;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xY;
|
||||
*A++ -= w* yY;
|
||||
|
||||
A += 6; // Equation 7
|
||||
*A++ += w* (xX*xX + xY*xY);
|
||||
*A++ += w* (xX*yX + xY*yY);
|
||||
*B++ -= w* (xX*X + xY*Y);
|
||||
|
||||
A+= 7; // Equation 8
|
||||
*A++ += w* (yX*yX + yY*yY);
|
||||
*B++ -= w* (yX*X + yY*Y);
|
||||
}
|
||||
b += w* (X*X + Y*Y);
|
||||
}
|
||||
|
||||
// Add two corresponding points, type involving at most 4 parameters
|
||||
void ComputeH::add_4parameters(float x, float y, float X, float Y, float w)
|
||||
{
|
||||
double *A = Ann, *B = Bn;
|
||||
|
||||
if(_type == Translation) {
|
||||
A[0] += w;
|
||||
A[3] += w;
|
||||
B[0] += w* (X - x);
|
||||
B[1] += w* (Y - y);
|
||||
b += w* ((X-x)*(X-x) + (Y-y)*(Y-y));
|
||||
return;
|
||||
}
|
||||
b += w* (X*X + Y*Y);
|
||||
if(_type == GeneralZoom) {
|
||||
A[0] += w* x*x;
|
||||
A[2] += w* x;
|
||||
B[0] += w* x*X;
|
||||
|
||||
A[5] += w* y*y;
|
||||
A[7] += w* y;
|
||||
B[1] += w* y*Y;
|
||||
|
||||
A[10]+= w;
|
||||
B[2] += w* X;
|
||||
|
||||
A[15]+= w;
|
||||
B[3] += w* Y;
|
||||
return;
|
||||
}
|
||||
|
||||
*A++ += w* (x*x + y*y); // Equation 1
|
||||
if(_type != Zoom) // Similarity or Rotation
|
||||
A++;
|
||||
*A++ += w* x;
|
||||
*A++ += w* y;
|
||||
*B++ += w* (x*X + y*Y);
|
||||
|
||||
if(_type != Zoom) { // Similarity or Rotation
|
||||
A++; // Equation 2
|
||||
*A++ += w* (x*x + y*y);
|
||||
*A++ += w* y;
|
||||
*A++ -= w* x;
|
||||
*B++ += w* (y*X - x*Y);
|
||||
A++; // Prepare for next line
|
||||
}
|
||||
|
||||
A++; // Equation 3
|
||||
*A++ += w;
|
||||
A++;
|
||||
*B++ += w* X;
|
||||
|
||||
A += n-1; // Equation 4
|
||||
*A++ += w;
|
||||
*B++ += w* Y;
|
||||
}
|
||||
|
||||
// Add corresponding lines of equation ux + by + x = 0
|
||||
void ComputeH::add(float x, float y, float z, float X, float Y, float Z,
|
||||
float w)
|
||||
{
|
||||
float s = 1.0f / (float)sqrt(x*x + y*y);
|
||||
x *= s;
|
||||
y *= s;
|
||||
z *= s;
|
||||
s = 1.0f / (float)sqrt(X*X + Y*Y);
|
||||
X *= s;
|
||||
Y *= s;
|
||||
Z *= s;
|
||||
if(_type <= Similarity) { // Separate for readability
|
||||
add_4parameters(x, y, z, X, Y, Z, w);
|
||||
return;
|
||||
}
|
||||
|
||||
double x2 = x*x, y2 = y*y, z2 = z*z, xy = x*y, xz = x*z, yz = y*z;
|
||||
double X2 = X*X, Y2 = Y*Y, Z2 = Z*Z, XY = X*Y, XZ = X*Z, YZ = Y*Z;
|
||||
double *A = Ann, *B = Bn;
|
||||
|
||||
*A++ += w* (y2+z2) * X2; // Equation 1
|
||||
*A++ -= w* xy * X2;
|
||||
*A++ += w* (y2+z2) * XY;
|
||||
*A++ -= w* xy * XY;
|
||||
*A++ -= w* xz * X2;
|
||||
*A++ -= w* xz * XY;
|
||||
if(_type == Projective) {
|
||||
*A++ += w* (y2+z2) * XZ;
|
||||
*A++ -= w* xy * XZ;
|
||||
}
|
||||
*B++ += w* xz * XZ;
|
||||
|
||||
A++; // Equation 2
|
||||
*A++ += w* (x2+z2) * X2;
|
||||
*A++ -= w* xy * XY;
|
||||
*A++ += w* (x2+z2) * XY;
|
||||
*A++ -= w* yz * X2;
|
||||
*A++ -= w* yz * XY;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xy * XZ;
|
||||
*A++ += w* (x2+z2) * XZ;
|
||||
}
|
||||
*B++ -= w* yz * XZ;
|
||||
|
||||
A += 2; // Equation 3
|
||||
*A++ += w* (y2+z2) * Y2;
|
||||
*A++ -= w* xy * Y2;
|
||||
*A++ -= w* xz * XY;
|
||||
*A++ -= w* xz * Y2;
|
||||
if(_type == Projective) {
|
||||
*A++ += w* (y2+z2) * YZ;
|
||||
*A++ -= w* xy * YZ;
|
||||
}
|
||||
*B++ += w* xz * YZ;
|
||||
|
||||
A += 3; // Equation 4
|
||||
*A++ += w* (x2+z2) * Y2;
|
||||
*A++ -= w* yz * XY;
|
||||
*A++ -= w* yz * Y2;
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xy * YZ;
|
||||
*A++ += w* (x2+z2) * YZ;
|
||||
}
|
||||
*B++ += w* yz * YZ;
|
||||
|
||||
A += 4; // Equation 5
|
||||
*A++ += w* X2; // *(x2+y2=1)
|
||||
*A++ += w* XY; // *(x2+y2=1)
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xz * XZ;
|
||||
*A++ -= w* yz * XZ;
|
||||
}
|
||||
*B++ -= w* XZ; // *(x2+y2=1)
|
||||
|
||||
A += 5; // Equation 6
|
||||
*A++ += w* Y2; // *(x2+y2=1)
|
||||
*B++ -= w* YZ; // *(x2+y2=1)
|
||||
if(_type == Projective) {
|
||||
*A++ -= w* xz * YZ;
|
||||
*A++ -= w* yz * YZ;
|
||||
|
||||
A += 6; // Equation 7
|
||||
*A++ += w* (y2+z2) * Y2;
|
||||
*A++ -= w* xy * Z2;
|
||||
*B++ += w* xz * Z2;
|
||||
|
||||
A += 7; // Equation 8
|
||||
*A++ += w* (x2+z2) * Z2;
|
||||
*B++ += w* yz * Z2;
|
||||
}
|
||||
b += w* Z2; // *(x2+y2=1)
|
||||
}
|
||||
|
||||
// Add two corresponding lines, type involving at most 4 parameters
|
||||
void ComputeH::add_4parameters(float x, float y, float z,
|
||||
float X, float Y, float Z, float w)
|
||||
{
|
||||
double x2 = x*x, y2 = y*y, z2 = z*z, xy = x*y, xz = x*z, yz = y*z;
|
||||
double X2 = X*X, Y2 = Y*Y, Z2 = Z*Z, XY = X*Y, XZ = X*Z, YZ = Y*Z;
|
||||
double *A = Ann, *B = Bn;
|
||||
if(_type == Translation) {
|
||||
*A++ += w* X2; // *(x2+y2=1)
|
||||
*A++ += w* XY; // *(x2+y2=1)
|
||||
*B++ += w* (yz*XY + xz*X2 - XZ/* *(x2+y2=1) */);
|
||||
|
||||
A++;
|
||||
*A++ += w* Y2; // *(x2+y2=1)
|
||||
*B++ += w* (xz*XY + yz*Y2 - YZ/* *(x2+y2=1) */);
|
||||
|
||||
b += w* (z2 + Z2 + y2*X2 + x2*Z2 - 2*(xz*XZ + yz*YZ + xy*XZ));
|
||||
return;
|
||||
}
|
||||
b += w* Z2; // *(x2+y2=1)
|
||||
if(_type == GeneralZoom) {
|
||||
*A++ += w* (y2+z2) * X2;
|
||||
*A++ -= w* xy * XY;
|
||||
*A++ -= w* xz * X2;
|
||||
*A++ -= w* xz * XY;
|
||||
*B++ += w* xz * XZ;
|
||||
|
||||
A++;
|
||||
*A++ += w* (x2+z2) * Y2;
|
||||
*A++ -= w* yz * XY;
|
||||
*A++ -= w* yz * Y2;
|
||||
*B++ += w* yz * YZ;
|
||||
|
||||
A += 2;
|
||||
*A++ += w* X2; // *(x2+y2=1)
|
||||
*A++ += w* XY; // *(x2+y2=1)
|
||||
*B++ -= w* XZ; // *(x2+y2=1)
|
||||
|
||||
A += 3;
|
||||
*A++ += w* Y2; // *(x2+y2=1)
|
||||
*B++ -= w* YZ; // *(x2+y2=1)
|
||||
return;
|
||||
}
|
||||
|
||||
if(_type == Zoom) {
|
||||
*A++ += w* (z2/* *(X2+Y2=1)*/ + y2*X2 + x2*Y2 - 2*xy*XY);
|
||||
*A++ -= w* (yz*XY + xz*X2);
|
||||
*A++ -= w* (yz*Y2 + xz*XY);
|
||||
*B++ += w* (yz*YZ + xz*X2);
|
||||
} else { // Similarity or Rotation
|
||||
*A++ += w* (1 /* =x2+y2*/+ 2*(z2 - xy)) * X2;
|
||||
*A++ += w* (x2 - y2) * XY;
|
||||
*A++ -= w* (xz + yz) * X2;
|
||||
*A++ -= w* (xz + yz) * XY;
|
||||
*B++ += w* (xz + yz) * XZ;
|
||||
|
||||
A++;
|
||||
*A++ += w* (1 /* =x2+y2*/+ 2*(z2 + xy)) * Y2;
|
||||
*A++ += w* (xz - yz) * XY;
|
||||
*A++ += w* (xz - yz) * Y2;
|
||||
*B++ += w* (yz - xz) * YZ;
|
||||
A++; // Prepare for next line
|
||||
}
|
||||
|
||||
A++;
|
||||
*A++ += w* X2; // *(x2+y2=1)
|
||||
*A++ += w* XY; // *(x2+y2=1)
|
||||
*B++ -= w* XZ; // *(x2+y2=1)
|
||||
|
||||
A += n-1;
|
||||
*A++ += w* Y2; // *(x2+y2=1)
|
||||
*B++ -= w* YZ; // *(x2+y2=1)
|
||||
}
|
||||
|
||||
// Wrap vector of unknowns `v' into structure `map'
|
||||
void ComputeH::wrap(Homography& h, const vector<double>& v) const
|
||||
{
|
||||
int i = 0;
|
||||
h.mat()(0,0) = (_type==Translation)? 1.0f: v(i++);
|
||||
h.mat()(0,1) = (_type==Translation || _type==Zoom || _type==GeneralZoom) ?
|
||||
0: v(i++);
|
||||
if(n >= 6) {
|
||||
h.mat()(1,0) = v(i++);
|
||||
h.mat()(1,1) = v(i++);
|
||||
} else {
|
||||
h.mat()(1,0) = -h.mat()(0,1);
|
||||
h.mat()(1,1) = (_type==GeneralZoom)? v(i++): h.mat()(0,0);
|
||||
}
|
||||
h.mat()(0,2) = v(i++);
|
||||
h.mat()(1,2) = v(i++);
|
||||
if(_type == Projective) {
|
||||
h.mat()(2,0) = v(i++);
|
||||
h.mat()(2,1) = v(i++);
|
||||
} else
|
||||
h.mat()(2,0) = h.mat()(2,1) = 0;
|
||||
h.mat()(2,2) = 1.0;
|
||||
}
|
||||
|
||||
/// Unwrap parameters in \a h into vector of unknowns \a v.
|
||||
void ComputeH::unwrap(const Homography& h, vector<double>& v) const
|
||||
{
|
||||
int i = 0;
|
||||
if(_type != Translation) {
|
||||
v(i++) = h.mat()(0,0);
|
||||
if(_type != Zoom) {
|
||||
if(_type != GeneralZoom) {
|
||||
v(i++) = h.mat()(0,1); // Rotation or Similarity or...
|
||||
if(n >= 6) // Affine or Projective
|
||||
v(i++) = h.mat()(1,0);
|
||||
}
|
||||
if(_type==GeneralZoom || _type==Affine || _type==Projective)
|
||||
v(i++) = h.mat()(1,1);
|
||||
}
|
||||
}
|
||||
v(i++) = h.mat()(0,2);
|
||||
v(i++) = h.mat()(1,2);
|
||||
if(_type == Projective) {
|
||||
v(i++) = h.mat()(2,0);
|
||||
v(i++) = h.mat()(2,1);
|
||||
}
|
||||
}
|
||||
|
||||
// Sum of weights (=#correspondences)
|
||||
float ComputeH::weight() const
|
||||
{
|
||||
// Diagonal coefficient affecting translation
|
||||
int i = (_type == Projective) ? 6 : n;
|
||||
return static_cast<float>(Ann[(i-1)*(n+1)]); // Element (i-1,i-1)
|
||||
}
|
||||
|
||||
|
||||
// Return quadratic error when mapping with `motion'
|
||||
float ComputeH::q_error(const Homography& map) const
|
||||
{
|
||||
vector<double> v(n);
|
||||
unwrap(map, v);
|
||||
return q_error(v);
|
||||
}
|
||||
|
||||
// Idem, with arguments in a vector
|
||||
float ComputeH::q_error(const vector<double>& v) const
|
||||
{
|
||||
double e = b;
|
||||
// Diagonal terms
|
||||
const double* A = Ann + n*n-1;
|
||||
for(int i = n-1; i >= 0; i--, A -= n+1)
|
||||
e += *A * v(i) * v(i);
|
||||
// Cross terms
|
||||
A = Ann + (n-1)*n; // Last row
|
||||
for(int i = n-1; i >= 0; i--, A -= n) {
|
||||
double vi = v(i);
|
||||
e -= 2.0 * Bn[i] * vi;
|
||||
for(int j = n-1; j > i; j--)
|
||||
e += 2.0 * A[j] * vi * v(j);
|
||||
}
|
||||
return static_cast<float>(e);
|
||||
}
|
||||
|
||||
// LSE for rotation: solve linear system under quadratic constraint
|
||||
bool ComputeH::compute_rotation(vector<double>& B) const
|
||||
{
|
||||
if(Ann[15] <= 0) // No point added or absurd value
|
||||
return false;
|
||||
B(0) = Ann[15] * Bn[0] - Ann[2] * Bn[2] - Ann[3] * Bn[3];
|
||||
B(1) = Ann[15] * Bn[1] - Ann[3] * Bn[2] + Ann[2] * Bn[3];
|
||||
double root = sqrt(B(0)*B(0) + B(1)*B(1));
|
||||
if(root < minEigenValue)
|
||||
return false;
|
||||
// Test first solution
|
||||
double lambda1 = (Ann[2]*Ann[2] + Ann[3]*Ann[3] + root) / Ann[15];
|
||||
B(0) /= root;
|
||||
B(1) /= root;
|
||||
B(2) = (-Ann[2]*Bn[0] - Ann[3]*Bn[1] + lambda1 * Bn[2]) / root;
|
||||
B(3) = (-Ann[3]*Bn[0] + Ann[2]*Bn[1] + lambda1 * Bn[3]) / root;
|
||||
float v1 = q_error(B);
|
||||
// Test second solution
|
||||
vector<double> C(4);
|
||||
double lambda2 = (Ann[2]*Ann[2] + Ann[3]*Ann[3] - root) / Ann[15];
|
||||
C(0) = -B(0);
|
||||
C(1) = -B(1);
|
||||
C(2) = -(-Ann[2]*Bn[0] - Ann[3]*Bn[1] + lambda2 * Bn[2]) / root;
|
||||
C(3) = -(-Ann[3]*Bn[0] + Ann[2]*Bn[1] + lambda2 * Bn[3]) / root;
|
||||
if(v1 > q_error(C)) // Keep second solution
|
||||
B = C;
|
||||
return true;
|
||||
}
|
||||
|
||||
// Return LSE motion and the sum of weights
|
||||
float ComputeH::compute(Homography& map) const
|
||||
{
|
||||
vector<double> B(n);
|
||||
B.read(Bn);
|
||||
|
||||
if(_type == Rotation) {
|
||||
if(! compute_rotation(B))
|
||||
return 0;
|
||||
} else {
|
||||
matrix<double> A(n,n);
|
||||
A.read(Ann);
|
||||
Normalization left, right;
|
||||
if(_type == Projective && !normalize(left, A, B, right))
|
||||
return 0;
|
||||
A.symUpper();
|
||||
|
||||
vector<double> oldB(B);
|
||||
if(! solveLU(A, B))
|
||||
return 0;
|
||||
|
||||
if(_type == Projective && ! de_normalize(left, B, right))
|
||||
return 0;
|
||||
}
|
||||
|
||||
wrap(map, B);
|
||||
return weight();
|
||||
}
|
||||
|
||||
// Normalize independently original and final points so that the new
|
||||
// origin is their centroid and their mean square distance (to it) is 2
|
||||
bool ComputeH::normalize(Normalization& left,
|
||||
matrix<double>& A, vector<double>& B,
|
||||
Normalization& right) const
|
||||
{
|
||||
double w = A(5,5); // Total weight
|
||||
if(w < minEigenValue)
|
||||
return false;
|
||||
double invW = 1.0 / w;
|
||||
|
||||
// Find normalizations (zoom-translation)
|
||||
right.s = (A(0,0) + A(1,1)) - (A(0,4)*A(0,4) + A(1,4)*A(1,4))*invW;
|
||||
if(right.s < minEigenValue)
|
||||
return false;
|
||||
right.s = sqrt(2.0*w / right.s);
|
||||
right.x = - invW * right.s * A(0,4);
|
||||
right.y = - invW * right.s * A(1,4);
|
||||
|
||||
left.s = b - (B(4)*B(4) + B(5)*B(5))*invW;
|
||||
if(left.s < minEigenValue)
|
||||
return false;
|
||||
left.s = sqrt(2.0*w / left.s);
|
||||
left.x = - invW * left.s * B(4);
|
||||
left.y = - invW * left.s * B(5);
|
||||
double norm = left.x*left.x + left.y*left.y;
|
||||
|
||||
double s2 = right.s*right.s, sS = right.s*left.s, S2 = left.s*left.s;
|
||||
|
||||
// Normalization of vector B
|
||||
double b0 = B(0), b1 = B(1), b2 = B(2), b3 = B(3);
|
||||
B(0) = sS * B(0) - w*right.x*left.x;
|
||||
B(1) = sS * B(1) - w*right.y*left.x;
|
||||
B(2) = sS * B(2) - w*right.x*left.y;
|
||||
B(3) = sS * B(3) - w*right.y*left.y;
|
||||
B(4) = B(5) = 0;
|
||||
B(6) = sS*(left.s*B(6) - 2*(left.x*b0 + left.y*b2)) +
|
||||
w*right.x*(norm - 2.0);
|
||||
B(7) = sS*(left.s*B(7) - 2*(left.x*b1 + left.y*b3)) +
|
||||
w*right.y*(norm - 2.0);
|
||||
|
||||
// Normalization of matrix A
|
||||
double a0 = A(0,0), a1 = A(0,1), a6 = A(0,6), a7 = A(0,7), a9 = A(1,1);
|
||||
double a15 = A(1,7), a22 = A(2,6), a23 = A(2,7), a31 = A(3,7);
|
||||
|
||||
A(0,0) = s2 * A(0,0) - w*right.x*right.x;
|
||||
A(0,1) = s2 * A(0,1) - w*right.x*right.y;
|
||||
A(0,4) = 0;
|
||||
A(0,6) = right.s*(sS*A(0,6) - right.s*left.x*a0 - left.s*right.x*b0) +
|
||||
w*right.x*left.x*right.x - right.x * B(0);
|
||||
A(0,7) = right.s*(sS*A(0,7) - right.s*left.x*a1 - left.s*right.x*b1) +
|
||||
w*right.x*left.x*right.y - right.y * B(0);
|
||||
|
||||
A(1,1) = s2 * A(1,1) - w*right.y*right.y;
|
||||
A(1,4) = 0;
|
||||
A(1,6) = A(0,7);
|
||||
A(1,7) = right.s*(sS*A(1,7) - right.s*left.x*a9 - left.s*right.y*b1) +
|
||||
w*right.y*left.x*right.y - right.y * B(1);
|
||||
|
||||
A(2,2) = A(0,0);
|
||||
A(2,3) = A(0,1);
|
||||
A(2,5) = 0;
|
||||
A(2,6) = right.s*(sS*A(2,6) - right.s*left.y*a0 - left.s*right.x*b2) +
|
||||
w*right.x*left.y*right.x - right.x * B(2);
|
||||
A(2,7) = right.s*(sS*A(2,7) - right.s*left.y*a1 - left.s*right.x*b3) +
|
||||
w*right.x*left.y*right.y - right.y * B(2);
|
||||
|
||||
A(3,3) = A(1,1);
|
||||
A(3,5) = 0;
|
||||
A(3,6) = A(2,7);
|
||||
A(3,7) = right.s*(sS*A(3,7) - right.s*left.y*a9 - left.s*right.y*b3) +
|
||||
w*right.y*left.y*right.y - right.y * B(3);
|
||||
|
||||
A(4,6) = -B(0);
|
||||
A(4,7) = -B(1);
|
||||
|
||||
A(5,6) = -B(2);
|
||||
A(5,7) = -B(3);
|
||||
|
||||
A(6,6) = s2*(S2*A(6,6) - 2*left.s*(left.x*a6+left.y*a22) + a0*norm) -
|
||||
2*right.x*(B(6) + w*right.x);
|
||||
A(6,7) = s2*(S2*A(6,7) - 2*left.s*(left.x*a7+left.y*a23) + a1*norm) -
|
||||
right.x*B(7) - right.y*B(6) - 2*w*right.x*right.y;
|
||||
|
||||
A(7,7) = s2*(S2*A(7,7) - 2*left.s*(left.x*a15+left.y*a31) + a9*norm) -
|
||||
2*right.y*(B(7) + w*right.y);
|
||||
return true;
|
||||
}
|
||||
|
||||
// `l' (left) and 'r' (right) representing zoom-translation normalizations,
|
||||
// and `B' the parameters of a projective motion,
|
||||
// compute l^-1 B r
|
||||
bool ComputeH::de_normalize(const Normalization& l,
|
||||
vector<double>& B,
|
||||
const Normalization& r)
|
||||
{
|
||||
// B := B r
|
||||
B(4) += r.x * B(0) + r.y * B(1); // Line 1
|
||||
B(0) *= r.s;
|
||||
B(1) *= r.s;
|
||||
|
||||
B(5) += r.x * B(2) + r.y * B(3); // Line 2
|
||||
B(2) *= r.s;
|
||||
B(3) *= r.s;
|
||||
|
||||
double f = r.x * B(6) + r.y * B(7) + 1.0; // Line 3
|
||||
if(-minEigenValue < f && f < minEigenValue)
|
||||
return false; // Origin of right normalization on line at infinity
|
||||
B(6) *= r.s;
|
||||
B(7) *= r.s;
|
||||
|
||||
// B := l^-1 B
|
||||
double s = 1.0 / (l.s * f);
|
||||
B(0) = (B(0) - l.x*B(6)) * s; // Line 1
|
||||
B(1) = (B(1) - l.x*B(7)) * s;
|
||||
B(4) = (B(4) - l.x* f ) * s;
|
||||
|
||||
B(2) = (B(2) - l.y*B(6)) * s; // Line 2
|
||||
B(3) = (B(3) - l.y*B(7)) * s;
|
||||
B(5) = (B(5) - l.y* f ) * s;
|
||||
|
||||
B(6) /= f; // Line 3
|
||||
B(7) /= f;
|
||||
return true;
|
||||
}
|
||||
|
||||
} // libNumerics
|
||||
73
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/homography.cpp
Executable file
73
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/homography.cpp
Executable file
|
|
@ -0,0 +1,73 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#include "homography.h"
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// Constructor.
|
||||
Homography::Homography()
|
||||
: m_H( matrix<double>::eye(3) )
|
||||
{}
|
||||
|
||||
/// Put to identity.
|
||||
void Homography::setId()
|
||||
{
|
||||
m_H = matrix<double>::eye(3);
|
||||
}
|
||||
|
||||
/// Set to translation.
|
||||
void Homography::setTrans(double dx, double dy)
|
||||
{
|
||||
setId();
|
||||
m_H(0,2) = dx;
|
||||
m_H(1,2) = dy;
|
||||
}
|
||||
|
||||
/// Set to zoom.
|
||||
void Homography::setZoom(double zx, double zy)
|
||||
{
|
||||
setId();
|
||||
m_H(0,0) = zx;
|
||||
m_H(1,1) = zy;
|
||||
}
|
||||
|
||||
/// Apply homography.
|
||||
void Homography::operator()(double& x, double& y) const
|
||||
{
|
||||
vector<double> m(3);
|
||||
m(0) = x;
|
||||
m(1) = y;
|
||||
m(2) = 1.0f;
|
||||
m = m_H * m;
|
||||
double z_1 = 1.0 / m(2);
|
||||
x = m(0) * z_1;
|
||||
y = m(1) * z_1;
|
||||
}
|
||||
|
||||
/// Compose homographies.
|
||||
Homography Homography::operator*(const Homography& rhs) const
|
||||
{
|
||||
Homography h;
|
||||
h.m_H = m_H * rhs.m_H;
|
||||
h.normalize();
|
||||
return h;
|
||||
}
|
||||
|
||||
/// Inverse homography.
|
||||
Homography Homography::inverse() const
|
||||
{
|
||||
Homography h;
|
||||
h.m_H = m_H.inv();
|
||||
h.normalize();
|
||||
return h;
|
||||
}
|
||||
|
||||
/// Put coef(2,2) to 1.
|
||||
void Homography::normalize()
|
||||
{
|
||||
m_H /= m_H(2,2);
|
||||
}
|
||||
|
||||
} // libNumerics
|
||||
83
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/homography.h
Executable file
83
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/homography.h
Executable file
|
|
@ -0,0 +1,83 @@
|
|||
#ifndef HOMOGRAPHY_H
|
||||
#define HOMOGRAPHY_H
|
||||
|
||||
#include "matrix.h"
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// 2-D homography transform.
|
||||
class Homography {
|
||||
public:
|
||||
Homography();
|
||||
|
||||
void setId();
|
||||
void setTrans(double dx, double dy);
|
||||
void setZoom(double zx, double zy);
|
||||
|
||||
matrix<double>& mat() { return m_H; }
|
||||
const matrix<double>& mat() const { return m_H; }
|
||||
|
||||
void operator()(double& x, double& y) const;
|
||||
Homography operator*(const Homography& rhs) const;
|
||||
Homography inverse() const;
|
||||
private:
|
||||
matrix<double> m_H;
|
||||
void normalize();
|
||||
};
|
||||
|
||||
/// Homography (and more restricted transforms) estimation.
|
||||
class ComputeH {
|
||||
public:
|
||||
enum Type { Translation, // (2 parameters)
|
||||
Rotation, // Rotation/Translation (3 parameters)
|
||||
Zoom, // Zoom/Translation (3 parameters)
|
||||
GeneralZoom, // Non uniform zoom/Translation (4 parameters)
|
||||
Similarity, // Zoom/Rotation/Translation (4 parameters)
|
||||
Affine, // (6 parameters)
|
||||
Projective // (8 parameters)
|
||||
};
|
||||
static Type restrict(Type t); // Return less general motion
|
||||
public:
|
||||
ComputeH(Type type);
|
||||
~ComputeH();
|
||||
|
||||
Type type() const { return _type; }
|
||||
void clear();
|
||||
|
||||
/// Add corresponding points (x1,y1) and (x2,y2)
|
||||
void add(float x1, float y1, float x2, float y2, float w = 1.0f);
|
||||
/// Add corresponding lines of equation u x + v y + w = 0
|
||||
void add(float a1, float b1, float c1,
|
||||
float a2, float b2, float c2, float w = 1.0f);
|
||||
|
||||
float weight() const; ///< Sum of weights (=#correspondences)
|
||||
float q_error(const Homography& map) const; ///< Quadratic error
|
||||
float compute(Homography& map) const; ///< LSE motion, return support weight
|
||||
private:
|
||||
Type _type;
|
||||
int n; ///< Dimension of matrix = # unknown parameters
|
||||
double Ann[64], Bn[8], b; // Min (X 1) (A B) (X 1)^T is X^T = Ann^-1 Bn
|
||||
|
||||
static int size(Type type);
|
||||
void add_4parameters(float x1, float y1, float x2, float y2, float w);
|
||||
void add_4parameters(float a1, float b1, float c1,
|
||||
float a2, float b2, float c2, float w);
|
||||
void wrap(Homography& map, const vector<double>& v) const;
|
||||
void unwrap(const Homography& map, vector<double>& v) const;
|
||||
float q_error(const vector<double>& v) const; // Quadratic error
|
||||
|
||||
bool compute_rotation(vector<double>& B) const;
|
||||
|
||||
/// For Projective, data normalization is required
|
||||
class Normalization { public: double x, y, s; };
|
||||
bool normalize(Normalization& left,
|
||||
matrix<double>& A, vector<double>& B,
|
||||
Normalization& right) const;
|
||||
static bool de_normalize(const Normalization& left,
|
||||
vector<double>& B,
|
||||
const Normalization& right);
|
||||
};
|
||||
|
||||
} // libNumerics
|
||||
|
||||
#endif
|
||||
565
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/matrix.cpp
Executable file
565
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/matrix.cpp
Executable file
|
|
@ -0,0 +1,565 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifdef MATRIX_H // Do nothing if not included from matrix.h
|
||||
|
||||
#define INDEX(i,j) ((i) * m_cols + (j))
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// Constructor for \a m*\a n matrix.
|
||||
/// \param m number of rows.
|
||||
/// \param n number of columns.
|
||||
template <typename T>
|
||||
matrix<T>::matrix(int m, int n)
|
||||
{
|
||||
alloc(m, n);
|
||||
}
|
||||
|
||||
/// Copy constructor.
|
||||
template <typename T>
|
||||
matrix<T>::matrix(const matrix<T>& m)
|
||||
{
|
||||
alloc(m.m_rows, m.m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] = m.p[i];
|
||||
}
|
||||
|
||||
/// Destructor.
|
||||
template <typename T>
|
||||
matrix<T>::~matrix()
|
||||
{
|
||||
free();
|
||||
}
|
||||
|
||||
/// Assignment operator.
|
||||
template <typename T>
|
||||
matrix<T>& matrix<T>::operator=(const matrix<T>& m)
|
||||
{
|
||||
if(&m == this) return *this;
|
||||
if(m.nElements() != nElements()){
|
||||
free();
|
||||
alloc(m.m_rows, m.m_cols);
|
||||
} else {
|
||||
m_rows = m.m_rows;
|
||||
m_cols = m.m_cols;
|
||||
}
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] = m.p[i];
|
||||
return *this;
|
||||
}
|
||||
|
||||
/// Access the coefficient on the \a i-th row, \a j-th column.
|
||||
template <typename T>
|
||||
inline T matrix<T>::operator() (int i, int j) const
|
||||
{
|
||||
assert(i >= 0 && i < m_rows && j >= 0 && j < m_cols);
|
||||
return p[INDEX(i,j)];
|
||||
}
|
||||
|
||||
/// Access the coefficient on the \a i-th row, \a j-th column.
|
||||
template <typename T>
|
||||
inline T& matrix<T>::operator() (int i, int j)
|
||||
{
|
||||
assert(i >= 0 && i < m_rows && j >= 0 && j < m_cols);
|
||||
return p[INDEX(i,j)];
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline T matrix<T>::operator() (int i) const
|
||||
{
|
||||
assert(i >= 0 && i < nElements());
|
||||
return p[i];
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline T& matrix<T>::operator() (int i)
|
||||
{
|
||||
assert(i >= 0 && i < nElements());
|
||||
return p[i];
|
||||
}
|
||||
|
||||
/// Set matrix at constant value.
|
||||
///
|
||||
/// Assign all coefficients to the value \a a.
|
||||
template <typename T>
|
||||
inline void matrix<T>::operator=(T a)
|
||||
{
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] = a;
|
||||
}
|
||||
|
||||
/// Multiply a matrix by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator*(T a) const
|
||||
{
|
||||
matrix<T> prod(m_rows, m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
prod.p[i] = a * p[i];
|
||||
return prod;
|
||||
}
|
||||
|
||||
/// Multiply a matrix by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
void matrix<T>::operator*=(T a)
|
||||
{
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] *= a;
|
||||
}
|
||||
|
||||
/// Divide a matrix by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator/(T a) const
|
||||
{
|
||||
return (*this) * ((T)1/a);
|
||||
}
|
||||
|
||||
/// Divide a matrix by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
void matrix<T>::operator/=(T a)
|
||||
{
|
||||
*this *= (T)1 / a;
|
||||
}
|
||||
|
||||
/// Matrix sum.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator+(const matrix<T>& m) const
|
||||
{
|
||||
assert(m.m_rows == m_rows && m.m_cols == m_cols);
|
||||
matrix<T> sum(m_rows,m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
sum.p[i] = p[i] + m.p[i];
|
||||
return sum;
|
||||
}
|
||||
|
||||
/// Matrix sum.
|
||||
template <typename T>
|
||||
void matrix<T>::operator+=(const matrix<T>& m)
|
||||
{
|
||||
assert(m.m_rows == m_rows && m.m_cols == m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] += m.p[i];
|
||||
}
|
||||
|
||||
/// Matrix subtraction.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator-(const matrix<T>& m) const
|
||||
{
|
||||
assert(m.m_rows == m_rows && m.m_cols == m_cols);
|
||||
matrix<T> sub(m_rows,m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
sub.p[i] = p[i] - m.p[i];
|
||||
return sub;
|
||||
}
|
||||
|
||||
/// Matrix subtraction.
|
||||
template <typename T>
|
||||
void matrix<T>::operator-=(const matrix<T>& m)
|
||||
{
|
||||
assert(m.m_rows == m_rows && m.m_cols == m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] -= m.p[i];
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator-() const
|
||||
{
|
||||
matrix<T> opp(m_rows, m_cols);
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
opp.p[i] = -p[i];
|
||||
return opp;
|
||||
}
|
||||
|
||||
/// Matrix multiplication.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::operator*(const matrix<T>& m) const
|
||||
{
|
||||
assert(m_cols == m.m_rows);
|
||||
matrix<T> prod(m_rows, m.m_cols);
|
||||
T* out = prod.p;
|
||||
for(int i = 0; i < prod.m_rows; i++) {
|
||||
const T* left = p + i*m_cols;
|
||||
for(int j = 0; j < prod.m_cols; j++, out++) {
|
||||
const T* right = m.p + j;
|
||||
*out = 0;
|
||||
for(int k = 0; k < m_cols; k++) {
|
||||
*out += left[k] * *right;
|
||||
right += m.m_cols;
|
||||
}
|
||||
}
|
||||
}
|
||||
return prod;
|
||||
}
|
||||
|
||||
/// Matrix-vector multiplication.
|
||||
template <typename T>
|
||||
vector<T> matrix<T>::operator*(const vector<T>& m) const
|
||||
{
|
||||
assert(m_cols == m.m_rows);
|
||||
vector<T> prod(m_rows);
|
||||
T* out = prod.p;
|
||||
for(int i = 0; i < prod.m_rows; i++, out++) {
|
||||
const T* left = p + i*m_cols;
|
||||
const T* right = m.p;
|
||||
*out = 0;
|
||||
for(int k = 0; k < m_cols; k++)
|
||||
*out += left[k] * right[k];
|
||||
}
|
||||
return prod;
|
||||
}
|
||||
|
||||
/// Tranposed of matrix.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::t() const
|
||||
{
|
||||
matrix<T> t(ncol(), nrow());
|
||||
T* out = t.p;
|
||||
for(int i = 0; i < t.nrow(); i++) {
|
||||
const T* in = p + i;
|
||||
for(int j = 0; j < t.ncol(); j++) {
|
||||
*out++ = *in;
|
||||
in += ncol();
|
||||
}
|
||||
}
|
||||
return t;
|
||||
}
|
||||
|
||||
/// Symmetrize upper part of matrix.
|
||||
template <typename T>
|
||||
void matrix<T>::symUpper()
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
for(int i = 1; i < m_rows; i++) {
|
||||
const T* in = p + i;
|
||||
T* out = p + m_cols*i;
|
||||
for(int j = 0; j < i; j++) {
|
||||
*out++ = *in;
|
||||
in += m_cols;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/// Symmetrize lower part of matrix.
|
||||
template <typename T>
|
||||
void matrix<T>::symLower()
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
for(int i = 1; i < m_rows; i++) {
|
||||
const T* in = p + m_cols*i;
|
||||
T* out = p + i;
|
||||
for(int j = 0; j < i; j++) {
|
||||
*out = *in++;
|
||||
out += m_cols;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
vector<T> matrix<T>::diag() const
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
vector<T> t(m_rows);
|
||||
for(int i = 0; i < m_rows; i++)
|
||||
t.p[i] = p[i*(m_cols+1)];
|
||||
return t;
|
||||
}
|
||||
|
||||
/// Matrix made of zeros.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::zeros(int m, int n)
|
||||
{
|
||||
matrix<T> M(m,n);
|
||||
for(int i = M.nElements()-1; i >= 0; i--)
|
||||
M.p[i] = (T)0;
|
||||
return M;
|
||||
}
|
||||
|
||||
/// Matrix made of ones.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::ones(int m, int n)
|
||||
{
|
||||
matrix<T> M(m,n);
|
||||
for(int i = M.nElements()-1; i >= 0; i--)
|
||||
M.p[i] = (T)1;
|
||||
return M;
|
||||
}
|
||||
|
||||
/// Identity matrix.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::eye(int n)
|
||||
{
|
||||
matrix<T> M(n,n);
|
||||
for(int i = M.nElements()-1; i >= 0; i--)
|
||||
M.p[i] = (T)0;
|
||||
for(int i = n-1; i >= 0; i--)
|
||||
M.p[i*(n+1)] = (T)1;
|
||||
return M;
|
||||
}
|
||||
|
||||
/// Extract the submatrix [i0,i1]x[j0,j1].
|
||||
/// \param i0 first row
|
||||
/// \param i1 last row
|
||||
/// \param j0 first column
|
||||
/// \param j1 last column
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::copy(int i0, int i1, int j0, int j1) const
|
||||
{
|
||||
assert(0 <= i0 && i0 <= i1 && i1 <= m_rows &&
|
||||
0 <= j0 && j0 <= j1 && j1 <= m_cols);
|
||||
matrix<T> sub(i1-i0+1,j1-j0+1);
|
||||
T* out = sub.p;
|
||||
for(int i = i0; i <= i1; i++) {
|
||||
const T* in = p + INDEX(i, j0);
|
||||
for(int j = j0; j <= j1; j++)
|
||||
*out++ = *in++;
|
||||
}
|
||||
return sub;
|
||||
}
|
||||
|
||||
/// Extract the columns of index in [j0,j1].
|
||||
/// \param j0 first column
|
||||
/// \param j1 last column
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::copyCols(int j0, int j1) const
|
||||
{
|
||||
return copy(0, lastRow(), j0, j1);
|
||||
}
|
||||
|
||||
/// Extract the rows of index in [i0,i1].
|
||||
/// \param i0 first row
|
||||
/// \param i1 last row
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::copyRows(int i0, int i1) const
|
||||
{
|
||||
return copy(i0, i1, 0, lastCol());
|
||||
}
|
||||
|
||||
/// Paste a matrix in another one, at position (\a i0,\a j0)
|
||||
/// \param i0 first row where to paste in
|
||||
/// \param j0 first column where to paste in
|
||||
/// \param matrix to paste
|
||||
template <typename T>
|
||||
void matrix<T>::paste(int i0, int j0, const matrix<T>& m)
|
||||
{
|
||||
assert(i0 >= 0 && i0+m.m_rows <= m_rows &&
|
||||
j0 >= 0 && j0+m.m_cols <= m_cols);
|
||||
const T* in = m.p;
|
||||
for(int i = 0; i < m.m_rows; i++) {
|
||||
T* out = p + INDEX(i0+i, j0);
|
||||
for(int j = 0; j < m.m_cols; j++)
|
||||
*out++ = *in++;
|
||||
}
|
||||
}
|
||||
|
||||
/// Concatenate matrices.
|
||||
template <typename T>
|
||||
matrix<T> cat(const matrix<T>& m1, const matrix<T>& m2)
|
||||
{
|
||||
assert(m1.m_rows == m2.m_rows);
|
||||
matrix<T> m(m1.m_rows, m1.m_cols+m2.m_cols);
|
||||
m.paste(0, 0, m1);
|
||||
m.paste(0, m1.m_cols, m2);
|
||||
return m;
|
||||
}
|
||||
|
||||
/// Copy column number \a j.
|
||||
template <typename T>
|
||||
vector<T> matrix<T>::col(int j) const
|
||||
{
|
||||
assert(j >= 0 && j < m_cols);
|
||||
vector<T> c(m_rows);
|
||||
const T* in = p + j;
|
||||
for(int i = 0; i < m_rows; i++) {
|
||||
c(i) = *in;
|
||||
in += m_cols;
|
||||
}
|
||||
return c;
|
||||
}
|
||||
|
||||
/// Copy row number \a i.
|
||||
template <typename T>
|
||||
inline matrix<T> matrix<T>::row(int i) const
|
||||
{
|
||||
return copy(i, i, 0, lastCol());
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void swap(matrix<T>& A, matrix<T>& B)
|
||||
{
|
||||
int i=A.m_rows;
|
||||
A.m_rows = B.m_rows;
|
||||
B.m_rows = i;
|
||||
i = A.m_cols;
|
||||
A.m_cols = B.m_cols;
|
||||
B.m_cols = i;
|
||||
T* p = A.p;
|
||||
A.p = B.p;
|
||||
B.p = p;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
void matrix<T>::swapRows(int i0, int i1)
|
||||
{
|
||||
assert(0 <= i0 && i0 < m_rows &&
|
||||
0 <= i1 && i1 < m_rows);
|
||||
T* row0 = p + i0*m_cols;
|
||||
T* row1 = p + i1*m_cols;
|
||||
for(int j = m_cols-1; j >= 0; j--) {
|
||||
T tmp = *row0; *row0++ = *row1; *row1++ = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
void matrix<T>::swapCols(int j0, int j1)
|
||||
{
|
||||
assert(0 <= j0 && j0 < m_cols &&
|
||||
0 <= j1 && j1 < m_cols);
|
||||
T* col0 = p + j0;
|
||||
T* col1 = p + j1;
|
||||
for(int i = m_rows-1; i >= 0; i--) {
|
||||
T tmp = *col0; *col0 = *col1; *col1 = tmp;
|
||||
col0 += m_cols;
|
||||
col1 += m_cols;
|
||||
}
|
||||
}
|
||||
|
||||
/// Copy the array values in a matrix, row by row.
|
||||
/// \param m number of rows
|
||||
/// \param n number of columns
|
||||
/// \param v an array of scalar of size m*n
|
||||
template <typename T> template <typename U>
|
||||
void matrix<T>::read(const U* v)
|
||||
{
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
p[i] = (T)v[i];
|
||||
}
|
||||
|
||||
/// Read the coefficients from \a m.
|
||||
template <typename T>
|
||||
inline void matrix<T>::read(const matrix<T>& m)
|
||||
{
|
||||
assert(m.nElements() == nElements());
|
||||
read(m.p);
|
||||
}
|
||||
|
||||
/// Copy the matrix coefficients in an array.
|
||||
///
|
||||
/// The matrix is scanned row by row.
|
||||
template <typename T>
|
||||
void matrix<T>::write(T* vect) const
|
||||
{
|
||||
for(int i = nElements()-1; i >= 0; i--)
|
||||
vect[i] = p[i];
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
void matrix<T>::alloc(int m, int n)
|
||||
{
|
||||
assert(m > 0 && n > 0);
|
||||
m_rows = m;
|
||||
m_cols = n;
|
||||
p = new T[m*n];
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline void matrix<T>::free()
|
||||
{
|
||||
delete [] p;
|
||||
p = NULL;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline int matrix<T>::nElements() const
|
||||
{
|
||||
return m_rows*m_cols;
|
||||
}
|
||||
|
||||
/// Submatrix without row \a i0 and col \a j0.
|
||||
template <typename T>
|
||||
matrix<T>& matrix<T>::sub(matrix<T>& s, int i0, int j0) const
|
||||
{
|
||||
const T* in = p;
|
||||
T* out = s.p;
|
||||
for(int i = 0; i < i0; i++) {
|
||||
for(int j = 0; j < j0; j++)
|
||||
*out++ = *in++;
|
||||
++in; // Skip col j0
|
||||
for(int j = j0+1; j < m_cols; j++)
|
||||
*out++ = *in++;
|
||||
}
|
||||
in += m_cols; // Skip row i0
|
||||
for(int i = i0+1; i < m_rows; i++) {
|
||||
for(int j = 0; j < j0; j++)
|
||||
*out++ = *in++;
|
||||
++in; // Skip col j0
|
||||
for(int j = j0+1; j < m_cols; j++)
|
||||
*out++ = *in++;
|
||||
}
|
||||
return s;
|
||||
}
|
||||
|
||||
/// Trace.
|
||||
template <typename T>
|
||||
T matrix<T>::tr() const
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
T res = (T)0;
|
||||
for(int i = 0; i < m_rows; i++)
|
||||
res += p[i*(m_cols+1)];
|
||||
return res;
|
||||
}
|
||||
|
||||
/// Determinant. Slow, use only for small matrices.
|
||||
template <typename T>
|
||||
T matrix<T>::det() const
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
if(m_rows == 1)
|
||||
return p[0];
|
||||
if(m_rows == 2)
|
||||
return (p[0]*p[3]-p[1]*p[2]);
|
||||
T res = (T)0;
|
||||
T sign = (T)1;
|
||||
matrix<T> s(m_rows-1, m_cols-1);
|
||||
for(int j = 0; j < m_cols; j++) {
|
||||
res += sign*p[j]*sub(s,0,j).det();
|
||||
sign = -sign;
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
/// Inverse. Slow, use only for small matrices.
|
||||
template <typename T>
|
||||
matrix<T> matrix<T>::inv() const
|
||||
{
|
||||
assert(m_rows == m_cols);
|
||||
matrix<T> res(m_rows, m_cols);
|
||||
if(m_rows == 1)
|
||||
res.p[0] = (T)1/p[0];
|
||||
else {
|
||||
T d = (T)1 / det();
|
||||
T signi = (T)1;
|
||||
T* out = res.p;
|
||||
matrix<T> s(m_rows-1, m_cols-1);
|
||||
for(int i = 0; i < m_rows; i++) {
|
||||
T signj = signi;
|
||||
for(int j = 0; j < m_cols; j++) {
|
||||
*out++ = signj*d*sub(s,j,i).det();
|
||||
signj = -signj;
|
||||
}
|
||||
signi = -signi;
|
||||
}
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
} // namespace libNumerics
|
||||
|
||||
#undef INDEX
|
||||
|
||||
#endif // MATRIX_H
|
||||
175
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/matrix.h
Executable file
175
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/matrix.h
Executable file
|
|
@ -0,0 +1,175 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifndef MATRIX_H
|
||||
#define MATRIX_H
|
||||
|
||||
#include <iostream>
|
||||
#include <cassert>
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
// Forward declaration, definition below
|
||||
template <typename T> class vector;
|
||||
template <typename T> class matrix;
|
||||
|
||||
template <typename T> matrix<T> cat(const matrix<T>&, const matrix<T>&);
|
||||
template <typename T> void swap(matrix<T>&, matrix<T>&);
|
||||
|
||||
/// Matrix class
|
||||
template <typename T>
|
||||
class matrix
|
||||
{
|
||||
public:
|
||||
static matrix<T> zeros(int m) { return zeros(m,m); }
|
||||
static matrix<T> zeros(int m, int n);
|
||||
static matrix<T> ones(int m) { return ones(m,m); }
|
||||
static matrix<T> ones(int m, int n);
|
||||
static matrix<T> eye(int n); ///< Identity matrix.
|
||||
|
||||
public:
|
||||
matrix(int m, int n);
|
||||
matrix(const matrix<T>& m);
|
||||
virtual ~matrix();
|
||||
matrix<T>& operator=(const matrix<T>& m);
|
||||
|
||||
int nrow() const { return m_rows; } ///< The number of rows.
|
||||
int ncol() const { return m_cols; } ///< The number of columns.
|
||||
T operator() (int i, int j) const;
|
||||
T& operator() (int i, int j);
|
||||
T operator() (int i) const;
|
||||
T& operator() (int i);
|
||||
|
||||
void operator=(T a);
|
||||
matrix<T> operator*(T a) const;
|
||||
matrix<T> operator/(T a) const;
|
||||
void operator*=(T a);
|
||||
void operator/=(T a);
|
||||
/// Product by scalar.
|
||||
friend matrix<T> operator*(T a, const matrix<T>& m)
|
||||
{ return m * a; }
|
||||
|
||||
matrix<T> operator+(const matrix<T>& m) const;
|
||||
matrix<T> operator-(const matrix<T>& m) const;
|
||||
matrix<T> operator-() const; ///< Matrix opposite.
|
||||
matrix<T> operator*(const matrix<T>& m) const;
|
||||
vector<T> operator*(const vector<T>& m) const;
|
||||
|
||||
void operator+=(const matrix<T>& m);
|
||||
void operator-=(const matrix<T>& m);
|
||||
|
||||
matrix<T> t() const; ///< Transpose.
|
||||
vector<T> diag() const; ///< Diagonal of matrix.
|
||||
T tr() const;
|
||||
T det() const;
|
||||
matrix<T> inv() const;
|
||||
|
||||
void symUpper();
|
||||
void symLower();
|
||||
|
||||
matrix<T> copy(int i0, int i1, int j0, int j1) const;
|
||||
matrix<T> copyCols(int j0, int j1) const;
|
||||
matrix<T> copyRows(int i0, int i1) const;
|
||||
void paste(int i0, int j0, const matrix<T>& block);
|
||||
friend matrix<T> cat<T>(const matrix<T>& left, const matrix<T>& right);
|
||||
vector<T> col(int j) const; ///< Copy column.
|
||||
matrix<T> row(int i) const; ///< Copy row.
|
||||
int lastCol() const {return m_cols-1;} ///< Index of last column.
|
||||
int lastRow() const {return m_rows-1;} ///< Index of last row.
|
||||
|
||||
friend void swap<T>(matrix<T>&, matrix<T>&);
|
||||
void swapRows(int i0, int i1);
|
||||
void swapCols(int j0, int j1);
|
||||
|
||||
template <typename U>
|
||||
void read(const U* v);
|
||||
void read(const matrix<T>& v);
|
||||
void write(T* vect) const;
|
||||
|
||||
protected:
|
||||
int m_rows; ///< Number of rows.
|
||||
int m_cols; ///< Number of columns.
|
||||
T* p; ///< 1-D array of coefficients.
|
||||
|
||||
void alloc(int m, int n); ///< Allocate the array value.
|
||||
void free(); ///< Free the array value.
|
||||
int nElements() const; ///< Number of elements in the matrix.
|
||||
matrix<T>& sub(matrix<T>& s, int i, int j) const;
|
||||
}; // class matrix
|
||||
|
||||
/// Column vector class (template)
|
||||
template <typename T>
|
||||
class vector : public matrix<T>
|
||||
{
|
||||
public:
|
||||
explicit vector(int m);
|
||||
vector(T x);
|
||||
vector(T x, T y);
|
||||
vector(T x, T y, T z);
|
||||
vector(const vector<T>& v);
|
||||
virtual ~vector() {}
|
||||
using matrix<T>::operator=;
|
||||
vector<T>& operator=(const vector<T>& v);
|
||||
// void operator=(T a);
|
||||
|
||||
vector<T> operator*(T a) const;
|
||||
vector<T> operator/(T a) const;
|
||||
/// Product of a vector by a scalar.
|
||||
friend vector<T> operator*(T a, const vector<T>& v)
|
||||
{ return v * a; }
|
||||
|
||||
vector<T> operator+(const vector<T>& v) const;
|
||||
vector<T> operator-(const vector<T>& v) const;
|
||||
vector<T> operator-() const; ///< Vector opposite.
|
||||
|
||||
matrix<T> operator*(const matrix<T>& m) const;
|
||||
matrix<T> diag() const;
|
||||
T qnorm() const;
|
||||
|
||||
vector<T> copy(int i0, int i1) const;
|
||||
void paste(int i0, const vector<T>& v);
|
||||
};
|
||||
|
||||
} // namespace libNumerics
|
||||
|
||||
/// Output matrix coefficients.
|
||||
template <typename T>
|
||||
inline std::ostream& operator<<(std::ostream& out,
|
||||
const libNumerics::matrix<T>& m)
|
||||
{
|
||||
for(int i = 0; i < m.nrow(); ++i) {
|
||||
out << ((i==0)? "[": ";");
|
||||
for (int j = 0; j < m.ncol(); ++j)
|
||||
out << " " << m(i,j);
|
||||
}
|
||||
out << " ]";
|
||||
return out;
|
||||
}
|
||||
|
||||
/// Input matrix. Need to know the dimensions in advance...
|
||||
template <class T>
|
||||
inline std::istream& operator>>(std::istream& in,
|
||||
libNumerics::matrix<T>& m)
|
||||
{
|
||||
char c;
|
||||
for(int i=0; i < m.nrow(); ++i) {
|
||||
in >> c;
|
||||
for(int j=0; j < m.ncol(); ++j)
|
||||
in >> m(i,j);
|
||||
}
|
||||
in >> c;
|
||||
return in;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
T dot(const libNumerics::vector<T>& u, const libNumerics::vector<T>& v);
|
||||
template <typename T>
|
||||
libNumerics::vector<T> cross(const libNumerics::vector<T>& u,
|
||||
const libNumerics::vector<T>& v);
|
||||
|
||||
// Need to see definitions for templates...
|
||||
#include "matrix.cpp"
|
||||
#include "vector.cpp"
|
||||
|
||||
#endif
|
||||
487
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/numerics.cpp
Executable file
487
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/numerics.cpp
Executable file
|
|
@ -0,0 +1,487 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#include "numerics.h"
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
#include <limits>
|
||||
#include <algorithm>
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
const flnum MinLM::DEFAULT_RELATIVE_TOL = 1E-3;
|
||||
const flnum MinLM::DEFAULT_LAMBDA_INIT = 1E-3;
|
||||
const flnum MinLM::DEFAULT_LAMBDA_FACT = 10.0;
|
||||
const flnum MinLM::EPSILON_KERNEL = 1E-9;
|
||||
|
||||
inline flnum ABS(flnum x)
|
||||
{ return (x >= 0)? x: -x; }
|
||||
|
||||
/// Resolution by LU decomposition with pivot.
|
||||
bool solveLU(const matrix<flnum>& A, const vector<flnum>& B, vector<flnum>& X)
|
||||
{
|
||||
X = B;
|
||||
return solveLU(A, X);
|
||||
}
|
||||
|
||||
/// Replace X by A^{-1}X, by LU solver.
|
||||
bool solveLU(matrix<flnum> A, vector<flnum>& X)
|
||||
{
|
||||
assert(A.nrow() == A.ncol());
|
||||
int n = A.nrow();
|
||||
vector<flnum> rowscale(n); // Implicit scaling of each row
|
||||
std::vector<int> permut(n,0); // Permutation of rows
|
||||
|
||||
// Get the implicit scaling information of each row
|
||||
for(int i=0; i< n; i++) {
|
||||
flnum max = 0.0;
|
||||
for(int j=0; j< n; j++) {
|
||||
flnum tmp = ABS(A(i,j));
|
||||
if (tmp> max)
|
||||
max = tmp;
|
||||
}
|
||||
if(max == 0.0)
|
||||
return false;
|
||||
rowscale(i) = 1.0/max;
|
||||
}
|
||||
// Perform the decomposition
|
||||
for(int k=0; k < n; k++) {
|
||||
// Search for largest pivot element
|
||||
flnum max = rowscale(k)*ABS(A(k,k));
|
||||
int imax = k;
|
||||
for(int i=k+1; i < n; i++) {
|
||||
flnum tmp = rowscale(i)*ABS(A(i,k));
|
||||
if(tmp > max) {
|
||||
max = tmp;
|
||||
imax = i;
|
||||
}
|
||||
}
|
||||
if(max == 0.0)
|
||||
return false;
|
||||
|
||||
// Interchange rows if needed
|
||||
if(k != imax) {
|
||||
A.swapRows(k, imax);
|
||||
rowscale(imax) = rowscale(k); // Scale of row k no longer needed
|
||||
}
|
||||
permut[k] = imax; // permut(k) was not initialized before
|
||||
flnum Akk = 1/A(k,k);
|
||||
for(int i=k+1; i < n; i++) {
|
||||
flnum tmp = A(i,k) *= Akk; // Divide by pivot
|
||||
for (int j=k+1;j < n; j++) // Reduce the row
|
||||
A(i,j) -= tmp*A(k,j);
|
||||
}
|
||||
}
|
||||
// Forward substitution
|
||||
for (int k=0; k < n; k++) {
|
||||
flnum sum = X(permut[k]);
|
||||
X(permut[k]) = X(k);
|
||||
for(int j = 0; j < k; j++)
|
||||
sum -= A(k,j)*X(j);
|
||||
X(k) = sum;
|
||||
}
|
||||
// Backward substitution
|
||||
for(int k=n-1; k >= 0; k--) {
|
||||
flnum sum = X(k);
|
||||
for(int j=k+1; j < n; j++)
|
||||
sum -= A(k,j)*X(j);
|
||||
X(k) = sum/A(k,k);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
/// Decompose A into U diag(W) V^T with U(m,n) and V(n,n) having orthonormal
|
||||
/// vectors.
|
||||
SVD::SVD(const matrix<flnum>& A)
|
||||
: m_U(A), m_V(A.ncol(),A.ncol()), m_W(A.ncol())
|
||||
{
|
||||
compute();
|
||||
sort();
|
||||
}
|
||||
|
||||
/// SVD computation. Initial matrix stored in m_U as input.
|
||||
void SVD::compute()
|
||||
{
|
||||
const flnum EPSILON = std::numeric_limits<flnum>::epsilon();
|
||||
const int SVD_MAX_ITS = 30;
|
||||
|
||||
int rows = m_U.nrow();
|
||||
int cols = m_U.ncol();
|
||||
flnum g, scale, anorm;
|
||||
vector<flnum> RV1(cols);
|
||||
|
||||
// Householder reduction to bidiagonal form:
|
||||
anorm = g = scale = 0.0;
|
||||
for (int i=0; i< cols; i++) {
|
||||
int l = i + 1;
|
||||
RV1(i) = scale*g;
|
||||
g = scale = 0.0;
|
||||
if(i< rows) {
|
||||
for (int k=i; k< rows; k++)
|
||||
scale += ABS(m_U(k,i));
|
||||
if (scale != 0.0) {
|
||||
flnum invScale=1.0/scale, s=0.0;
|
||||
for (int k=i; k< rows; k++) {
|
||||
m_U(k,i) *= invScale;
|
||||
s += m_U(k,i) * m_U(k,i);
|
||||
}
|
||||
flnum f = m_U(i,i);
|
||||
g = - withSignOf(std::sqrt(s),f);
|
||||
flnum h = 1.0 / (f*g - s);
|
||||
m_U(i,i) = f - g;
|
||||
for (int j=l; j< cols; j++) {
|
||||
s = 0.0;
|
||||
for (int k=i; k< rows; k++)
|
||||
s += m_U(k,i) * m_U(k,j);
|
||||
f = s * h;
|
||||
for (int k=i; k< rows; k++)
|
||||
m_U(k,j) += f * m_U(k,i);
|
||||
}
|
||||
for (int k=i; k< rows; k++)
|
||||
m_U(k,i) *= scale;
|
||||
}
|
||||
}
|
||||
m_W(i) = scale * g;
|
||||
g = scale = 0.0;
|
||||
if ( i< rows && i< cols-1 ) {
|
||||
for (int k=l; k< cols; k++)
|
||||
scale += ABS(m_U(i,k));
|
||||
if (scale != 0.0) {
|
||||
flnum invScale=1.0/scale, s=0.0;
|
||||
for (int k=l; k< cols; k++) {
|
||||
m_U(i,k) *= invScale;
|
||||
s += m_U(i,k) * m_U(i,k);
|
||||
}
|
||||
flnum f = m_U(i,l);
|
||||
g = - withSignOf(std::sqrt(s),f);
|
||||
flnum h = 1.0 / (f*g - s);
|
||||
m_U(i,l) = f - g;
|
||||
for (int k=l; k< cols; k++)
|
||||
RV1(k) = m_U(i,k) * h;
|
||||
for (int j=l; j< rows; j++) {
|
||||
s = 0.0;
|
||||
for (int k=l; k< cols; k++)
|
||||
s += m_U(j,k) * m_U(i,k);
|
||||
for (int k=l; k< cols; k++)
|
||||
m_U(j,k) += s * RV1(k);
|
||||
}
|
||||
for (int k=l; k< cols; k++)
|
||||
m_U(i,k) *= scale;
|
||||
}
|
||||
}
|
||||
anorm = std::max(anorm, ABS(m_W(i)) + ABS(RV1(i)) );
|
||||
}
|
||||
|
||||
// Accumulation of right-hand transformations:
|
||||
m_V(cols-1,cols-1) = 1.0;
|
||||
for (int i= cols-2; i>=0; i--) {
|
||||
m_V(i,i) = 1.0;
|
||||
int l = i+1;
|
||||
g = RV1(l);
|
||||
if (g != 0.0) {
|
||||
flnum invgUil = 1.0 / (m_U(i,l)*g);
|
||||
for (int j=l; j< cols; j++)
|
||||
m_V(j,i) = m_U(i,j) * invgUil;
|
||||
for (int j=l; j< cols; j++){
|
||||
flnum s = 0.0;
|
||||
for (int k=l; k< cols; k++)
|
||||
s += m_U(i,k) * m_V(k,j);
|
||||
for (int k=l; k< cols; k++)
|
||||
m_V(k,j) += s * m_V(k,i);
|
||||
}
|
||||
}
|
||||
for (int j=l; j< cols; j++)
|
||||
m_V(i,j) = m_V(j,i) = 0.0;
|
||||
}
|
||||
|
||||
// Accumulation of left-hand transformations:
|
||||
for (int i=std::min(rows,cols)-1; i>=0; i--) {
|
||||
int l = i+1;
|
||||
g = m_W(i);
|
||||
for (int j=l; j< cols; j++)
|
||||
m_U(i,j) = 0.0;
|
||||
if (g != 0.0) {
|
||||
g = 1.0 / g;
|
||||
flnum invUii = 1.0 / m_U(i,i);
|
||||
for (int j=l; j< cols; j++) {
|
||||
flnum s = 0.0;
|
||||
for (int k=l; k< rows; k++)
|
||||
s += m_U(k,i) * m_U(k,j);
|
||||
flnum f = (s * invUii) * g;
|
||||
for (int k=i; k< rows; k++)
|
||||
m_U(k,j) += f * m_U(k,i);
|
||||
}
|
||||
for (int j=i; j< rows; j++)
|
||||
m_U(j,i) *= g;
|
||||
} else
|
||||
for (int j=i; j< rows; j++)
|
||||
m_U(j,i) = 0.0;
|
||||
m_U(i,i) = m_U(i,i) + 1.0;
|
||||
}
|
||||
|
||||
// Diagonalization of the bidiagonal form:
|
||||
for (int k=cols-1; k>=0; k--) { // Loop over singular values
|
||||
for (int its=1; its<=SVD_MAX_ITS; its++) {
|
||||
bool flag = false;
|
||||
int l = k;
|
||||
int nm = k-1;
|
||||
while(l>0 && ABS(RV1(l)) > EPSILON*anorm) { // Test for splitting
|
||||
if(ABS(m_W(nm)) <= EPSILON*anorm) {
|
||||
flag = true;
|
||||
break;
|
||||
}
|
||||
l--;
|
||||
nm--;
|
||||
}
|
||||
if (flag) { // Cancellation of RV1(l), if l > 0
|
||||
flnum c=0.0, s=1.0;
|
||||
for (int i=l; i< k+1; i++) {
|
||||
flnum f = s * RV1(i);
|
||||
RV1(i) = c * RV1(i);
|
||||
if (ABS(f)<=EPSILON*anorm)
|
||||
break;
|
||||
g = m_W(i);
|
||||
flnum h = SVD::hypot(f,g);
|
||||
m_W(i) = h;
|
||||
h = 1.0 / h;
|
||||
c = g * h;
|
||||
s = - f * h;
|
||||
for (int j=0; j< rows; j++)
|
||||
rotate(m_U(j,nm),m_U(j,i), c,s);
|
||||
}
|
||||
}
|
||||
flnum z = m_W(k);
|
||||
if (l==k) { // Convergence of the singular value
|
||||
if (z< 0.0) { // Singular value is made nonnegative
|
||||
m_W(k) = -z;
|
||||
for (int j=0; j< cols; j++)
|
||||
m_V(j,k) = - m_V(j,k);
|
||||
}
|
||||
break;
|
||||
}
|
||||
// Exception if convergence to the singular value not reached:
|
||||
if(its==SVD_MAX_ITS) throw SvdConvergenceError();
|
||||
flnum x = m_W(l); // Get QR shift value from bottom 2x2 minor
|
||||
nm = k-1;
|
||||
flnum y = m_W(nm);
|
||||
g = RV1(nm);
|
||||
flnum h = RV1(k);
|
||||
flnum f = ( (y-z)*(y+z) + (g-h)*(g+h) ) / ( 2.0*h*y );
|
||||
g = SVD::hypot(f,1.0);
|
||||
f = ( (x-z)*(x+z) + h*(y/(f+withSignOf(g,f)) - h) ) / x;
|
||||
// Next QR transformation (through Givens reflections)
|
||||
flnum c=1.0, s=1.0;
|
||||
for (int j=l; j<=nm; j++) {
|
||||
int i = j+1;
|
||||
g = RV1(i);
|
||||
y = m_W(i);
|
||||
h = s * g;
|
||||
g = c * g;
|
||||
z = SVD::hypot(f,h);
|
||||
RV1(j) = z;
|
||||
z = 1.0 / z;
|
||||
c = f * z;
|
||||
s = h * z;
|
||||
f = x*c + g*s;
|
||||
g = g*c - x*s;
|
||||
h = y * s;
|
||||
y *= c;
|
||||
for(int jj=0; jj < cols; jj++)
|
||||
rotate(m_V(jj,j),m_V(jj,i), c,s);
|
||||
z = SVD::hypot(f,h);
|
||||
m_W(j) = z;
|
||||
if (z!=0.0) { // Rotation can be arbitrary if z = 0.0
|
||||
z = 1.0 / z;
|
||||
c = f * z;
|
||||
s = h * z;
|
||||
}
|
||||
f = c*g + s*y;
|
||||
x = c*y - s*g;
|
||||
for(int jj=0; jj < rows; jj++)
|
||||
rotate(m_U(jj,j),m_U(jj,i), c,s);
|
||||
}
|
||||
RV1(l) = 0.0;
|
||||
RV1(k) = f;
|
||||
m_W(k) = x;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/// Recompose from SVD. This should be the initial matrix.
|
||||
matrix<flnum> SVD::compose() const
|
||||
{
|
||||
return m_U * m_W.diag() * m_V.t();
|
||||
}
|
||||
|
||||
flnum SVD::withSignOf(flnum a, flnum b)
|
||||
{ return b >= 0 ? (a >= 0 ? a : -a) : (a >= 0 ? -a : a); }
|
||||
|
||||
/// Replace hypot of math.h by robust numeric implementation.
|
||||
flnum SVD::hypot(flnum a, flnum b)
|
||||
{
|
||||
a = ABS(a);
|
||||
b = ABS(b);
|
||||
if(a > b) {
|
||||
b /= a;
|
||||
return a*std::sqrt(1.0 + b*b);
|
||||
} else if(b) {
|
||||
a /= b;
|
||||
return b*std::sqrt(1.0 + a*a);
|
||||
}
|
||||
return 0.0;
|
||||
}
|
||||
|
||||
/// Utility function used while computing SVD.
|
||||
void SVD::rotate(flnum& a, flnum& b, flnum c, flnum s)
|
||||
{
|
||||
flnum d = a;
|
||||
a = +d*c +b*s;
|
||||
b = -d*s +b*c;
|
||||
}
|
||||
|
||||
class SVDElement {
|
||||
public:
|
||||
SVDElement(const vector<flnum>& W, int i)
|
||||
: m_val(W(i)), m_i(i) {}
|
||||
bool operator<(const SVDElement& e) const
|
||||
{ return (m_val>e.m_val); }
|
||||
|
||||
flnum m_val;
|
||||
int m_i;
|
||||
};
|
||||
|
||||
/// Sort SVD by decreasing order of singular value.
|
||||
void SVD::sort()
|
||||
{
|
||||
std::vector<SVDElement> vec;
|
||||
for(int i=0; i < m_U.ncol(); i++)
|
||||
vec.push_back( SVDElement(m_W, i) );
|
||||
std::sort(vec.begin(), vec.end());
|
||||
// Apply permutation
|
||||
for(int i=m_U.ncol()-1; i >=0; i--)
|
||||
if(vec[i].m_i != i) { // Find cycle of i
|
||||
const vector<flnum> colU = m_U.col(i);
|
||||
const vector<flnum> colV = m_V.col(i);
|
||||
const flnum w = m_W(i);
|
||||
int j = i;
|
||||
while(vec[j].m_i != i) {
|
||||
m_U.paste(0,j, m_U.col(vec[j].m_i));
|
||||
m_V.paste(0,j, m_V.col(vec[j].m_i));
|
||||
m_W(j) = m_W(vec[j].m_i);
|
||||
std::swap(j,vec[j].m_i);
|
||||
}
|
||||
vec[j].m_i = j;
|
||||
m_U.paste(0,j, colU);
|
||||
m_V.paste(0,j, colV);
|
||||
m_W(j) = w;
|
||||
}
|
||||
}
|
||||
|
||||
/// Constructor.
|
||||
MinLM::MinLM()
|
||||
: iterations(0), relativeTol(DEFAULT_RELATIVE_TOL),
|
||||
lambdaInit(DEFAULT_LAMBDA_INIT), lambdaFact(DEFAULT_LAMBDA_FACT)
|
||||
{}
|
||||
|
||||
/// In equation JtJ X = B, remove columns of J close to 0, so that JtJ can be
|
||||
/// invertible
|
||||
void MinLM::compress(matrix<flnum>& JtJ, vector<flnum>& B)
|
||||
{
|
||||
flnum max=0;
|
||||
for(int i=0; i < JtJ.nrow(); i++)
|
||||
if(JtJ(i,i) > max)
|
||||
max = JtJ(i,i);
|
||||
max *= EPSILON_KERNEL;
|
||||
m_nullCols.clear();
|
||||
for(int i=0; i < JtJ.nrow(); i++)
|
||||
if(JtJ(i,i) <= max)
|
||||
m_nullCols.push_back(i);
|
||||
if( m_nullCols.empty() )
|
||||
return;
|
||||
int n=(int)m_nullCols.size();
|
||||
matrix<flnum> JtJ2(JtJ.nrow()-m_nullCols.size(),
|
||||
JtJ.ncol()-m_nullCols.size());
|
||||
vector<flnum> B2(B.nrow()-(int)m_nullCols.size());
|
||||
for(int i=0,i2=0; i < JtJ.nrow(); i++) {
|
||||
if(i-i2 < n && m_nullCols[i-i2]==i)
|
||||
continue;
|
||||
for(int j=0,j2=0; j < JtJ.ncol(); j++) {
|
||||
if(j-j2 < n && m_nullCols[j-j2]==j)
|
||||
continue;
|
||||
JtJ2(i2,j2) = JtJ(i,j);
|
||||
j2++;
|
||||
}
|
||||
B2(i2) = B(i);
|
||||
i2++;
|
||||
}
|
||||
swap(JtJ,JtJ2);
|
||||
swap(B,B2);
|
||||
}
|
||||
|
||||
/// Insert 0 in rows of B that were removed by \c compress()
|
||||
void MinLM::uncompress(vector<flnum>& B)
|
||||
{
|
||||
if(m_nullCols.empty())
|
||||
return;
|
||||
int n=(int)m_nullCols.size();
|
||||
vector<flnum> B2(B.nrow()+(int)m_nullCols.size());
|
||||
for(int i=0,i2=0; i2 < B2.nrow(); i2++)
|
||||
if(i2-i < n && m_nullCols[i2-i]==i2)
|
||||
B2(i2)=0;
|
||||
else
|
||||
B2(i2) = B(i++);
|
||||
swap(B,B2);
|
||||
}
|
||||
|
||||
/// Perform minimization.
|
||||
/// \a targetRMSE is the root mean square error aimed at.
|
||||
/// Return the reached RMSE. Since the class does not know the dimension, the
|
||||
/// real RMSE should be this value multiplied by sqrt(dim). For example, for 2-D
|
||||
/// points this would be sqrt(2) times the returned value.
|
||||
flnum MinLM::minimize(vector<flnum>& P, const vector<flnum>& yData,
|
||||
flnum targetRMSE, int maxIters)
|
||||
{
|
||||
flnum errorMax = targetRMSE*targetRMSE*yData.nrow();
|
||||
vector<flnum> yModel( yData.nrow() );
|
||||
modelData(P, yModel);
|
||||
vector<flnum> E( yData-yModel );
|
||||
flnum error = E.qnorm();
|
||||
matrix<flnum> J( yData.nrow(), P.nrow() );
|
||||
modelJacobian(P, J);
|
||||
matrix<flnum> Jt = J.t();
|
||||
matrix<flnum> JtJ = Jt*J;
|
||||
vector<flnum> B = Jt*E;
|
||||
compress(JtJ, B);
|
||||
|
||||
flnum lambda = lambdaInit;
|
||||
for(iterations=0; iterations < maxIters && error > errorMax; iterations++) {
|
||||
matrix<flnum> H(JtJ);
|
||||
for(int i = 0; i < H.nrow(); i++)
|
||||
H(i,i) *= 1+lambda;
|
||||
vector<flnum> dP( P.nrow() );
|
||||
solveLU(H, B, dP);
|
||||
uncompress(dP);
|
||||
vector<flnum> tryP = P + dP;
|
||||
modelData(tryP, yModel);
|
||||
E = yData - yModel;
|
||||
flnum tryError = E.qnorm();
|
||||
if(ABS(tryError-error) <= relativeTol*error)
|
||||
break;
|
||||
if(tryError > error)
|
||||
lambda *= lambdaFact;
|
||||
else {
|
||||
lambda /= lambdaFact;
|
||||
error = tryError;
|
||||
P = tryP;
|
||||
modelJacobian(P, J);
|
||||
Jt = J.t();
|
||||
JtJ = Jt*J;
|
||||
B = Jt*E;
|
||||
compress(JtJ, B);
|
||||
}
|
||||
}
|
||||
return sqrt(error/yData.nrow());
|
||||
}
|
||||
|
||||
} // namespace libNumerics
|
||||
66
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/numerics.h
Executable file
66
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/numerics.h
Executable file
|
|
@ -0,0 +1,66 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifndef NUMERICS_H
|
||||
#define NUMERICS_H
|
||||
|
||||
#include "matrix.h"
|
||||
#include <vector>
|
||||
|
||||
namespace libNumerics {
|
||||
class NumericsException {};
|
||||
class SvdConvergenceError : public NumericsException {};
|
||||
typedef double flnum;
|
||||
|
||||
/// Solve system AX = B.
|
||||
bool solveLU(const matrix<flnum>& A, const vector<flnum>& B,
|
||||
vector<flnum>& X);
|
||||
bool solveLU(matrix<flnum> A, vector<flnum>& B);
|
||||
|
||||
/// Singular Value Decomposition
|
||||
class SVD {
|
||||
public:
|
||||
SVD(const matrix<flnum>& A);
|
||||
matrix<flnum>& U() { return m_U; }
|
||||
vector<flnum>& W() { return m_W; }
|
||||
matrix<flnum>& V() { return m_V; }
|
||||
matrix<flnum> compose() const;
|
||||
|
||||
private:
|
||||
matrix<flnum> m_U, m_V;
|
||||
vector<flnum> m_W;
|
||||
static flnum withSignOf(flnum a, flnum b);
|
||||
static flnum hypot(flnum a, flnum b);
|
||||
static void rotate(flnum& a, flnum& b, flnum c, flnum s);
|
||||
void compute();
|
||||
void sort();
|
||||
};
|
||||
|
||||
/// Levenberg-Marquardt minimization.
|
||||
class MinLM {
|
||||
static const flnum DEFAULT_RELATIVE_TOL;
|
||||
static const flnum DEFAULT_LAMBDA_INIT;
|
||||
static const flnum DEFAULT_LAMBDA_FACT;
|
||||
static const flnum EPSILON_KERNEL;
|
||||
public:
|
||||
MinLM();
|
||||
flnum minimize(vector<flnum>& P, const vector<flnum>& ydata,
|
||||
flnum targetRMSE=0.1, int maxIters=300);
|
||||
virtual void modelData(const vector<flnum>& P,
|
||||
vector<flnum>& ymodel) const = 0;
|
||||
virtual void modelJacobian(const vector<flnum>& P,
|
||||
matrix<flnum>& J) const = 0;
|
||||
int iterations;
|
||||
flnum relativeTol;
|
||||
flnum lambdaInit;
|
||||
flnum lambdaFact;
|
||||
private:
|
||||
std::vector<int> m_nullCols;
|
||||
void compress(matrix<flnum>& JtJ, vector<flnum>& B);
|
||||
void uncompress(vector<flnum>& B);
|
||||
};
|
||||
|
||||
} // namespace libNumerics
|
||||
|
||||
#endif
|
||||
55
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/rodrigues.cpp
Executable file
55
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/rodrigues.cpp
Executable file
|
|
@ -0,0 +1,55 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifdef RODRIGUES_H
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
template <class T>
|
||||
matrix<T> skew(const vector<T>& v)
|
||||
{
|
||||
assert(v.nrow() == 3);
|
||||
matrix<T> M(3,3);
|
||||
M(0,0) = M(1,1) = M(2,2) = 0;
|
||||
M(1,2) = -(M(2,1)=v(0));
|
||||
M(2,0) = -(M(0,2)=v(1));
|
||||
M(0,1) = -(M(1,0)=v(2));
|
||||
return M;
|
||||
}
|
||||
|
||||
template <class T>
|
||||
matrix<T> rotation(vector<T> w)
|
||||
{
|
||||
assert(w.nrow() == 3);
|
||||
T n = sqrt(w.qnorm());
|
||||
T c = cos(n);
|
||||
matrix<T> R = c*matrix<T>::eye(3);
|
||||
if(n) {
|
||||
w /= n;
|
||||
R += skew(sin(n)*w);
|
||||
R += (1-c)*w*w.t();
|
||||
}
|
||||
return R;
|
||||
}
|
||||
|
||||
template <class T>
|
||||
vector<T> rotationAxis(const matrix<T>& R)
|
||||
{
|
||||
assert(R.nrow() == 3 && R.ncol() == 3);
|
||||
vector<T> w(3);
|
||||
T n = acos(0.5*(R.tr()-1));
|
||||
if(n == 0)
|
||||
w = 0;
|
||||
else {
|
||||
w(0) = R(2,1)-R(1,2);
|
||||
w(1) = R(0,2)-R(2,0);
|
||||
w(2) = R(1,0)-R(0,1);
|
||||
w *= n/(2*sin(n));
|
||||
}
|
||||
return w;
|
||||
}
|
||||
|
||||
} // libNumerics
|
||||
|
||||
#endif // RODRIGUES_H
|
||||
24
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/rodrigues.h
Executable file
24
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/rodrigues.h
Executable file
|
|
@ -0,0 +1,24 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifndef RODRIGUES_H
|
||||
#define RODRIGUES_H
|
||||
|
||||
#include "matrix.h"
|
||||
#include <math.h>
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// Skew-symmetric matrix of 3-vector v.
|
||||
template <class T> matrix<T> skew(const vector<T>& v);
|
||||
/// Rodrigues's rotation: exp(w_x).
|
||||
template <class T> matrix<T> rotation(vector<T> w);
|
||||
/// Inverse Rodrigues's formula: w s.t. R=exp(w_x).
|
||||
template <class T> vector<T> rotationAxis(const matrix<T>& R);
|
||||
|
||||
} // libNumerics
|
||||
|
||||
#include "rodrigues.cpp"
|
||||
|
||||
#endif
|
||||
179
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/vector.cpp
Executable file
179
ongoing/ASIFT_tests/demo_ASIFT_src/libNumerics/vector.cpp
Executable file
|
|
@ -0,0 +1,179 @@
|
|||
// Authors: Unknown. Please, if you are the author of this file, or if you
|
||||
// know who are the authors of this file, let us know, so we can give the
|
||||
// adequate credits and/or get the adequate authorizations.
|
||||
|
||||
#ifdef MATRIX_H // Do nothing if not included from matrix.h
|
||||
|
||||
namespace libNumerics {
|
||||
|
||||
/// Constructor
|
||||
template <typename T>
|
||||
vector<T>::vector(int m)
|
||||
: matrix<T>(m, 1)
|
||||
{}
|
||||
|
||||
/// 1-vector constructor.
|
||||
template <typename T>
|
||||
vector<T>::vector(T x)
|
||||
: matrix<T>(1,1)
|
||||
{
|
||||
this->p[0] = x;
|
||||
}
|
||||
|
||||
/// 2-vector constructor.
|
||||
template <typename T>
|
||||
vector<T>::vector(T x, T y)
|
||||
: matrix<T>(2,1)
|
||||
{
|
||||
this->p[0] = x;
|
||||
this->p[1] = y;
|
||||
}
|
||||
|
||||
/// 3-vector constructor.
|
||||
template <typename T>
|
||||
vector<T>::vector(T x, T y, T z)
|
||||
: matrix<T>(3,1)
|
||||
{
|
||||
this->p[0] = x;
|
||||
this->p[1] = y;
|
||||
this->p[2] = z;
|
||||
}
|
||||
|
||||
/// Copy constructor
|
||||
template <typename T>
|
||||
vector<T>::vector(const vector<T>& v)
|
||||
: matrix<T>(v)
|
||||
{}
|
||||
|
||||
/// Assignment operator
|
||||
template <typename T>
|
||||
vector<T>& vector<T>::operator=(const vector<T>& v)
|
||||
{
|
||||
matrix<T>::operator=(v);
|
||||
return *this;
|
||||
}
|
||||
|
||||
/// Multiply a vector by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
vector<T> vector<T>::operator*(T a) const
|
||||
{
|
||||
vector<T> v(this->m_rows);
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
v.p[i] = a*this->p[i];
|
||||
return v;
|
||||
}
|
||||
|
||||
/// Divide a vector by scalar.
|
||||
/// \param a a scalar.
|
||||
template <typename T>
|
||||
inline vector<T> vector<T>::operator/(T a) const
|
||||
{
|
||||
return operator*( (T)1/a );
|
||||
}
|
||||
|
||||
/// Addition of vectors.
|
||||
template <typename T>
|
||||
vector<T> vector<T>::operator+(const vector<T>& v) const
|
||||
{
|
||||
assert(this->m_rows == v.m_rows);
|
||||
vector<T> sum(this->m_rows);
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
sum.p[i] = this->p[i] + v.p[i];
|
||||
return sum;
|
||||
}
|
||||
|
||||
/// Subtraction of vectors.
|
||||
template <typename T>
|
||||
vector<T> vector<T>::operator-(const vector<T>& v) const
|
||||
{
|
||||
assert(this->m_rows == v.m_rows);
|
||||
vector<T> sub(this->m_rows);
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
sub.p[i] = this->p[i] - v.p[i];
|
||||
return sub;
|
||||
}
|
||||
|
||||
/// Opposite of vector.
|
||||
template <typename T>
|
||||
vector<T> vector<T>::operator-() const
|
||||
{
|
||||
vector<T> v(this->m_rows);
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
v.p[i] = -this->p[i];
|
||||
return v;
|
||||
}
|
||||
|
||||
/// Vector times matrix.
|
||||
template <typename T>
|
||||
matrix<T> vector<T>::operator*(const matrix<T>& m) const
|
||||
{
|
||||
return matrix<T>::operator*(m);
|
||||
}
|
||||
|
||||
/// Diagonal matrix defined by its diagonal vector.
|
||||
template <typename T>
|
||||
matrix<T> vector<T>::diag() const
|
||||
{
|
||||
matrix<T> d(this->m_rows, this->m_rows);
|
||||
d = (T)0;
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
d(i,i) = this->p[i];
|
||||
return d;
|
||||
}
|
||||
|
||||
/// Square L^2 norm of vector.
|
||||
template <typename T>
|
||||
T vector<T>::qnorm() const
|
||||
{
|
||||
T q = (T)0;
|
||||
for(int i = this->m_rows-1; i >= 0; i--)
|
||||
q += this->p[i]*this->p[i];
|
||||
return q;
|
||||
}
|
||||
|
||||
/// Subvector from \a i0 to \a i1.
|
||||
template <typename T>
|
||||
vector<T> vector<T>::copy(int i0, int i1) const
|
||||
{
|
||||
assert(0 <= i0 && i0 <= i1 && i1 <= this->m_rows);
|
||||
vector<T> v(i1-i0+1);
|
||||
for(int i=i0; i <= i1; i++)
|
||||
v.p[i-i0] = this->p[i];
|
||||
return v;
|
||||
}
|
||||
|
||||
/// Paste vector \a v from row i0.
|
||||
template <typename T>
|
||||
void vector<T>::paste(int i0, const vector<T>& v)
|
||||
{
|
||||
matrix<T>::paste(i0, 0, v);
|
||||
}
|
||||
|
||||
} // namespace libNumerics
|
||||
|
||||
/// Scalar product.
|
||||
template <typename T>
|
||||
T dot(const libNumerics::vector<T>& u, const libNumerics::vector<T>& v)
|
||||
{
|
||||
assert(u.nrow() == v.nrow());
|
||||
T d = (T)0;
|
||||
for(int i = u.nrow()-1; i >= 0; i--)
|
||||
d += u(i)*v(i);
|
||||
return d;
|
||||
}
|
||||
|
||||
/// Cross product.
|
||||
template <typename T>
|
||||
libNumerics::vector<T> cross(const libNumerics::vector<T>& u,
|
||||
const libNumerics::vector<T>& v)
|
||||
{
|
||||
assert(u.nrow() == 3 && v.nrow() == 3);
|
||||
libNumerics::vector<T> w(3);
|
||||
w(0) = u(1)*v(2) - u(2)*v(1);
|
||||
w(1) = u(2)*v(0) - u(0)*v(2);
|
||||
w(2) = u(0)*v(1) - u(1)*v(0);
|
||||
return w;
|
||||
}
|
||||
|
||||
#endif // MATRIX_H
|
||||
Loading…
Add table
Add a link
Reference in a new issue