GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-05-02 00:34:14 +08:00
Code Issues Packages Projects Releases Wiki Activity

include the fixes of the third edition

Browse Source
This commit is contained in:
Gael Guennebaud 2009-07-06 15:01:30 +02:00
parent 0c2232e5d9
commit f84bd3e7b1
1 changed files with 66 additions and 63 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

129
Eigen/src/SVD/SVD.h
View File

@ -111,7 +111,7 @@ template<typename MatrixType> class SVD
protected:
// Computes (a^2 + b^2)^(1/2) without destructive underflow or overflow.
inline static Scalar pythagora(Scalar a, Scalar b)
inline static Scalar pythag(Scalar a, Scalar b)
{
Scalar abs_a = ei_abs(a);
Scalar abs_b = ei_abs(b);
@ -138,14 +138,13 @@ template<typename MatrixType> class SVD
/** Computes / recomputes the SVD decomposition A = U S V^* of \a matrix
*
* \note this code has been adapted from Numerical Recipes, second edition.
* \note this code has been adapted from Numerical Recipes, third edition.
*/
template<typename MatrixType>
void SVD<MatrixType>::compute(const MatrixType& matrix)
{
const int m = matrix.rows();
const int n = matrix.cols();
const int nu = std::min(m,n);
m_matU.resize(m, m);
m_matU.setZero();
@ -158,22 +157,24 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
MatrixType A = matrix;
SingularValuesType& W = m_sigma;
int flag,i,its,j,jj,k,l,nm;
bool flag;
int i,its,j,jj,k,l,nm;
Scalar anorm, c, f, g, h, s, scale, x, y, z;
bool convergence = true;
Scalar eps = precision<Scalar>();
Matrix<Scalar,Dynamic,1> rv1(n);
g = scale = anorm = 0;
// Householder reduction to bidiagonal form.
for (i=0; i<n; i++)
{
l = i+1;
l = i+2;
rv1[i] = scale*g;
g = s = scale = 0.0;
if (i < m)
{
scale = A.col(i).end(m-i).cwise().abs().sum();
if (scale)
if (scale != Scalar(0))
{
for (k=i; k<m; k++)
{
@ -184,7 +185,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
g = -sign( ei_sqrt(s), f );
h = f*g - s;
A(i, i)=f-g;
for (j=l; j<n; j++)
for (j=l-1; j<n; j++)
{
s = A.col(i).end(m-i).dot(A.col(j).end(m-i));
f = s/h;
@ -193,43 +194,42 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
A.col(i).end(m-i) *= scale;
}
}
W[i] = scale *g;
W[i] = scale * g;
g = s = scale = 0.0;
if (i < m && i != (n-1))
if (i+1 <= m && i+1 != n)
{
scale = A.row(i).end(n-l).cwise().abs().sum();
if (scale)
scale = A.row(i).end(n-l+1).cwise().abs().sum();
if (scale != Scalar(0))
{
for (k=l; k<n; k++)
for (k=l-1; k<n; k++)
{
A(i, k) /= scale;
s += A(i, k)*A(i, k);
}
f = A(i, l);
f = A(i,l-1);
g = -sign(ei_sqrt(s),f);
h = f*g - s;
A(i, l) = f-g;
for (k=l; k<n; k++)
rv1[k] = A(i, k)/h;
for (j=l; j<m; j++)
A(i,l-1) = f-g;
rv1.end(n-l+1) = A.row(i).end(n-l+1)/h;
for (j=l-1; j<m; j++)
{
s = A.row(j).end(n-l).dot(A.row(i).end(n-l));
A.row(j).end(n-l) += s*rv1.end(n-l).transpose();
s = A.row(j).end(n-l+1).dot(A.row(i).end(n-l+1));
A.row(j).end(n-l+1) += s*rv1.end(n-l+1).transpose();
}
A.row(i).end(n-l) *= scale;
A.row(i).end(n-l+1) *= scale;
}
}
anorm = std::max( anorm, (ei_abs(W[i])+ei_abs(rv1[i])) );
}
// Accumulation of right-hand transformations.
for (i=(n-1); i>=0; i--)
for (i=n-1; i>=0; i--)
{
//Accumulation of right-hand transformations.
if (i < (n-1))
if (i < n-1)
{
if (g)
if (g != Scalar(0.0))
{
for (j=l; j<n;j++) //Double division to avoid possible underflow.
for (j=l; j<n; j++) //Double division to avoid possible underflow.
V(j, i) = (A(i, j)/A(i, l))/g;
for (j=l; j<n; j++)
{
@ -249,65 +249,68 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
{
l = i+1;
g = W[i];
for (j=l; j<n; j++)
A(i, j)=0.0;
if (g)
if (n-l>0)
A.row(i).end(n-l).setZero();
if (g != Scalar(0.0))
{
g = (Scalar)1.0/g;
g = Scalar(1.0)/g;
for (j=l; j<n; j++)
{
s = A.col(i).end(m-i).dot(A.col(j).end(m-i));
f = (s/A(i, i))*g;
s = A.col(i).end(m-l).dot(A.col(j).end(m-l));
f = (s/A(i,i))*g;
A.col(j).end(m-i) += f * A.col(i).end(m-i);
}
A.col(i).end(m-i) *= g;
}
else
A.col(i).end(m-i).setZero();
++A(i, i);
++A(i,i);
}
// Diagonalization of the bidiagonal form: Loop over
// singular values, and over allowed iterations.
for (k=(n-1); k>=0; k--)
for (k=n-1; k>=0; k--)
{
for (its=1; its<=max_iters; its++)
for (its=0; its<max_iters; its++)
{
flag=1;
flag = true;
for (l=k; l>=0; l--)
{
// Test for splitting.
nm=l-1;
nm = l-1;
// Note that rv1[1] is always zero.
if ((double)(ei_abs(rv1[l])+anorm) == anorm)
//if ((double)(ei_abs(rv1[l])+anorm) == anorm)
if (l==0 || ei_abs(rv1[l]) <= eps*anorm)
{
flag=0;
flag = false;
break;
}
if ((double)(ei_abs(W[nm])+anorm) == anorm)
//if ((double)(ei_abs(W[nm])+anorm) == anorm)
if (ei_abs(W[nm]) <= eps*anorm)
break;
}
if (flag)
{
c=0.0; //Cancellation of rv1[l], if l > 1.
s=1.0;
for (i=l ;i<=k; i++)
c = 0.0; //Cancellation of rv1[l], if l > 0.
s = 1.0;
for (i=l ;i<k+1; i++)
{
f = s*rv1[i];
rv1[i] = c*rv1[i];
if ((double)(ei_abs(f)+anorm) == anorm)
//if ((double)(ei_abs(f)+anorm) == anorm)
if (ei_abs(f) <= eps*anorm)
break;
g = W[i];
h = pythagora(f,g);
h = pythag(f,g);
W[i] = h;
h = (Scalar)1.0/h;
h = Scalar(1.0)/h;
c = g*h;
s = -f*h;
for (j=0; j<m; j++)
{
y = A(j, nm);
z = A(j, i);
A(j, nm) = y*c + z*s;
A(j, i) = z*c - y*s;
y = A(j,nm);
z = A(j,i);
A(j,nm) = y*c + z*s;
A(j,i) = z*c - y*s;
}
}
}
@ -320,7 +323,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
}
break;
}
if (its == max_iters)
if (its+1 == max_iters)
{
convergence = false;
}
@ -329,19 +332,19 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
y = W[nm];
g = rv1[nm];
h = rv1[k];
f = ((y-z)*(y+z) + (g-h)*(g+h))/((Scalar)2.0*h*y);
g = pythagora(f,1.0);
f = ((y-z)*(y+z) + (g-h)*(g+h))/(Scalar(2.0)*h*y);
g = pythag(f,1.0);
f = ((x-z)*(x+z) + h*((y/(f+sign(g,f)))-h))/x;
c = s = 1.0;
//Next QR transformation:
for (j=l; j<= nm;j++)
for (j=l; j<=nm; j++)
{
i = j+1;
g = rv1[i];
y = W[i];
h = s*g;
g = c*g;
z = pythagora(f,h);
z = pythag(f,h);
rv1[j] = z;
c = f/z;
s = h/z;
@ -351,15 +354,15 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
y *= c;
for (jj=0; jj<n; jj++)
{
x = V(jj, j);
z = V(jj, i);
V(jj, j) = x*c + z*s;
V(jj, i) = z*c - x*s;
x = V(jj,j);
z = V(jj,i);
V(jj,j) = x*c + z*s;
V(jj,i) = z*c - x*s;
}
z = pythagora(f,h);
z = pythag(f,h);
W[j] = z;
// Rotation can be arbitrary if z = 0.
if (z)
if (z!=Scalar(0))
{
z = Scalar(1.0)/z;
c = f*z;
@ -369,10 +372,10 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
x = c*y - s*g;
for (jj=0; jj<m; jj++)
{
y = A(jj, j);
z = A(jj, i);
A(jj, j) = y*c + z*s;
A(jj, i) = z*c - y*s;
y = A(jj,j);
z = A(jj,i);
A(jj,j) = y*c + z*s;
A(jj,i) = z*c - y*s;
}
}
rv1[l] = 0.0;