Fix non UTF8-encoded thirdparty files

This commit is contained in:
Rémi Verschelde 2019-05-22 10:34:57 +02:00
parent 0acdeb2e12
commit b7e737639f
3 changed files with 26 additions and 40 deletions

View file

@ -4388,7 +4388,7 @@ private:
class Solver
{
public:
// Solve the symmetric system: At·A·x = At·b
// Solve the symmetric system: At·A·x = At·b
static bool LeastSquaresSolver(const sparse::Matrix &A, const FullVector &b, FullVector &x, float epsilon = 1e-5f)
{
xaDebugAssert(A.width() == x.dimension());
@ -4477,22 +4477,22 @@ private:
* Gradient method.
*
* Solving sparse linear systems:
* (1) A·x = b
* (1) A·x = b
*
* The conjugate gradient algorithm solves (1) only in the case that A is
* symmetric and positive definite. It is based on the idea of minimizing the
* function
*
* (2) f(x) = 1/2·x·A·x - b·x
* (2) f(x) = 1/2·x·A·x - b·x
*
* This function is minimized when its gradient
*
* (3) df = A·x - b
* (3) df = A·x - b
*
* is zero, which is equivalent to (1). The minimization is carried out by
* generating a succession of search directions p.k and improved minimizers x.k.
* At each stage a quantity alfa.k is found that minimizes f(x.k + alfa.k·p.k),
* and x.k+1 is set equal to the new point x.k + alfa.k·p.k. The p.k and x.k are
* At each stage a quantity alfa.k is found that minimizes f(x.k + alfa.k·p.k),
* and x.k+1 is set equal to the new point x.k + alfa.k·p.k. The p.k and x.k are
* built up in such a way that x.k+1 is also the minimizer of f over the whole
* vector space of directions already taken, {p.1, p.2, . . . , p.k}. After N
* iterations you arrive at the minimizer over the entire vector space, i.e., the
@ -4520,7 +4520,7 @@ private:
float delta_new;
float alpha;
float beta;
// r = b - A·x;
// r = b - A·x;
sparse::copy(b, r);
sparse::sgemv(-1, A, x, 1, r);
// p = r;
@ -4529,24 +4529,24 @@ private:
delta_0 = delta_new;
while (i < i_max && delta_new > epsilon * epsilon * delta_0) {
i++;
// q = A·p
// q = A·p
mult(A, p, q);
// alpha = delta_new / p·q
// alpha = delta_new / p·q
alpha = delta_new / sparse::dot( p, q );
// x = alfa·p + x
// x = alfa·p + x
sparse::saxpy(alpha, p, x);
if ((i & 31) == 0) { // recompute r after 32 steps
// r = b - A·x
// r = b - A·x
sparse::copy(b, r);
sparse::sgemv(-1, A, x, 1, r);
} else {
// r = r - alpha·q
// r = r - alpha·q
sparse::saxpy(-alpha, q, r);
}
delta_old = delta_new;
delta_new = sparse::dot( r, r );
beta = delta_new / delta_old;
// p = beta·p + r
// p = beta·p + r
sparse::scal(beta, p);
sparse::saxpy(1, r, p);
}
@ -4572,35 +4572,35 @@ private:
float delta_new;
float alpha;
float beta;
// r = b - A·x
// r = b - A·x
sparse::copy(b, r);
sparse::sgemv(-1, A, x, 1, r);
// p = M^-1 · r
// p = M^-1 · r
preconditioner.apply(r, p);
delta_new = sparse::dot(r, p);
delta_0 = delta_new;
while (i < i_max && delta_new > epsilon * epsilon * delta_0) {
i++;
// q = A·p
// q = A·p
mult(A, p, q);
// alpha = delta_new / p·q
// alpha = delta_new / p·q
alpha = delta_new / sparse::dot(p, q);
// x = alfa·p + x
// x = alfa·p + x
sparse::saxpy(alpha, p, x);
if ((i & 31) == 0) { // recompute r after 32 steps
// r = b - A·x
// r = b - A·x
sparse::copy(b, r);
sparse::sgemv(-1, A, x, 1, r);
} else {
// r = r - alfa·q
// r = r - alfa·q
sparse::saxpy(-alpha, q, r);
}
// s = M^-1 · r
// s = M^-1 · r
preconditioner.apply(r, s);
delta_old = delta_new;
delta_new = sparse::dot( r, s );
beta = delta_new / delta_old;
// p = s + beta·p
// p = s + beta·p
sparse::scal(beta, p);
sparse::saxpy(1, s, p);
}