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fixed single-precision SVD accuracy on some very ill-conditioned matrices (ticket #1448)

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This commit is contained in:
Vadim Pisarevsky 2011-12-03 19:49:44 +00:00
parent 2547f7554e
commit 5353b97605
1 changed files with 24 additions and 21 deletions
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45
modules/core/src/lapack.cpp
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@ -533,10 +533,12 @@ template<> inline int VBLAS<double>::givensx(double* a, double* b, int n, double
#endif #endif
template<typename _Tp> void template<typename _Tp> void
JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int n, int n1) JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep, int m, int n, int n1)
{ {
VBLAS<_Tp> vblas; VBLAS<_Tp> vblas;
_Tp eps = std::numeric_limits<_Tp>::epsilon()*10; AutoBuffer<double> Wbuf(n);
double* W = Wbuf;
_Tp eps = DBL_EPSILON*10;
int i, j, k, iter, max_iter = std::max(m, 30); int i, j, k, iter, max_iter = std::max(m, 30);
_Tp c, s; _Tp c, s;
double sd; double sd;
@ -548,7 +550,7 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
for( k = 0, s = 0; k < m; k++ ) for( k = 0, s = 0; k < m; k++ )
{ {
_Tp t = At[i*astep + k]; _Tp t = At[i*astep + k];
s += t*t; s += (double)t*t;
} }
W[i] = s; W[i] = s;
@ -567,12 +569,11 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
for( i = 0; i < n-1; i++ ) for( i = 0; i < n-1; i++ )
for( j = i+1; j < n; j++ ) for( j = i+1; j < n; j++ )
{ {
_Tp *Ai = At + i*astep, *Aj = At + j*astep, a = W[i], p = 0, b = W[j]; _Tp *Ai = At + i*astep, *Aj = At + j*astep;
double a = W[i], p = 0, b = W[j];
k = vblas.dot(Ai, Aj, m, &p); for( k = 0; k < m; k++ )
p += (double)Ai[k]*Aj[k];
for( ; k < m; k++ )
p += Ai[k]*Aj[k];
if( std::abs(p) <= eps*std::sqrt((double)a*b) ) if( std::abs(p) <= eps*std::sqrt((double)a*b) )
continue; continue;
@ -581,7 +582,7 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
double beta = a - b, gamma = hypot((double)p, beta), delta; double beta = a - b, gamma = hypot((double)p, beta), delta;
if( beta < 0 ) if( beta < 0 )
{ {
delta = (_Tp)((gamma - beta)*0.5); delta = (gamma - beta)*0.5;
s = (_Tp)std::sqrt(delta/gamma); s = (_Tp)std::sqrt(delta/gamma);
c = (_Tp)(p/(gamma*s*2)); c = (_Tp)(p/(gamma*s*2));
} }
@ -589,13 +590,13 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
{ {
c = (_Tp)std::sqrt((gamma + beta)/(gamma*2)); c = (_Tp)std::sqrt((gamma + beta)/(gamma*2));
s = (_Tp)(p/(gamma*c*2)); s = (_Tp)(p/(gamma*c*2));
delta = (_Tp)(p*p*0.5/(gamma + beta)); delta = p*p*0.5/(gamma + beta);
} }
if( iter % 2 ) if( iter % 2 )
{ {
W[i] = (_Tp)(W[i] + delta); W[i] += delta;
W[j] = (_Tp)(W[j] - delta); W[j] -= delta;
k = vblas.givens(Ai, Aj, m, c, s); k = vblas.givens(Ai, Aj, m, c, s);
@ -609,14 +610,13 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
else else
{ {
a = b = 0; a = b = 0;
k = vblas.givensx(Ai, Aj, m, c, s, &a, &b); for( k = 0; k < m; k++ )
for( ; k < m; k++ )
{ {
_Tp t0 = c*Ai[k] + s*Aj[k]; _Tp t0 = c*Ai[k] + s*Aj[k];
_Tp t1 = -s*Ai[k] + c*Aj[k]; _Tp t1 = -s*Ai[k] + c*Aj[k];
Ai[k] = t0; Aj[k] = t1; Ai[k] = t0; Aj[k] = t1;
a += t0*t0; b += t1*t1; a += (double)t0*t0; b += (double)t1*t1;
} }
W[i] = a; W[j] = b; W[i] = a; W[j] = b;
} }
@ -647,7 +647,7 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
_Tp t = At[i*astep + k]; _Tp t = At[i*astep + k];
sd += (double)t*t; sd += (double)t*t;
} }
W[i] = s = (_Tp)std::sqrt(sd); W[i] = std::sqrt(sd);
} }
for( i = 0; i < n-1; i++ ) for( i = 0; i < n-1; i++ )
@ -677,9 +677,9 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
RNG rng(0x12345678); RNG rng(0x12345678);
for( i = 0; i < n1; i++ ) for( i = 0; i < n1; i++ )
{ {
s = i < n ? W[i] : 0; sd = i < n ? W[i] : 0;
while( s == 0 ) while( sd == 0 )
{ {
// if we got a zero singular value, then in order to get the corresponding left singular vector // if we got a zero singular value, then in order to get the corresponding left singular vector
// we generate a random vector, project it to the previously computed left singular vectors, // we generate a random vector, project it to the previously computed left singular vectors,
@ -715,13 +715,16 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* W, _Tp* Vt, size_t vstep, int m, int
_Tp t = At[i*astep + k]; _Tp t = At[i*astep + k];
sd += (double)t*t; sd += (double)t*t;
} }
s = (_Tp)std::sqrt(sd); sd = std::sqrt(sd);
} }
s = 1/s; s = (_Tp)(1/sd);
for( k = 0; k < m; k++ ) for( k = 0; k < m; k++ )
At[i*astep + k] *= s; At[i*astep + k] *= s;
} }
for( i = 0; i < n; i++ )
_W[i] = (_Tp)W[i];
} }
@ -837,7 +840,7 @@ SVBkSb( int m, int n, const float* w, size_t wstep,
v, (int)(vstep/sizeof(v[0])), vT, v, (int)(vstep/sizeof(v[0])), vT,
b, (int)(bstep/sizeof(b[0])), nb, b, (int)(bstep/sizeof(b[0])), nb,
x, (int)(xstep/sizeof(x[0])), x, (int)(xstep/sizeof(x[0])),
(double*)alignPtr(buffer, sizeof(double)), FLT_EPSILON*10 ); (double*)alignPtr(buffer, sizeof(double)), (float)(DBL_EPSILON*2) );
} }
static void static void