📄 cxsvd.cpp
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if( f < 0 )
g = -g;
f = x - (z / x) * z + (h / x) * (y / (f + g) - h);
/* next QR transformation */
c = s = 1;
for( i = l + 1; i <= k; i++ )
{
g = e[i];
y = w[i];
h = s * g;
g *= c;
z = pythag( f, h );
e[i - 1] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = -x * s + g * c;
h = y * s;
y *= c;
if( vT )
icvGivens_64f( n, vT + ldvT * (i - 1), vT + ldvT * i, c, s );
z = pythag( f, h );
w[i - 1] = z;
/* rotation can be arbitrary if z == 0 */
if( z != 0 )
{
c = f / z;
s = h / z;
}
f = c * g + s * y;
x = -s * g + c * y;
if( uT )
icvGivens_64f( m, uT + lduT * (i - 1), uT + lduT * i, c, s );
}
e[l] = 0;
e[k] = f;
w[k] = x;
} /* end of iteration loop */
if( iters > MAX_ITERS )
break;
if( z < 0 )
{
w[k] = -z;
if( vT )
{
for( j = 0; j < n; j++ )
vT[j + k * ldvT] = -vT[j + k * ldvT];
}
}
} /* end of diagonalization loop */
/* sort singular values and corresponding values */
for( i = 0; i < nm; i++ )
{
k = i;
for( j = i + 1; j < nm; j++ )
if( w[k] < w[j] )
k = j;
if( k != i )
{
double t;
CV_SWAP( w[i], w[k], t );
if( vT )
for( j = 0; j < n; j++ )
CV_SWAP( vT[j + ldvT*k], vT[j + ldvT*i], t );
if( uT )
for( j = 0; j < m; j++ )
CV_SWAP( uT[j + lduT*k], uT[j + lduT*i], t );
}
}
}
static void
icvSVD_32f( float* a, int lda, int m, int n,
float* w,
float* uT, int lduT, int nu,
float* vT, int ldvT,
float* buffer )
{
float* e;
float* temp;
float *w1, *e1;
float *hv;
double ku0 = 0, kv0 = 0;
double anorm = 0;
float *a1, *u0 = uT, *v0 = vT;
double scale, h;
int i, j, k, l;
int nm, m1, n1;
int nv = n;
int iters = 0;
float* hv0 = (float*)cvStackAlloc( (m+2)*sizeof(hv0[0])) + 1;
e = buffer;
w1 = w;
e1 = e + 1;
nm = n;
temp = buffer + nm;
memset( w, 0, nm * sizeof( w[0] ));
memset( e, 0, nm * sizeof( e[0] ));
m1 = m;
n1 = n;
/* transform a to bi-diagonal form */
for( ;; )
{
int update_u;
int update_v;
if( m1 == 0 )
break;
scale = h = 0;
update_u = uT && m1 > m - nu;
hv = update_u ? uT : hv0;
for( j = 0, a1 = a; j < m1; j++, a1 += lda )
{
double t = a1[0];
scale += fabs( hv[j] = (float)t );
}
if( scale != 0 )
{
double f = 1./scale, g, s = 0;
for( j = 0; j < m1; j++ )
{
double t = (hv[j] = (float)(hv[j]*f));
s += t * t;
}
g = sqrt( s );
f = hv[0];
if( f >= 0 )
g = -g;
hv[0] = (float)(f - g);
h = 1. / (f * g - s);
memset( temp, 0, n1 * sizeof( temp[0] ));
/* calc temp[0:n-i] = a[i:m,i:n]'*hv[0:m-i] */
icvMatrAXPY_32f( m1, n1 - 1, a + 1, lda, hv, temp + 1, 0 );
for( k = 1; k < n1; k++ ) temp[k] = (float)(temp[k]*h);
/* modify a: a[i:m,i:n] = a[i:m,i:n] + hv[0:m-i]*temp[0:n-i]' */
icvMatrAXPY_32f( m1, n1 - 1, temp + 1, 0, hv, a + 1, lda );
*w1 = (float)(g*scale);
}
w1++;
/* store -2/(hv'*hv) */
if( update_u )
{
if( m1 == m )
ku0 = h;
else
hv[-1] = (float)h;
}
a++;
n1--;
if( vT )
vT += ldvT + 1;
if( n1 == 0 )
break;
scale = h = 0;
update_v = vT && n1 > n - nv;
hv = update_v ? vT : hv0;
for( j = 0; j < n1; j++ )
{
double t = a[j];
scale += fabs( hv[j] = (float)t );
}
if( scale != 0 )
{
double f = 1./scale, g, s = 0;
for( j = 0; j < n1; j++ )
{
double t = (hv[j] = (float)(hv[j]*f));
s += t * t;
}
g = sqrt( s );
f = hv[0];
if( f >= 0 )
g = -g;
hv[0] = (float)(f - g);
h = 1. / (f * g - s);
hv[-1] = 0.f;
/* update a[i:m:i+1:n] = a[i:m,i+1:n] + (a[i:m,i+1:n]*hv[0:m-i])*... */
icvMatrAXPY3_32f( m1, n1, hv, lda, a, h );
*e1 = (float)(g*scale);
}
e1++;
/* store -2/(hv'*hv) */
if( update_v )
{
if( n1 == n )
kv0 = h;
else
hv[-1] = (float)h;
}
a += lda;
m1--;
if( uT )
uT += lduT + 1;
}
m1 -= m1 != 0;
n1 -= n1 != 0;
/* accumulate left transformations */
if( uT )
{
m1 = m - m1;
uT = u0 + m1 * lduT;
for( i = m1; i < nu; i++, uT += lduT )
{
memset( uT + m1, 0, (m - m1) * sizeof( uT[0] ));
uT[i] = 1.;
}
for( i = m1 - 1; i >= 0; i-- )
{
double s;
int lh = nu - i;
l = m - i;
hv = u0 + (lduT + 1) * i;
h = i == 0 ? ku0 : hv[-1];
assert( h <= 0 );
if( h != 0 )
{
uT = hv;
icvMatrAXPY3_32f( lh, l-1, hv+1, lduT, uT+1, h );
s = hv[0] * h;
for( k = 0; k < l; k++ ) hv[k] = (float)(hv[k]*s);
hv[0] += 1;
}
else
{
for( j = 1; j < l; j++ )
hv[j] = 0;
for( j = 1; j < lh; j++ )
hv[j * lduT] = 0;
hv[0] = 1;
}
}
uT = u0;
}
/* accumulate right transformations */
if( vT )
{
n1 = n - n1;
vT = v0 + n1 * ldvT;
for( i = n1; i < nv; i++, vT += ldvT )
{
memset( vT + n1, 0, (n - n1) * sizeof( vT[0] ));
vT[i] = 1.;
}
for( i = n1 - 1; i >= 0; i-- )
{
double s;
int lh = nv - i;
l = n - i;
hv = v0 + (ldvT + 1) * i;
h = i == 0 ? kv0 : hv[-1];
assert( h <= 0 );
if( h != 0 )
{
vT = hv;
icvMatrAXPY3_32f( lh, l-1, hv+1, ldvT, vT+1, h );
s = hv[0] * h;
for( k = 0; k < l; k++ ) hv[k] = (float)(hv[k]*s);
hv[0] += 1;
}
else
{
for( j = 1; j < l; j++ )
hv[j] = 0;
for( j = 1; j < lh; j++ )
hv[j * ldvT] = 0;
hv[0] = 1;
}
}
vT = v0;
}
for( i = 0; i < nm; i++ )
{
double tnorm = fabs( w[i] );
tnorm += fabs( e[i] );
if( anorm < tnorm )
anorm = tnorm;
}
anorm *= FLT_EPSILON;
/* diagonalization of the bidiagonal form */
for( k = nm - 1; k >= 0; k-- )
{
double z = 0;
iters = 0;
for( ;; ) /* do iterations */
{
double c, s, f, g, x, y;
int flag = 0;
/* test for splitting */
for( l = k; l >= 0; l-- )
{
if( fabs( e[l] ) <= anorm )
{
flag = 1;
break;
}
assert( l > 0 );
if( fabs( w[l - 1] ) <= anorm )
break;
}
if( !flag )
{
c = 0;
s = 1;
for( i = l; i <= k; i++ )
{
f = s * e[i];
e[i] = (float)(e[i]*c);
if( anorm + fabs( f ) == anorm )
break;
g = w[i];
h = pythag( f, g );
w[i] = (float)h;
c = g / h;
s = -f / h;
if( uT )
icvGivens_32f( m, uT + lduT * (l - 1), uT + lduT * i, c, s );
}
}
z = w[k];
if( l == k || iters++ == MAX_ITERS )
break;
/* shift from bottom 2x2 minor */
x = w[l];
y = w[k - 1];
g = e[k - 1];
h = e[k];
f = 0.5 * (((g + z) / h) * ((g - z) / y) + y / h - h / y);
g = pythag( f, 1 );
if( f < 0 )
g = -g;
f = x - (z / x) * z + (h / x) * (y / (f + g) - h);
/* next QR transformation */
c = s = 1;
for( i = l + 1; i <= k; i++ )
{
g = e[i];
y = w[i];
h = s * g;
g *= c;
z = pythag( f, h );
e[i - 1] = (float)z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = -x * s + g * c;
h = y * s;
y *= c;
if( vT )
icvGivens_32f( n, vT + ldvT * (i - 1), vT + ldvT * i, c, s );
z = pythag( f, h );
w[i - 1] = (float)z;
/* rotation can be arbitrary if z == 0 */
if( z != 0 )
{
c = f / z;
s = h / z;
}
f = c * g + s * y;
x = -s * g + c * y;
if( uT )
icvGivens_32f( m, uT + lduT * (i - 1), uT + lduT * i, c, s );
}
e[l] = 0;
e[k] = (float)f;
w[k] = (float)x;
} /* end of iteration loop */
if( iters > MAX_ITERS )
break;
if( z < 0 )
{
w[k] = (float)(-z);
if( vT )
{
for( j = 0; j < n; j++ )
vT[j + k * ldvT] = -vT[j + k * ldvT];
}
}
} /* end of diagonalization loop */
/* sort singular values and corresponding vectors */
for( i = 0; i < nm; i++ )
{
k = i;
for( j = i + 1; j < nm; j++ )
if( w[k] < w[j] )
k = j;
if( k != i )
{
float t;
CV_SWAP( w[i], w[k], t );
if( vT )
for( j = 0; j < n; j++ )
CV_SWAP( vT[j + ldvT*k], vT[j + ldvT*i], t );
if( uT )
for( j = 0; j < m; j++ )
CV_SWAP( uT[j + lduT*k], uT[j + lduT*i], t );
}
}
}
static void
icvSVBkSb_64f( int m, int n, const double* w,
const double* uT, int lduT,
const double* vT, int ldvT,
const double* b, int ldb, int nb,
double* x, int ldx, double* buffer )
{
double threshold = 0;
int i, j, nm = MIN( m, n );
if( !b )
nb = m;
for( i = 0; i < n; i++ )
memset( x + i*ldx, 0, nb*sizeof(x[0]));
for( i = 0; i < nm; i++ )
threshold += w[i];
threshold *= 2*DBL_EPSILON;
/* vT * inv(w) * uT * b */
for( i = 0; i < nm; i++, uT += lduT, vT += ldvT )
{
double wi = w[i];
if( wi > threshold )
{
wi = 1./wi;
if( nb == 1 )
{
double s = 0;
if( b )
{
if( ldb == 1 )
{
for( j = 0; j <= m - 4; j += 4 )
s += uT[j]*b[j] + uT[j+1]*b[j+1] + uT[j+2]*b[j+2] + uT[j+3]*b[j+3];
for( ; j < m; j++ )
s += uT[j]*b[j];
}
else
{
for( j = 0; j < m; j++ )
s += uT[j]*b[j*ldb];
}
}
else
s = uT[0];
s *= wi;
if( ldx == 1 )
{
for( j = 0; j <= n - 4; j += 4 )
{
double t0 = x[j] + s*vT[j];
double t1 = x[j+1] + s*vT[j+1];
x[j] = t0;
x[j+1] = t1;
t0 = x[j+2] + s*vT[j+2];
t1 = x[j+3] + s*vT[j+3];
x[j+2] = t0;
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