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wdsp/lmath.c
Uladzimir Karpenka 89c8a0e2b5 first commit
2026-06-01 15:58:45 +03:00

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/* lmath.c
This file is part of a program that implements a Software-Defined Radio.
Copyright (C) 2015, 2016, 2023 Warren Pratt, NR0V
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
The author can be reached by email at
warren@wpratt.com
*/
#include "comm.h"
void dR (int n, double* r, double* y, double* z)
{
int i, j, k;
double alpha, beta, gamma;
memset (z, 0, (n - 1) * sizeof (double)); // work space
y[0] = -r[1];
alpha = -r[1];
beta = 1.0;
for (k = 0; k < n - 1; k++)
{
beta *= 1.0 - alpha * alpha;
gamma = 0.0;
for (i = k + 1, j = 0; i > 0; i--, j++)
gamma += r[i] * y[j];
alpha = - (r[k + 2] + gamma) / beta;
for (i = 0, j = k; i <= k; i++, j--)
z[i] = y[i] + alpha * y[j];
memcpy (y, z, (k + 1) * sizeof (double));
y[k + 1] = alpha;
}
}
void trI (
int n,
double* r,
double* B,
double* y,
double* v,
double* dR_z
)
{
int i, j, ni, nj;
double gamma, t, scale, b;
memset (y, 0, (n - 1) * sizeof (double)); // work space
memset (v, 0, (n - 1) * sizeof (double)); // work space
scale = 1.0 / r[0];
for (i = 0; i < n; i++)
r[i] *= scale;
dR(n - 1, r, y, dR_z);
t = 0.0;
for (i = 0; i < n - 1; i++)
t += r[i + 1] * y[i];
gamma = 1.0 / (1.0 + t);
for (i = 0, j = n - 2; i < n - 1; i++, j--)
v[i] = gamma * y[j];
B[0] = gamma;
for (i = 1, j = n - 2; i < n; i++, j--)
B[i] = v[j];
for (i = 1; i <= (n - 1) / 2; i++)
for (j = i; j < n - i; j++)
B[i * n + j] = B[(i - 1) * n + (j - 1)] + (v[n - j - 1] * v[n - i - 1] - v[i - 1] * v[j - 1]) / gamma;
for (i = 0; i <= (n - 1)/2; i++)
for (j = i; j < n - i; j++)
{
b = B[i * n + j] *= scale;
B[j * n + i] = b;
ni = n - i - 1;
nj = n - j - 1;
B[ni * n + nj] = b;
B[nj * n + ni] = b;
}
}
void asolve(int xsize, int asize, double* x, double* a, double* r, double* z)
{
int i, j, k;
double beta, alpha, t;
memset(r, 0, (asize + 1) * sizeof(double)); // work space
memset(z, 0, (asize + 1) * sizeof(double)); // work space
for (i = 0; i <= asize; i++)
{
for (j = 0; j < xsize; j++)
r[i] += x[j] * x[j - i];
}
z[0] = 1.0;
beta = r[0];
for (k = 0; k < asize; k++)
{
alpha = 0.0;
for (j = 0; j <= k; j++)
alpha -= z[j] * r[k + 1 - j];
alpha /= beta;
for (i = 0; i <= (k + 1) / 2; i++)
{
t = z[k + 1 - i] + alpha * z[i];
z[i] = z[i] + alpha * z[k + 1 - i];
z[k + 1 - i] = t;
}
beta *= 1.0 - alpha * alpha;
}
for (i = 0; i < asize; i++)
{
a[i] = - z[i + 1];
if (a[i] != a[i]) a[i] = 0.0;
}
}
void median (int n, double* a, double* med)
{
int S0, S1, i, j, m, k;
double x, t;
S0 = 0;
S1 = n - 1;
k = n / 2;
while (S1 > S0 + 1)
{
m = (S0 + S1) / 2;
t = a[m];
a[m] = a[S0 + 1];
a[S0 + 1] = t;
if (a[S0] > a[S1])
{
t = a[S0];
a[S0] = a[S1];
a[S1] = t;
}
if (a[S0 + 1] > a[S1])
{
t = a[S0 + 1];
a[S0 + 1] = a[S1];
a[S1] = t;
}
if (a[S0] > a[S0 + 1])
{
t = a[S0];
a[S0] = a[S0 + 1];
a[S0 + 1] = t;
}
i = S0 + 1;
j = S1;
x = a[S0 + 1];
do i++; while (a[i] < x);
do j--; while (a[j] > x);
while (j >= i)
{
t = a[i];
a[i] = a[j];
a[j] = t;
do i++; while (a[i] < x);
do j--; while (a[j] > x);
}
a[S0 + 1] = a[j];
a[j] = x;
if (j >= k) S1 = j - 1;
if (j <= k) S0 = i;
}
if (S1 == S0 + 1 && a[S1] < a[S0])
{
t = a[S0];
a[S0] = a[S1];
a[S1] = t;
}
*med = a[k];
}
BLDR create_builder(int points, int ints)
{
// for the create function, 'points' and 'ints' are the MAXIMUM values that will be encountered
BLDR a = (BLDR)malloc0 (sizeof(bldr));
a->catxy = (double*)malloc0(2 * points * sizeof(double));
a->sx = (double*)malloc0( points * sizeof(double));
a->sy = (double*)malloc0( points * sizeof(double));
a->h = (double*)malloc0( ints * sizeof(double));
a->p = (int*) malloc0( ints * sizeof(int));
a->np = (int*) malloc0( ints * sizeof(int));
a->taa = (double*)malloc0( ints * sizeof(double));
a->tab = (double*)malloc0( ints * sizeof(double));
a->tag = (double*)malloc0( ints * sizeof(double));
a->tad = (double*)malloc0( ints * sizeof(double));
a->tbb = (double*)malloc0( ints * sizeof(double));
a->tbg = (double*)malloc0( ints * sizeof(double));
a->tbd = (double*)malloc0( ints * sizeof(double));
a->tgg = (double*)malloc0( ints * sizeof(double));
a->tgd = (double*)malloc0( ints * sizeof(double));
a->tdd = (double*)malloc0( ints * sizeof(double));
int nsize = 3 * ints + 1;
int intp1 = ints + 1;
int intm1 = ints - 1;
a->A = (double*)malloc0(intp1 * intp1 * sizeof(double));
a->B = (double*)malloc0(intp1 * intp1 * sizeof(double));
a->C = (double*)malloc0(intm1 * intp1 * sizeof(double));
a->D = (double*)malloc0(intp1 * sizeof(double));
a->E = (double*)malloc0(intp1 * intp1 * sizeof(double));
a->F = (double*)malloc0(intm1 * intp1 * sizeof(double));
a->G = (double*)malloc0(intp1 * sizeof(double));
a->MAT = (double*)malloc0(nsize * nsize * sizeof(double));
a->RHS = (double*)malloc0(nsize * sizeof(double));
a->SLN = (double*)malloc0(nsize * sizeof(double));
a->z = (double*)malloc0(intp1 * sizeof(double));
a->zp = (double*)malloc0(intp1 * sizeof(double));
a->wrk = (double*)malloc0(nsize * sizeof(double));
a->ipiv = (int*) malloc0(nsize * sizeof(int));
return a;
}
void destroy_builder(BLDR a)
{
_aligned_free(a->ipiv);
_aligned_free(a->wrk);
_aligned_free(a->catxy);
_aligned_free(a->sx);
_aligned_free(a->sy);
_aligned_free(a->h);
_aligned_free(a->p);
_aligned_free(a->np);
_aligned_free(a->taa);
_aligned_free(a->tab);
_aligned_free(a->tag);
_aligned_free(a->tad);
_aligned_free(a->tbb);
_aligned_free(a->tbg);
_aligned_free(a->tbd);
_aligned_free(a->tgg);
_aligned_free(a->tgd);
_aligned_free(a->tdd);
_aligned_free(a->A);
_aligned_free(a->B);
_aligned_free(a->C);
_aligned_free(a->D);
_aligned_free(a->E);
_aligned_free(a->F);
_aligned_free(a->G);
_aligned_free(a->MAT);
_aligned_free(a->RHS);
_aligned_free(a->SLN);
_aligned_free(a->z);
_aligned_free(a->zp);
_aligned_free(a);
}
void flush_builder(BLDR a, int points, int ints)
{
memset(a->catxy, 0, 2 * points * sizeof(double));
memset(a->sx, 0, points * sizeof(double));
memset(a->sy, 0, points * sizeof(double));
memset(a->h, 0, ints * sizeof(double));
memset(a->p, 0, ints * sizeof(int));
memset(a->np, 0, ints * sizeof(int));
memset(a->taa, 0, ints * sizeof(double));
memset(a->tab, 0, ints * sizeof(double));
memset(a->tag, 0, ints * sizeof(double));
memset(a->tad, 0, ints * sizeof(double));
memset(a->tbb, 0, ints * sizeof(double));
memset(a->tbg, 0, ints * sizeof(double));
memset(a->tbd, 0, ints * sizeof(double));
memset(a->tgg, 0, ints * sizeof(double));
memset(a->tgd, 0, ints * sizeof(double));
memset(a->tdd, 0, ints * sizeof(double));
int nsize = 3 * ints + 1;
int intp1 = ints + 1;
int intm1 = ints - 1;
memset(a->A, 0, intp1 * intp1 * sizeof(double));
memset(a->B, 0, intp1 * intp1 * sizeof(double));
memset(a->C, 0, intm1 * intp1 * sizeof(double));
memset(a->D, 0, intp1 * sizeof(double));
memset(a->E, 0, intp1 * intp1 * sizeof(double));
memset(a->F, 0, intm1 * intp1 * sizeof(double));
memset(a->G, 0, intp1 * sizeof(double));
memset(a->MAT, 0, nsize * nsize * sizeof(double));
memset(a->RHS, 0, nsize * sizeof(double));
memset(a->SLN, 0, nsize * sizeof(double));
memset(a->z, 0, intp1 * sizeof(double));
memset(a->zp, 0, intp1 * sizeof(double));
memset(a->wrk, 0, nsize * sizeof(double));
memset(a->ipiv, 0, nsize * sizeof(int));
}
int fcompare(const void* a, const void* b)
{
if (*(double*)a < *(double*)b)
return -1;
else if (*(double*)a == *(double*)b)
return 0;
else
return 1;
}
void decomp(int n, double* a, int* piv, int* info, double* wrk)
{
int i, j, k;
int t_piv;
double m_row, mt_row, m_col, mt_col;
*info = 0;
for (i = 0; i < n; i++)
{
piv[i] = i;
m_row = 0.0;
for (j = 0; j < n; j++)
{
mt_row = a[n * i + j];
if (mt_row < 0.0) mt_row = -mt_row;
if (mt_row > m_row) m_row = mt_row;
}
if (m_row == 0.0)
{
*info = i;
goto cleanup;
}
wrk[i] = m_row;
}
for (k = 0; k < n - 1; k++)
{
j = k;
m_col = a[n * piv[k] + k] / wrk[piv[k]];
if (m_col < 0) m_col = -m_col;
for (i = k + 1; i < n; i++)
{
mt_col = a[n * piv[i] + k] / wrk[piv[k]];
if (mt_col < 0.0) mt_col = -mt_col;
if (mt_col > m_col)
{
m_col = mt_col;
j = i;
}
}
if (m_col == 0)
{
*info = -k;
goto cleanup;
}
t_piv = piv[k];
piv[k] = piv[j];
piv[j] = t_piv;
for (i = k + 1; i < n; i++)
{
a[n * piv[i] + k] /= a[n * piv[k] + k];
for (j = k + 1; j < n; j++)
a[n * piv[i] + j] -= a[n * piv[i] + k] * a[n * piv[k] + j];
}
}
if (a[n * n - 1] == 0.0)
*info = -n;
cleanup:
return;
}
void dsolve(int n, double* a, int* piv, double* b, double* x)
{
int j, k;
double sum;
for (k = 0; k < n; k++)
{
sum = 0.0;
for (j = 0; j < k; j++)
sum += a[n * piv[k] + j] * x[j];
x[k] = b[piv[k]] - sum;
}
for (k = n - 1; k >= 0; k--)
{
sum = 0.0;
for (j = k + 1; j < n; j++)
sum += a[n * piv[k] + j] * x[j];
x[k] = (x[k] - sum) / a[n * piv[k] + k];
}
}
void cull(int* n, int ints, double* x, double* t, double ptol)
{
int k = 0;
int i = *n;
int ntopint;
int npx;
while (x[i - 1] > t[ints - 1])
i--;
ntopint = *n - i;
npx = (int)(ntopint * (1.0 - ptol));
i = *n;
while ((k < npx) && (x[--i] > t[ints]))
k++;
*n -= k;
}
void xbuilder(BLDR a, int points, double* x, double* y, int ints, double* t, int* info, double* c, double ptol)
{
double u, v, alpha, beta, gamma, delta;
int nsize = 3 * ints + 1;
int intp1 = ints + 1;
int intm1 = ints - 1;
int i, j, k, m;
int dinfo;
flush_builder(a, points, ints);
for (i = 0; i < points; i++)
{
a->catxy[2 * i + 0] = x[i];
a->catxy[2 * i + 1] = y[i];
}
qsort(a->catxy, points, 2 * sizeof(double), fcompare);
for (i = 0; i < points; i++)
{
a->sx[i] = a->catxy[2 * i + 0];
a->sy[i] = a->catxy[2 * i + 1];
}
cull(&points, ints, a->sx, t, ptol);
if (points <= 0 || a->sx[points - 1] > t[ints])
{
*info = -1000;
goto cleanup;
}
else *info = 0;
for (j = 0; j < ints; j++)
a->h[j] = t[j + 1] - t[j];
a->p[0] = 0;
j = 0;
for (i = 0; i < points; i++)
{
if (a->sx[i] <= t[j + 1])
a->np[j]++;
else
{
a->p[++j] = i;
while (a->sx[i] > t[j + 1])
a->p[++j] = i;
a->np[j] = 1;
}
}
for (i = 0; i < ints; i++)
for (j = a->p[i]; j < a->p[i] + a->np[i]; j++)
{
u = (a->sx[j] - t[i]) / a->h[i];
v = u - 1.0;
alpha = (2.0 * u + 1.0) * v * v;
beta = u * u * (1.0 - 2.0 * v);
gamma = a->h[i] * u * v * v;
delta = a->h[i] * u * u * v;
a->taa[i] += alpha * alpha;
a->tab[i] += alpha * beta;
a->tag[i] += alpha * gamma;
a->tad[i] += alpha * delta;
a->tbb[i] += beta * beta;
a->tbg[i] += beta * gamma;
a->tbd[i] += beta * delta;
a->tgg[i] += gamma * gamma;
a->tgd[i] += gamma * delta;
a->tdd[i] += delta * delta;
a->D[i + 0] += 2.0 * a->sy[j] * alpha;
a->D[i + 1] += 2.0 * a->sy[j] * beta;
a->G[i + 0] += 2.0 * a->sy[j] * gamma;
a->G[i + 1] += 2.0 * a->sy[j] * delta;
}
for (i = 0; i < ints; i++)
{
a->A[(i + 0) * intp1 + (i + 0)] += 2.0 * a->taa[i];
a->A[(i + 1) * intp1 + (i + 1)] = 2.0 * a->tbb[i];
a->A[(i + 0) * intp1 + (i + 1)] = 2.0 * a->tab[i];
a->A[(i + 1) * intp1 + (i + 0)] = 2.0 * a->tab[i];
a->B[(i + 0) * intp1 + (i + 0)] += 2.0 * a->tag[i];
a->B[(i + 1) * intp1 + (i + 1)] = 2.0 * a->tbd[i];
a->B[(i + 0) * intp1 + (i + 1)] = 2.0 * a->tbg[i];
a->B[(i + 1) * intp1 + (i + 0)] = 2.0 * a->tad[i];
a->E[(i + 0) * intp1 + (i + 0)] += 2.0 * a->tgg[i];
a->E[(i + 1) * intp1 + (i + 1)] = 2.0 * a->tdd[i];
a->E[(i + 0) * intp1 + (i + 1)] = 2.0 * a->tgd[i];
a->E[(i + 1) * intp1 + (i + 0)] = 2.0 * a->tgd[i];
}
for (i = 0; i < intm1; i++)
{
a->C[i * intp1 + (i + 0)] = +3.0 * a->h[i + 1] / a->h[i];
a->C[i * intp1 + (i + 2)] = -3.0 * a->h[i] / a->h[i + 1];
a->C[i * intp1 + (i + 1)] = -a->C[i * intp1 + (i + 0)] - a->C[i * intp1 + (i + 2)];
a->F[i * intp1 + (i + 0)] = a->h[i + 1];
a->F[i * intp1 + (i + 1)] = 2.0 * (a->h[i] + a->h[i + 1]);
a->F[i * intp1 + (i + 2)] = a->h[i];
}
for (i = 0, k = 0; i < intp1; i++, k++)
{
for (j = 0, m = 0; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->A[i * intp1 + j];
for (j = 0, m = intp1; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->B[j * intp1 + i];
for (j = 0, m = 2 * intp1; j < intm1; j++, m++)
a->MAT[k * nsize + m] = a->C[j * intp1 + i];
a->RHS[k] = a->D[i];
}
for (i = 0, k = intp1; i < intp1; i++, k++)
{
for (j = 0, m = 0; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->B[i * intp1 + j];
for (j = 0, m = intp1; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->E[i * intp1 + j];
for (j = 0, m = 2 * intp1; j < intm1; j++, m++)
a->MAT[k * nsize + m] = a->F[j * intp1 + i];
a->RHS[k] = a->G[i];
}
for (i = 0, k = 2 * intp1; i < intm1; i++, k++)
{
for (j = 0, m = 0; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->C[i * intp1 + j];
for (j = 0, m = intp1; j < intp1; j++, m++)
a->MAT[k * nsize + m] = a->F[i * intp1 + j];
for (j = 0, m = 2 * intp1; j < intm1; j++, m++)
a->MAT[k * nsize + m] = 0.0;
a->RHS[k] = 0.0;
}
decomp(nsize, a->MAT, a->ipiv, &dinfo, a->wrk);
dsolve(nsize, a->MAT, a->ipiv, a->RHS, a->SLN);
if (dinfo != 0)
{
*info = dinfo;
goto cleanup;
}
for (i = 0; i <= ints; i++)
{
a->z[i] = a->SLN[i];
a->zp[i] = a->SLN[i + ints + 1];
}
for (i = 0; i < ints; i++)
{
c[4 * i + 0] = a->z[i];
c[4 * i + 1] = a->zp[i];
c[4 * i + 2] = -3.0 / (a->h[i] * a->h[i]) * (a->z[i] - a->z[i + 1]) - 1.0 / a->h[i] * (2.0 * a->zp[i] + a->zp[i + 1]);
c[4 * i + 3] = 2.0 / (a->h[i] * a->h[i] * a->h[i]) * (a->z[i] - a->z[i + 1]) + 1.0 / (a->h[i] * a->h[i]) * (a->zp[i] + a->zp[i + 1]);
}
cleanup:
return;
}
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