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klujax.cpp
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klujax.cpp
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// version: 0.2.6
// author: Floris Laporte
#include <iostream>
#include <vector>
#include <klu.h>
#include <pybind11/pybind11.h>
namespace py = pybind11;
void coo_to_csc_analyze(int n_col, int n_nz, int *Ai, int *Aj, int *Bi, int *Bp,
int *Bk) {
// compute number of non-zero entries per row of A
for (int n = 0; n < n_nz; n++) {
Bp[Aj[n]] += 1;
}
// cumsum the n_nz per row to get Bp
int cumsum = 0;
int temp = 0;
for (int j = 0; j < n_col; j++) {
temp = Bp[j];
Bp[j] = cumsum;
cumsum += temp;
}
// write Ai, Ax into Bi, Bk
int col = 0;
int dest = 0;
for (int n = 0; n < n_nz; n++) {
col = Aj[n];
dest = Bp[col];
Bi[dest] = Ai[n];
Bk[dest] = n;
Bp[col] += 1;
}
int last = 0;
for (int i = 0; i <= n_col; i++) {
temp = Bp[i];
Bp[i] = last;
last = temp;
}
}
void solve_f64(void *out, void **in) {
// get args
int n_col = *reinterpret_cast<int *>(in[0]);
int n_lhs = *reinterpret_cast<int *>(in[1]);
int n_rhs = *reinterpret_cast<int *>(in[2]);
int Anz = *reinterpret_cast<int *>(in[3]);
int *Ai = reinterpret_cast<int *>(in[4]);
int *Aj = reinterpret_cast<int *>(in[5]);
double *Ax = reinterpret_cast<double *>(in[6]);
double *b = reinterpret_cast<double *>(in[7]);
double *result = reinterpret_cast<double *>(out);
// copy b into result
for (int i = 0; i < n_lhs * n_col * n_rhs; i++) {
result[i] = b[i];
}
// get COO -> CSC transformation information
int *Bk = new int[Anz](); // Ax -> Bx transformation indices
int *Bi = new int[Anz]();
int *Bp = new int[n_col + 1]();
coo_to_csc_analyze(n_col, Anz, Ai, Aj, Bi, Bp, Bk);
// initialize KLU for given sparsity pattern
klu_symbolic *Symbolic;
klu_numeric *Numeric;
klu_common Common;
klu_defaults(&Common);
Symbolic = klu_analyze(n_col, Bp, Bi, &Common);
// solve for other elements in batch:
// NOTE: same sparsity pattern for each element in batch assumed
double *Bx = new double[Anz]();
for (int i = 0; i < n_lhs; i++) {
int m = i * Anz;
int n = i * n_rhs * n_col;
// convert COO Ax to CSC Bx
for (int k = 0; k < Anz; k++) {
Bx[k] = Ax[m + Bk[k]];
}
// solve using KLU
Numeric = klu_factor(Bp, Bi, Bx, Symbolic, &Common);
klu_solve(Symbolic, Numeric, n_col, n_rhs, &result[n], &Common);
}
// clean up
klu_free_symbolic(&Symbolic, &Common);
klu_free_numeric(&Numeric, &Common);
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
}
void solve_c128(void *out, void **in) {
// get args
int n_col = *reinterpret_cast<int *>(in[0]);
int n_lhs = *reinterpret_cast<int *>(in[1]);
int n_rhs = *reinterpret_cast<int *>(in[2]);
int Anz = *reinterpret_cast<int *>(in[3]);
int *Ai = reinterpret_cast<int *>(in[4]);
int *Aj = reinterpret_cast<int *>(in[5]);
double *Ax = reinterpret_cast<double *>(in[6]);
double *b = reinterpret_cast<double *>(in[7]);
double *result = reinterpret_cast<double *>(out);
// copy b into result
for (int i = 0; i < 2 * n_lhs * n_col * n_rhs; i++) {
result[i] = b[i];
}
// get COO -> CSC transformation information
int *Bk = new int[Anz](); // Ax -> Bx transformation indices
int *Bi = new int[Anz](); // CSC row indices
int *Bp = new int[n_col + 1](); // CSC column pointers
coo_to_csc_analyze(n_col, Anz, Ai, Aj, Bi, Bp, Bk);
// initialize KLU for given sparsity pattern
klu_symbolic *Symbolic;
klu_numeric *Numeric;
klu_common Common;
klu_defaults(&Common);
Symbolic = klu_analyze(n_col, Bp, Bi, &Common);
// solve for other elements in batch:
// NOTE: same sparsity pattern for each element in batch assumed
double *Bx = new double[2 * Anz]();
for (int i = 0; i < n_lhs; i++) {
int m = 2 * i * Anz;
int n = 2 * i * n_rhs * n_col;
// convert COO Ax to CSC Bx
for (int k = 0; k < Anz; k++) {
Bx[2 * k] = Ax[m + 2 * Bk[k]];
Bx[2 * k + 1] = Ax[m + 2 * Bk[k] + 1];
}
// solve using KLU
Numeric = klu_z_factor(Bp, Bi, Bx, Symbolic, &Common);
klu_z_solve(Symbolic, Numeric, n_col, n_rhs, &result[n], &Common);
}
// clean up
klu_free_symbolic(&Symbolic, &Common);
klu_free_numeric(&Numeric, &Common);
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
}
void coo_mul_vec_f64(void *out, void **in) {
// get args
int n_col = *reinterpret_cast<int *>(in[0]);
int n_lhs = *reinterpret_cast<int *>(in[1]);
int n_rhs = *reinterpret_cast<int *>(in[2]);
int Anz = *reinterpret_cast<int *>(in[3]);
int *Ai = reinterpret_cast<int *>(in[4]);
int *Aj = reinterpret_cast<int *>(in[5]);
double *Ax = reinterpret_cast<double *>(in[6]);
double *b = reinterpret_cast<double *>(in[7]);
double *result = reinterpret_cast<double *>(out);
// initialize empty result
for (int i = 0; i < n_lhs * n_col * n_rhs; i++) {
result[i] = 0.0;
}
// fill result
for (int i = 0; i < n_lhs; i++) {
int m = i * Anz;
int n = i * n_rhs * n_col;
for (int j = 0; j < n_rhs; j++) {
for (int k = 0; k < Anz; k++) {
result[n + Ai[k] + j * n_col] += Ax[m + k] * b[n + Aj[k] + j * n_col];
}
}
}
}
void coo_mul_vec_c128(void *out, void **in) {
// get args
int n_col = *reinterpret_cast<int *>(in[0]);
int n_lhs = *reinterpret_cast<int *>(in[1]);
int n_rhs = *reinterpret_cast<int *>(in[2]);
int Anz = *reinterpret_cast<int *>(in[3]);
int *Ai = reinterpret_cast<int *>(in[4]);
int *Aj = reinterpret_cast<int *>(in[5]);
double *Ax = reinterpret_cast<double *>(in[6]);
double *b = reinterpret_cast<double *>(in[7]);
double *result = reinterpret_cast<double *>(out);
// initialize empty result
for (int i = 0; i < 2 * n_lhs * n_col * n_rhs; i++) {
result[i] = 0.0;
}
// fill result
for (int i = 0; i < n_lhs; i++) {
int m = 2 * i * Anz;
int n = 2 * i * n_rhs * n_col;
for (int j = 0; j < n_rhs; j++) {
for (int k = 0; k < Anz; k++) {
result[n + 2 * (Ai[k] + j * n_col)] += // real part
Ax[m + 2 * k] * b[n + 2 * (Aj[k] + j * n_col)] - // real * real
Ax[m + 2 * k + 1] *
b[n + 2 * (Aj[k] + j * n_col) + 1]; // imag * imag
result[n + 2 * (Ai[k] + j * n_col) + 1] += // imag part
Ax[m + 2 * k] * b[n + 2 * (Aj[k] + j * n_col) + 1] + // real * imag
Ax[m + 2 * k + 1] * b[n + 2 * (Aj[k] + j * n_col)]; // imag * real
}
}
}
}
PYBIND11_MODULE(klujax_cpp, m) {
m.def(
"solve_f64",
[]() {
const char *name = "xla._CUSTOM_CALL_TARGET";
return py::capsule((void *)&solve_f64, name);
},
"solve a real-valued linear system of equations");
m.def(
"solve_c128",
[]() {
const char *name = "xla._CUSTOM_CALL_TARGET";
return py::capsule((void *)&solve_c128, name);
},
"solve a complex-valued linear system of equations");
m.def(
"coo_mul_vec_f64",
[]() {
const char *name = "xla._CUSTOM_CALL_TARGET";
return py::capsule((void *)&coo_mul_vec_f64, name);
},
"Multiply a real-valued COO sparse matrix with a vector.");
m.def(
"coo_mul_vec_c128",
[]() {
const char *name = "xla._CUSTOM_CALL_TARGET";
return py::capsule((void *)&coo_mul_vec_c128, name);
},
"Multiply a complex-valued COO sparse matrix with a vector.");
}