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klujax.cpp
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// version: 0.3.1
// Imports
#include "klu.h"
#include "pybind11/pybind11.h"
#include "xla/ffi/api/ffi.h"
#include <cmath>
namespace py = pybind11;
namespace ffi = xla::ffi;
// Helper functions
bool _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, Aj into Bi, Bk
int col = 0;
int dest = 0;
for (int n = 0; n < n_nz; n++) {
if (Aj[n] >= n_col) {
return false;
}
col = Aj[n];
dest = Bp[col];
if (Ai[n] >= n_col) {
return false;
}
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;
}
return true;
}
// Implementations
ffi::Error _solve_f64(ffi::Buffer<ffi::DataType::S32> buf_Ai,
ffi::Buffer<ffi::DataType::S32> buf_Aj,
ffi::Buffer<ffi::DataType::F64> buf_Ax,
ffi::Buffer<ffi::DataType::F64> buf_b,
ffi::Result<ffi::Buffer<ffi::DataType::F64>> buf_x) {
// get args
int *Ai = buf_Ai.typed_data();
int *Aj = buf_Aj.typed_data();
double *Ax = buf_Ax.typed_data();
double *b = buf_b.typed_data();
double *x = buf_x->typed_data();
int n_lhs = (int)buf_Ax.dimensions()[0];
int n_nz = (int)buf_Ax.dimensions()[1];
int n_rhs = (int)buf_x->dimensions()[1];
int n_col = (int)buf_x->dimensions()[2];
// copy b into result
for (int i = 0; i < n_lhs * n_col * n_rhs; i++) {
x[i] = b[i];
}
// get COO -> CSC transformation information
int *Bk = new int[n_nz](); // Ax -> Bx transformation indices
int *Bi = new int[n_nz]();
int *Bp = new int[n_col + 1]();
double *Bx = new double[n_nz]();
bool is_valid = _coo_to_csc_analyze(n_col, n_nz, Ai, Aj, Bi, Bp, Bk);
if (!is_valid) {
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
return ffi::Error::InvalidArgument(
"max(Ai, Aj) >= n_col. Broadcasted shapes: Ax: (n_lhs=" +
std::to_string(n_lhs) + ", n_nz=" + std::to_string(n_nz) +
"); b: (n_lhs=" + std::to_string(n_lhs) + ", n_col=" +
std::to_string(n_col) + ", n_rhs=" + std::to_string(n_rhs) +
"). You might want to transpose b?");
}
// 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
for (int i = 0; i < n_lhs; i++) {
int m = i * n_nz;
int n = i * n_rhs * n_col;
// convert COO Ax to CSC Bx
for (int k = 0; k < n_nz; 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, &x[n], &Common);
}
// clean up
klu_free_symbolic(&Symbolic, &Common);
klu_free_numeric(&Numeric, &Common);
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
return ffi::Error::Success();
}
ffi::Error
_coo_mul_vec_f64(ffi::Buffer<ffi::DataType::S32> buf_Ai,
ffi::Buffer<ffi::DataType::S32> buf_Aj,
ffi::Buffer<ffi::DataType::F64> buf_Ax,
ffi::Buffer<ffi::DataType::F64> buf_x,
ffi::Result<ffi::Buffer<ffi::DataType::F64>> buf_b) {
// get args
int *Ai = buf_Ai.typed_data();
int *Aj = buf_Aj.typed_data();
double *Ax = buf_Ax.typed_data();
double *x = buf_x.typed_data();
double *b = buf_b->typed_data();
int n_lhs = (int)buf_Ax.dimensions()[0];
int n_nz = (int)buf_Ax.dimensions()[1];
int n_rhs = (int)buf_b->dimensions()[1];
int n_col = (int)buf_b->dimensions()[2];
// initialize empty result
for (int i = 0; i < n_lhs * n_col * n_rhs; i++) {
b[i] = 0.0;
}
// fill result
for (int k = 0; k < n_nz; k++) {
if (Ai[k] >= n_col || Aj[k] >= n_col) {
return ffi::Error::InvalidArgument(
"max(Ai, Aj) >= n_col. Broadcasted shapes: Ax: (n_lhs=" +
std::to_string(n_lhs) + ", n_nz=" + std::to_string(n_nz) +
"); b: (n_lhs=" + std::to_string(n_lhs) + ", n_col=" +
std::to_string(n_col) + ", n_rhs=" + std::to_string(n_rhs) +
"). You might want to transpose b?");
}
for (int i = 0; i < n_lhs; i++) {
int m = i * n_nz;
int n = i * n_rhs * n_col;
for (int j = 0; j < n_rhs; j++) {
b[n + Ai[k] + j * n_col] += Ax[m + k] * x[n + Aj[k] + j * n_col];
}
}
}
return ffi::Error::Success();
}
ffi::Error _solve_c128(ffi::Buffer<ffi::DataType::S32> buf_Ai,
ffi::Buffer<ffi::DataType::S32> buf_Aj,
ffi::Buffer<ffi::DataType::C128> buf_Ax,
ffi::Buffer<ffi::DataType::C128> buf_b,
ffi::Result<ffi::Buffer<ffi::DataType::C128>> buf_x) {
// get args
int *Ai = buf_Ai.typed_data();
int *Aj = buf_Aj.typed_data();
double *Ax = (double *)buf_Ax.typed_data();
double *b = (double *)buf_b.typed_data();
double *x = (double *)buf_x->typed_data();
int n_lhs = (int)buf_Ax.dimensions()[0];
int n_nz = (int)buf_Ax.dimensions()[1];
int n_rhs = (int)buf_x->dimensions()[1];
int n_col = (int)buf_x->dimensions()[2];
// copy b into result
for (int i = 0; i < 2 * n_lhs * n_col * n_rhs; i++) {
x[i] = b[i];
}
// get COO -> CSC transformation information
int *Bk = new int[n_nz](); // Ax -> Bx transformation indices
int *Bi = new int[n_nz](); // CSC row indices
int *Bp = new int[n_col + 1](); // CSC column pointers
double *Bx = new double[2 * n_nz]();
bool is_valid = _coo_to_csc_analyze(n_col, n_nz, Ai, Aj, Bi, Bp, Bk);
if (!is_valid) {
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
return ffi::Error::InvalidArgument(
"max(Ai, Aj) >= n_col. Broadcasted shapes: Ax: (n_lhs=" +
std::to_string(n_lhs) + ", n_nz=" + std::to_string(n_nz) +
"); b: (n_lhs=" + std::to_string(n_lhs) + ", n_col=" +
std::to_string(n_col) + ", n_rhs=" + std::to_string(n_rhs) +
"). You might want to transpose b?");
}
// 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
for (int i = 0; i < n_lhs; i++) {
int m = 2 * i * n_nz;
int n = 2 * i * n_rhs * n_col;
// convert COO Ax to CSC Bx
for (int k = 0; k < n_nz; 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, &x[n], &Common);
}
// clean up
klu_free_symbolic(&Symbolic, &Common);
klu_free_numeric(&Numeric, &Common);
delete[] Bk;
delete[] Bi;
delete[] Bp;
delete[] Bx;
return ffi::Error::Success();
}
ffi::Error
_coo_mul_vec_c128(ffi::Buffer<ffi::DataType::S32> buf_Ai,
ffi::Buffer<ffi::DataType::S32> buf_Aj,
ffi::Buffer<ffi::DataType::C128> buf_Ax,
ffi::Buffer<ffi::DataType::C128> buf_x,
ffi::Result<ffi::Buffer<ffi::DataType::C128>> buf_b) {
// get args
int *Ai = buf_Ai.typed_data();
int *Aj = buf_Aj.typed_data();
double *Ax = (double *)buf_Ax.typed_data();
double *x = (double *)buf_x.typed_data();
double *b = (double *)buf_b->typed_data();
int n_lhs = (int)buf_Ax.dimensions()[0];
int n_nz = (int)buf_Ax.dimensions()[1];
int n_rhs = (int)buf_b->dimensions()[1];
int n_col = (int)buf_b->dimensions()[2];
// initialize empty result
for (int i = 0; i < 2 * n_lhs * n_col * n_rhs; i++) {
b[i] = 0.0;
}
// fill result
for (int k = 0; k < n_nz; k++) {
if (Ai[k] >= n_col || Aj[k] >= n_col) {
return ffi::Error::InvalidArgument(
"max(Ai, Aj) >= n_col. Broadcasted shapes: Ax: (n_lhs=" +
std::to_string(n_lhs) + ", n_nz=" + std::to_string(n_nz) +
"); b: (n_lhs=" + std::to_string(n_lhs) + ", n_col=" +
std::to_string(n_col) + ", n_rhs=" + std::to_string(n_rhs) +
"). You might want to transpose b?");
}
for (int i = 0; i < n_lhs; i++) {
int m = 2 * i * n_nz;
int n = 2 * i * n_rhs * n_col;
for (int j = 0; j < n_rhs; j++) {
b[n + 2 * (Ai[k] + j * n_col)] += // real part
Ax[m + 2 * k] * x[n + 2 * (Aj[k] + j * n_col)] - // real * real
Ax[m + 2 * k + 1] *
x[n + 2 * (Aj[k] + j * n_col) + 1]; // imag * imag
b[n + 2 * (Ai[k] + j * n_col) + 1] += // imag part
Ax[m + 2 * k] * x[n + 2 * (Aj[k] + j * n_col) + 1] + // real * imag
Ax[m + 2 * k + 1] * x[n + 2 * (Aj[k] + j * n_col)]; // imag * real
}
}
}
return ffi::Error::Success();
}
// XLA wrappers
XLA_FFI_DEFINE_HANDLER_SYMBOL( // A x = b
solve_f64, _solve_f64,
ffi::Ffi::Bind()
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Ai
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Aj
.Arg<ffi::Buffer<ffi::DataType::F64>>() // Ax
.Arg<ffi::Buffer<ffi::DataType::F64>>() // b
.Ret<ffi::Buffer<ffi::DataType::F64>>() // x
);
XLA_FFI_DEFINE_HANDLER_SYMBOL( // b = A x
coo_mul_vec_f64, _coo_mul_vec_f64,
ffi::Ffi::Bind()
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Ai
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Aj
.Arg<ffi::Buffer<ffi::DataType::F64>>() // Ax
.Arg<ffi::Buffer<ffi::DataType::F64>>() // x
.Ret<ffi::Buffer<ffi::DataType::F64>>() // b
);
XLA_FFI_DEFINE_HANDLER_SYMBOL( // A x = b
solve_c128, _solve_c128,
ffi::Ffi::Bind()
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Ai
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Aj
.Arg<ffi::Buffer<ffi::DataType::C128>>() // Ax
.Arg<ffi::Buffer<ffi::DataType::C128>>() // b
.Ret<ffi::Buffer<ffi::DataType::C128>>() // x
);
XLA_FFI_DEFINE_HANDLER_SYMBOL( // b = A x
coo_mul_vec_c128, _coo_mul_vec_c128,
ffi::Ffi::Bind()
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Ai
.Arg<ffi::Buffer<ffi::DataType::S32>>() // Aj
.Arg<ffi::Buffer<ffi::DataType::C128>>() // Ax
.Arg<ffi::Buffer<ffi::DataType::C128>>() // x
.Ret<ffi::Buffer<ffi::DataType::C128>>() // b
);
// Python wrappers
PYBIND11_MODULE(klujax_cpp, m) {
m.def("solve_f64", []() { return py::capsule((void *)&solve_f64); });
m.def("coo_mul_vec_f64",
[]() { return py::capsule((void *)&coo_mul_vec_f64); });
m.def("solve_c128", []() { return py::capsule((void *)&solve_c128); });
m.def("coo_mul_vec_c128",
[]() { return py::capsule((void *)&coo_mul_vec_c128); });
}