// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2013 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// modification, are permitted provided that the following conditions are met:
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// Author: keir@google.com (Keir Mierle)
#include "ceres/small_blas.h"
#include "gtest/gtest.h"
#include "ceres/internal/eigen.h"
namespace ceres {
namespace internal {
TEST(BLAS, MatrixMatrixMultiply) {
const double kTolerance = 1e-16;
const int kRowA = 3;
const int kColA = 5;
Matrix A(kRowA, kColA);
A.setOnes();
const int kRowB = 5;
const int kColB = 7;
Matrix B(kRowB, kColB);
B.setOnes();
for (int row_stride_c = kRowA; row_stride_c < 3 * kRowA; ++row_stride_c) {
for (int col_stride_c = kColB; col_stride_c < 3 * kColB; ++col_stride_c) {
Matrix C(row_stride_c, col_stride_c);
C.setOnes();
Matrix C_plus = C;
Matrix C_minus = C;
Matrix C_assign = C;
Matrix C_plus_ref = C;
Matrix C_minus_ref = C;
Matrix C_assign_ref = C;
for (int start_row_c = 0; start_row_c + kRowA < row_stride_c; ++start_row_c) {
for (int start_col_c = 0; start_col_c + kColB < col_stride_c; ++start_col_c) {
C_plus_ref.block(start_row_c, start_col_c, kRowA, kColB) +=
A * B;
MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, 1>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_plus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_plus_ref - C_plus).norm(), 0.0, kTolerance)
<< "C += A * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_plus_ref << "\n"
<< "C: \n" << C_plus;
C_minus_ref.block(start_row_c, start_col_c, kRowA, kColB) -=
A * B;
MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, -1>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_minus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_minus_ref - C_minus).norm(), 0.0, kTolerance)
<< "C -= A * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_minus_ref << "\n"
<< "C: \n" << C_minus;
C_assign_ref.block(start_row_c, start_col_c, kRowA, kColB) =
A * B;
MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, 0>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_assign.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_assign_ref - C_assign).norm(), 0.0, kTolerance)
<< "C = A * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_assign_ref << "\n"
<< "C: \n" << C_assign;
}
}
}
}
}
TEST(BLAS, MatrixTransposeMatrixMultiply) {
const double kTolerance = 1e-16;
const int kRowA = 5;
const int kColA = 3;
Matrix A(kRowA, kColA);
A.setOnes();
const int kRowB = 5;
const int kColB = 7;
Matrix B(kRowB, kColB);
B.setOnes();
for (int row_stride_c = kColA; row_stride_c < 3 * kColA; ++row_stride_c) {
for (int col_stride_c = kColB; col_stride_c < 3 * kColB; ++col_stride_c) {
Matrix C(row_stride_c, col_stride_c);
C.setOnes();
Matrix C_plus = C;
Matrix C_minus = C;
Matrix C_assign = C;
Matrix C_plus_ref = C;
Matrix C_minus_ref = C;
Matrix C_assign_ref = C;
for (int start_row_c = 0; start_row_c + kColA < row_stride_c; ++start_row_c) {
for (int start_col_c = 0; start_col_c + kColB < col_stride_c; ++start_col_c) {
C_plus_ref.block(start_row_c, start_col_c, kColA, kColB) +=
A.transpose() * B;
MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, 1>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_plus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_plus_ref - C_plus).norm(), 0.0, kTolerance)
<< "C += A' * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_plus_ref << "\n"
<< "C: \n" << C_plus;
C_minus_ref.block(start_row_c, start_col_c, kColA, kColB) -=
A.transpose() * B;
MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, -1>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_minus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_minus_ref - C_minus).norm(), 0.0, kTolerance)
<< "C -= A' * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_minus_ref << "\n"
<< "C: \n" << C_minus;
C_assign_ref.block(start_row_c, start_col_c, kColA, kColB) =
A.transpose() * B;
MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, 0>(
A.data(), kRowA, kColA,
B.data(), kRowB, kColB,
C_assign.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
EXPECT_NEAR((C_assign_ref - C_assign).norm(), 0.0, kTolerance)
<< "C = A' * B \n"
<< "row_stride_c : " << row_stride_c << "\n"
<< "col_stride_c : " << col_stride_c << "\n"
<< "start_row_c : " << start_row_c << "\n"
<< "start_col_c : " << start_col_c << "\n"
<< "Cref : \n" << C_assign_ref << "\n"
<< "C: \n" << C_assign;
}
}
}
}
}
TEST(BLAS, MatrixVectorMultiply) {
const double kTolerance = 1e-16;
const int kRowA = 5;
const int kColA = 3;
Matrix A(kRowA, kColA);
A.setOnes();
Vector b(kColA);
b.setOnes();
Vector c(kRowA);
c.setOnes();
Vector c_plus = c;
Vector c_minus = c;
Vector c_assign = c;
Vector c_plus_ref = c;
Vector c_minus_ref = c;
Vector c_assign_ref = c;
c_plus_ref += A * b;
MatrixVectorMultiply<kRowA, kColA, 1>(A.data(), kRowA, kColA,
b.data(),
c_plus.data());
EXPECT_NEAR((c_plus_ref - c_plus).norm(), 0.0, kTolerance)
<< "c += A * b \n"
<< "c_ref : \n" << c_plus_ref << "\n"
<< "c: \n" << c_plus;
c_minus_ref -= A * b;
MatrixVectorMultiply<kRowA, kColA, -1>(A.data(), kRowA, kColA,
b.data(),
c_minus.data());
EXPECT_NEAR((c_minus_ref - c_minus).norm(), 0.0, kTolerance)
<< "c += A * b \n"
<< "c_ref : \n" << c_minus_ref << "\n"
<< "c: \n" << c_minus;
c_assign_ref = A * b;
MatrixVectorMultiply<kRowA, kColA, 0>(A.data(), kRowA, kColA,
b.data(),
c_assign.data());
EXPECT_NEAR((c_assign_ref - c_assign).norm(), 0.0, kTolerance)
<< "c += A * b \n"
<< "c_ref : \n" << c_assign_ref << "\n"
<< "c: \n" << c_assign;
}
TEST(BLAS, MatrixTransposeVectorMultiply) {
const double kTolerance = 1e-16;
const int kRowA = 5;
const int kColA = 3;
Matrix A(kRowA, kColA);
A.setRandom();
Vector b(kRowA);
b.setRandom();
Vector c(kColA);
c.setOnes();
Vector c_plus = c;
Vector c_minus = c;
Vector c_assign = c;
Vector c_plus_ref = c;
Vector c_minus_ref = c;
Vector c_assign_ref = c;
c_plus_ref += A.transpose() * b;
MatrixTransposeVectorMultiply<kRowA, kColA, 1>(A.data(), kRowA, kColA,
b.data(),
c_plus.data());
EXPECT_NEAR((c_plus_ref - c_plus).norm(), 0.0, kTolerance)
<< "c += A' * b \n"
<< "c_ref : \n" << c_plus_ref << "\n"
<< "c: \n" << c_plus;
c_minus_ref -= A.transpose() * b;
MatrixTransposeVectorMultiply<kRowA, kColA, -1>(A.data(), kRowA, kColA,
b.data(),
c_minus.data());
EXPECT_NEAR((c_minus_ref - c_minus).norm(), 0.0, kTolerance)
<< "c += A' * b \n"
<< "c_ref : \n" << c_minus_ref << "\n"
<< "c: \n" << c_minus;
c_assign_ref = A.transpose() * b;
MatrixTransposeVectorMultiply<kRowA, kColA, 0>(A.data(), kRowA, kColA,
b.data(),
c_assign.data());
EXPECT_NEAR((c_assign_ref - c_assign).norm(), 0.0, kTolerance)
<< "c += A' * b \n"
<< "c_ref : \n" << c_assign_ref << "\n"
<< "c: \n" << c_assign;
}
} // namespace internal
} // namespace ceres