// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2013 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// Simple blas functions for use in the Schur Eliminator. These are
// fairly basic implementations which already yield a significant
// speedup in the eliminator performance.
#ifndef CERES_INTERNAL_SMALL_BLAS_H_
#define CERES_INTERNAL_SMALL_BLAS_H_
#include "ceres/internal/port.h"
#include "ceres/internal/eigen.h"
#include "glog/logging.h"
namespace ceres {
namespace internal {
// The following three macros are used to share code and reduce
// template junk across the various GEMM variants.
#define CERES_GEMM_BEGIN(name) \
template<int kRowA, int kColA, int kRowB, int kColB, int kOperation> \
inline void name(const double* A, \
const int num_row_a, \
const int num_col_a, \
const double* B, \
const int num_row_b, \
const int num_col_b, \
double* C, \
const int start_row_c, \
const int start_col_c, \
const int row_stride_c, \
const int col_stride_c)
#define CERES_GEMM_NAIVE_HEADER \
DCHECK_GT(num_row_a, 0); \
DCHECK_GT(num_col_a, 0); \
DCHECK_GT(num_row_b, 0); \
DCHECK_GT(num_col_b, 0); \
DCHECK_GE(start_row_c, 0); \
DCHECK_GE(start_col_c, 0); \
DCHECK_GT(row_stride_c, 0); \
DCHECK_GT(col_stride_c, 0); \
DCHECK((kRowA == Eigen::Dynamic) || (kRowA == num_row_a)); \
DCHECK((kColA == Eigen::Dynamic) || (kColA == num_col_a)); \
DCHECK((kRowB == Eigen::Dynamic) || (kRowB == num_row_b)); \
DCHECK((kColB == Eigen::Dynamic) || (kColB == num_col_b)); \
const int NUM_ROW_A = (kRowA != Eigen::Dynamic ? kRowA : num_row_a); \
const int NUM_COL_A = (kColA != Eigen::Dynamic ? kColA : num_col_a); \
const int NUM_ROW_B = (kColB != Eigen::Dynamic ? kRowB : num_row_b); \
const int NUM_COL_B = (kColB != Eigen::Dynamic ? kColB : num_col_b);
#define CERES_GEMM_EIGEN_HEADER \
const typename EigenTypes<kRowA, kColA>::ConstMatrixRef \
Aref(A, num_row_a, num_col_a); \
const typename EigenTypes<kRowB, kColB>::ConstMatrixRef \
Bref(B, num_row_b, num_col_b); \
MatrixRef Cref(C, row_stride_c, col_stride_c); \
#define CERES_CALL_GEMM(name) \
name<kRowA, kColA, kRowB, kColB, kOperation>( \
A, num_row_a, num_col_a, \
B, num_row_b, num_col_b, \
C, start_row_c, start_col_c, row_stride_c, col_stride_c);
// For the matrix-matrix functions below, there are three variants for
// each functionality. Foo, FooNaive and FooEigen. Foo is the one to
// be called by the user. FooNaive is a basic loop based
// implementation and FooEigen uses Eigen's implementation. Foo
// chooses between FooNaive and FooEigen depending on how many of the
// template arguments are fixed at compile time. Currently, FooEigen
// is called if all matrix dimensions are compile time
// constants. FooNaive is called otherwise. This leads to the best
// performance currently.
//
// The MatrixMatrixMultiply variants compute:
//
// C op A * B;
//
// The MatrixTransposeMatrixMultiply variants compute:
//
// C op A' * B
//
// where op can be +=, -=, or =.
//
// The template parameters (kRowA, kColA, kRowB, kColB) allow
// specialization of the loop at compile time. If this information is
// not available, then Eigen::Dynamic should be used as the template
// argument.
//
// kOperation = 1 -> C += A * B
// kOperation = -1 -> C -= A * B
// kOperation = 0 -> C = A * B
//
// The functions can write into matrices C which are larger than the
// matrix A * B. This is done by specifying the true size of C via
// row_stride_c and col_stride_c, and then indicating where A * B
// should be written into by start_row_c and start_col_c.
//
// Graphically if row_stride_c = 10, col_stride_c = 12, start_row_c =
// 4 and start_col_c = 5, then if A = 3x2 and B = 2x4, we get
//
// ------------
// ------------
// ------------
// ------------
// -----xxxx---
// -----xxxx---
// -----xxxx---
// ------------
// ------------
// ------------
//
CERES_GEMM_BEGIN(MatrixMatrixMultiplyEigen) {
CERES_GEMM_EIGEN_HEADER
Eigen::Block<MatrixRef, kRowA, kColB>
block(Cref, start_row_c, start_col_c, num_row_a, num_col_b);
if (kOperation > 0) {
block.noalias() += Aref * Bref;
} else if (kOperation < 0) {
block.noalias() -= Aref * Bref;
} else {
block.noalias() = Aref * Bref;
}
}
CERES_GEMM_BEGIN(MatrixMatrixMultiplyNaive) {
CERES_GEMM_NAIVE_HEADER
DCHECK_EQ(NUM_COL_A, NUM_ROW_B);
const int NUM_ROW_C = NUM_ROW_A;
const int NUM_COL_C = NUM_COL_B;
DCHECK_LE(start_row_c + NUM_ROW_C, row_stride_c);
DCHECK_LE(start_col_c + NUM_COL_C, col_stride_c);
for (int row = 0; row < NUM_ROW_C; ++row) {
for (int col = 0; col < NUM_COL_C; ++col) {
double tmp = 0.0;
for (int k = 0; k < NUM_COL_A; ++k) {
tmp += A[row * NUM_COL_A + k] * B[k * NUM_COL_B + col];
}
const int index = (row + start_row_c) * col_stride_c + start_col_c + col;
if (kOperation > 0) {
C[index] += tmp;
} else if (kOperation < 0) {
C[index] -= tmp;
} else {
C[index] = tmp;
}
}
}
}
CERES_GEMM_BEGIN(MatrixMatrixMultiply) {
#ifdef CERES_NO_CUSTOM_BLAS
CERES_CALL_GEMM(MatrixMatrixMultiplyEigen)
return;
#else
if (kRowA != Eigen::Dynamic && kColA != Eigen::Dynamic &&
kRowB != Eigen::Dynamic && kColB != Eigen::Dynamic) {
CERES_CALL_GEMM(MatrixMatrixMultiplyEigen)
} else {
CERES_CALL_GEMM(MatrixMatrixMultiplyNaive)
}
#endif
}
CERES_GEMM_BEGIN(MatrixTransposeMatrixMultiplyEigen) {
CERES_GEMM_EIGEN_HEADER
Eigen::Block<MatrixRef, kColA, kColB> block(Cref,
start_row_c, start_col_c,
num_col_a, num_col_b);
if (kOperation > 0) {
block.noalias() += Aref.transpose() * Bref;
} else if (kOperation < 0) {
block.noalias() -= Aref.transpose() * Bref;
} else {
block.noalias() = Aref.transpose() * Bref;
}
}
CERES_GEMM_BEGIN(MatrixTransposeMatrixMultiplyNaive) {
CERES_GEMM_NAIVE_HEADER
DCHECK_EQ(NUM_ROW_A, NUM_ROW_B);
const int NUM_ROW_C = NUM_COL_A;
const int NUM_COL_C = NUM_COL_B;
DCHECK_LE(start_row_c + NUM_ROW_C, row_stride_c);
DCHECK_LE(start_col_c + NUM_COL_C, col_stride_c);
for (int row = 0; row < NUM_ROW_C; ++row) {
for (int col = 0; col < NUM_COL_C; ++col) {
double tmp = 0.0;
for (int k = 0; k < NUM_ROW_A; ++k) {
tmp += A[k * NUM_COL_A + row] * B[k * NUM_COL_B + col];
}
const int index = (row + start_row_c) * col_stride_c + start_col_c + col;
if (kOperation > 0) {
C[index]+= tmp;
} else if (kOperation < 0) {
C[index]-= tmp;
} else {
C[index]= tmp;
}
}
}
}
CERES_GEMM_BEGIN(MatrixTransposeMatrixMultiply) {
#ifdef CERES_NO_CUSTOM_BLAS
CERES_CALL_GEMM(MatrixTransposeMatrixMultiplyEigen)
return;
#else
if (kRowA != Eigen::Dynamic && kColA != Eigen::Dynamic &&
kRowB != Eigen::Dynamic && kColB != Eigen::Dynamic) {
CERES_CALL_GEMM(MatrixTransposeMatrixMultiplyEigen)
} else {
CERES_CALL_GEMM(MatrixTransposeMatrixMultiplyNaive)
}
#endif
}
// Matrix-Vector multiplication
//
// c op A * b;
//
// where op can be +=, -=, or =.
//
// The template parameters (kRowA, kColA) allow specialization of the
// loop at compile time. If this information is not available, then
// Eigen::Dynamic should be used as the template argument.
//
// kOperation = 1 -> c += A' * b
// kOperation = -1 -> c -= A' * b
// kOperation = 0 -> c = A' * b
template<int kRowA, int kColA, int kOperation>
inline void MatrixVectorMultiply(const double* A,
const int num_row_a,
const int num_col_a,
const double* b,
double* c) {
#ifdef CERES_NO_CUSTOM_BLAS
const typename EigenTypes<kRowA, kColA>::ConstMatrixRef
Aref(A, num_row_a, num_col_a);
const typename EigenTypes<kColA>::ConstVectorRef bref(b, num_col_a);
typename EigenTypes<kRowA>::VectorRef cref(c, num_row_a);
// lazyProduct works better than .noalias() for matrix-vector
// products.
if (kOperation > 0) {
cref += Aref.lazyProduct(bref);
} else if (kOperation < 0) {
cref -= Aref.lazyProduct(bref);
} else {
cref = Aref.lazyProduct(bref);
}
#else
DCHECK_GT(num_row_a, 0);
DCHECK_GT(num_col_a, 0);
DCHECK((kRowA == Eigen::Dynamic) || (kRowA == num_row_a));
DCHECK((kColA == Eigen::Dynamic) || (kColA == num_col_a));
const int NUM_ROW_A = (kRowA != Eigen::Dynamic ? kRowA : num_row_a);
const int NUM_COL_A = (kColA != Eigen::Dynamic ? kColA : num_col_a);
for (int row = 0; row < NUM_ROW_A; ++row) {
double tmp = 0.0;
for (int col = 0; col < NUM_COL_A; ++col) {
tmp += A[row * NUM_COL_A + col] * b[col];
}
if (kOperation > 0) {
c[row] += tmp;
} else if (kOperation < 0) {
c[row] -= tmp;
} else {
c[row] = tmp;
}
}
#endif // CERES_NO_CUSTOM_BLAS
}
// Similar to MatrixVectorMultiply, except that A is transposed, i.e.,
//
// c op A' * b;
template<int kRowA, int kColA, int kOperation>
inline void MatrixTransposeVectorMultiply(const double* A,
const int num_row_a,
const int num_col_a,
const double* b,
double* c) {
#ifdef CERES_NO_CUSTOM_BLAS
const typename EigenTypes<kRowA, kColA>::ConstMatrixRef
Aref(A, num_row_a, num_col_a);
const typename EigenTypes<kRowA>::ConstVectorRef bref(b, num_row_a);
typename EigenTypes<kColA>::VectorRef cref(c, num_col_a);
// lazyProduct works better than .noalias() for matrix-vector
// products.
if (kOperation > 0) {
cref += Aref.transpose().lazyProduct(bref);
} else if (kOperation < 0) {
cref -= Aref.transpose().lazyProduct(bref);
} else {
cref = Aref.transpose().lazyProduct(bref);
}
#else
DCHECK_GT(num_row_a, 0);
DCHECK_GT(num_col_a, 0);
DCHECK((kRowA == Eigen::Dynamic) || (kRowA == num_row_a));
DCHECK((kColA == Eigen::Dynamic) || (kColA == num_col_a));
const int NUM_ROW_A = (kRowA != Eigen::Dynamic ? kRowA : num_row_a);
const int NUM_COL_A = (kColA != Eigen::Dynamic ? kColA : num_col_a);
for (int row = 0; row < NUM_COL_A; ++row) {
double tmp = 0.0;
for (int col = 0; col < NUM_ROW_A; ++col) {
tmp += A[col * NUM_COL_A + row] * b[col];
}
if (kOperation > 0) {
c[row] += tmp;
} else if (kOperation < 0) {
c[row] -= tmp;
} else {
c[row] = tmp;
}
}
#endif // CERES_NO_CUSTOM_BLAS
}
#undef CERES_GEMM_BEGIN
#undef CERES_GEMM_EIGEN_HEADER
#undef CERES_GEMM_NAIVE_HEADER
#undef CERES_CALL_GEMM
} // namespace internal
} // namespace ceres
#endif // CERES_INTERNAL_SMALL_BLAS_H_