Matrix.h

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/* Copyright 2017 Kristofer Björnson
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
 
#ifndef COM_DAFER45_TBTK_MATRIX
#define COM_DAFER45_TBTK_MATRIX
 
#include "TBTK/TBTKMacros.h"
 
#include <complex>
 
namespace TBTK{
 
template<typename DataType, unsigned int ROWS = 0, unsigned int COLS = 0>
class Matrix{
public:
    Matrix();
 
    Matrix(const Matrix<DataType, ROWS, COLS> &matrix);
 
    Matrix(Matrix<DataType, ROWS, COLS> &&matrix);
 
    ~Matrix();
 
    Matrix<DataType, ROWS, COLS>& operator=(
        const Matrix<DataType, ROWS, COLS> &rhs
    );
 
    Matrix<DataType, ROWS, COLS>& operator=(
        Matrix<DataType, ROWS, COLS> &&rhs
    );
 
    const DataType& at(unsigned int row, unsigned int col) const;
 
    DataType& at(unsigned int row, unsigned int col);
 
    unsigned int getNumRows() const;
 
    unsigned int getNumCols() const;
private:
    DataType data[ROWS*COLS];
};
 
template<typename DataType>
class Matrix<DataType, 0, 0>{
public:
    Matrix();
 
    Matrix(unsigned int rows, unsigned int cols);
 
    Matrix(const Matrix<DataType, 0, 0> &matrix);
 
    Matrix(Matrix<DataType, 0, 0> &&matrix);
 
    ~Matrix();
 
    Matrix<DataType, 0, 0>& operator=(const Matrix<DataType, 0, 0> &rhs);
 
    Matrix<DataType, 0, 0>& operator=(Matrix<DataType, 0, 0> &&rhs);
 
    const DataType& at(unsigned int row, unsigned int col) const;
 
    DataType& at(unsigned int row, unsigned int col);
 
    unsigned int getNumRows() const;
 
    unsigned int getNumCols() const;
 
    const Matrix<DataType, 0, 0> operator*(
        const Matrix<DataType, 0, 0> &rhs
    ) const;
private:
    DataType *data;
 
    unsigned int rows;
 
    unsigned int cols;
};
 
template<>
class Matrix<std::complex<double>, 0, 0>{
public:
    Matrix();
 
    Matrix(unsigned int rows, unsigned int cols);
 
    Matrix(const Matrix<std::complex<double>, 0, 0> &matrix);
 
    Matrix(Matrix<std::complex<double>, 0, 0> &&matrix);
 
    ~Matrix();
 
    Matrix<std::complex<double>, 0, 0>& operator=(
        const Matrix<std::complex<double>, 0, 0> &rhs
    );
 
    Matrix<std::complex<double>, 0, 0>& operator=(
        Matrix<std::complex<double>, 0, 0> &&rhs
    );
 
    const std::complex<double>& at(
        unsigned int row,
        unsigned int col
    ) const;
 
    std::complex<double>& at(unsigned int row, unsigned int col);
 
    unsigned int getNumRows() const;
 
    unsigned int getNumCols() const;
 
    const Matrix<std::complex<double>, 0, 0> operator*(
        const Matrix<std::complex<double>, 0, 0> &rhs
    ) const;
 
    void invert();
 
    std::complex<double> determinant();
private:
    std::complex<double> *data;
 
    unsigned int rows;
 
    unsigned int cols;
};
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>::Matrix(){
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>::Matrix(const Matrix<DataType, ROWS, COLS> &matrix){
    for(unsigned int n = 0; n < ROWS*COLS; n++)
        data[n] = matrix.data[n];
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>::Matrix(Matrix<DataType, ROWS, COLS> &&matrix){
    for(unsigned int n = 0; n < ROWS*COLS; n++)
        data[n] = matrix.data[n];
}
 
template<typename DataType>
Matrix<DataType, 0, 0>::Matrix(){
    data = nullptr;
}
 
template<typename DataType>
Matrix<DataType, 0, 0>::Matrix(unsigned int rows, unsigned int cols){
    this->rows = rows;
    this->cols = cols;
    data = new DataType[rows*cols];
}
 
template<typename DataType>
Matrix<DataType, 0, 0>::Matrix(const Matrix<DataType, 0, 0> &matrix){
    rows = matrix.rows;
    cols = matrix.cols;
    data = new DataType[rows*cols];
    for(unsigned int n = 0; n < rows*cols; n++)
        data[n] = matrix.data[n];
}
 
template<typename DataType>
Matrix<DataType, 0, 0>::Matrix(Matrix<DataType, 0, 0> &&matrix){
    rows = matrix.rows;
    cols = matrix.cols;
    data = matrix.data;
    matrix.data = nullptr;
}
 
inline Matrix<std::complex<double>, 0, 0>::Matrix(){
    data = nullptr;
}
 
inline Matrix<std::complex<double>, 0, 0>::Matrix(unsigned int rows, unsigned int cols){
    this->rows = rows;
    this->cols = cols;
    data = new std::complex<double>[rows*cols];
}
 
inline Matrix<std::complex<double>, 0, 0>::Matrix(
    const Matrix<std::complex<double>, 0, 0> &matrix
){
    rows = matrix.rows;
    cols = matrix.cols;
    data = new std::complex<double>[rows*cols];
    for(unsigned int n = 0; n < rows*cols; n++)
        data[n] = matrix.data[n];
}
 
inline Matrix<std::complex<double>, 0, 0>::Matrix(
    Matrix<std::complex<double>, 0, 0> &&matrix
){
    rows = matrix.rows;
    cols = matrix.cols;
    data = matrix.data;
    matrix.data = nullptr;
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>::~Matrix(){
}
 
template<typename DataType>
Matrix<DataType, 0, 0>::~Matrix(){
    if(data != nullptr)
        delete [] data;
}
 
inline Matrix<std::complex<double>, 0, 0>::~Matrix(){
    if(data != nullptr)
        delete [] data;
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>& Matrix<DataType, ROWS, COLS>::operator=(
    const Matrix<DataType, ROWS, COLS> &rhs
){
    if(this != &rhs){
        for(unsigned int n = 0; n < ROWS*COLS; n++)
            data[n] = rhs.data[n];
    }
 
    return *this;
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
Matrix<DataType, ROWS, COLS>& Matrix<DataType, ROWS, COLS>::operator=(
    Matrix<DataType, ROWS, COLS> &&rhs
){
    if(this != &rhs){
        for(unsigned int n = 0; n < ROWS*COLS; n++)
            data[n] = rhs.data[n];
    }
 
    return *this;
}
 
template<typename DataType>
Matrix<DataType, 0, 0>& Matrix<DataType, 0, 0>::operator=(
    const Matrix<DataType, 0, 0> &rhs
){
    if(this != &rhs){
        rows = rhs.rows;
        cols = rhs.cols;
 
        if(data != nullptr)
            delete [] data;
 
        data = new DataType[rows*cols];
        for(unsigned int n = 0; n < rows*cols; n++)
            data[n] = rhs.data[n];
    }
 
    return *this;
}
 
template<typename DataType>
Matrix<DataType, 0, 0>& Matrix<DataType, 0, 0>::operator=(
    Matrix<DataType, 0, 0> &&rhs
){
    if(this != &rhs){
        rows = rhs.rows;
        cols = rhs.cols;
 
        if(data != nullptr)
            delete [] data;
 
        data = rhs.data;
        rhs.data = nullptr;
    }
 
    return *this;
}
 
inline Matrix<std::complex<double>, 0, 0>& Matrix<std::complex<double>, 0, 0>::operator=(
    const Matrix<std::complex<double>, 0, 0> &rhs
){
    if(this != &rhs){
        rows = rhs.rows;
        cols = rhs.cols;
 
        if(data != nullptr)
            delete [] data;
 
        data = new std::complex<double>[rows*cols];
        for(unsigned int n = 0; n < rows*cols; n++)
            data[n] = rhs.data[n];
    }
 
    return *this;
}
 
inline Matrix<std::complex<double>, 0, 0>& Matrix<std::complex<double>, 0, 0>::operator=(
    Matrix<std::complex<double>, 0, 0> &&rhs
){
    if(this != &rhs){
        rows = rhs.rows;
        cols = rhs.cols;
 
        if(data != nullptr)
            delete [] data;
 
        data = rhs.data;
        rhs.data = nullptr;
    }
 
    return *this;
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
const DataType& Matrix<DataType, ROWS, COLS>::at(
    unsigned int row,
    unsigned int col
) const{
    return data[row + ROWS*col];
}
 
template<typename DataType>
const DataType& Matrix<DataType, 0, 0>::at(
    unsigned int row,
    unsigned int col
) const{
    return data[row + rows*col];
}
 
inline const std::complex<double>& Matrix<std::complex<double>, 0, 0>::at(
    unsigned int row,
    unsigned int col
) const{
    return data[row + rows*col];
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
DataType& Matrix<DataType, ROWS, COLS>::at(
    unsigned int row,
    unsigned int col
){
    return data[row + ROWS*col];
}
 
template<typename DataType>
DataType& Matrix<DataType, 0, 0>::at(
    unsigned int row,
    unsigned int col
){
    return data[row + rows*col];
}
 
inline std::complex<double>& Matrix<std::complex<double>, 0, 0>::at(
    unsigned int row,
    unsigned int col
){
    return data[row + rows*col];
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
unsigned int Matrix<DataType, ROWS, COLS>::getNumRows() const{
    return ROWS;
}
 
template<typename DataType>
unsigned int Matrix<DataType, 0, 0>::getNumRows() const{
    return rows;
}
 
inline unsigned int Matrix<std::complex<double>, 0, 0>::getNumRows() const{
    return rows;
}
 
template<typename DataType, unsigned int ROWS, unsigned int COLS>
unsigned int Matrix<DataType, ROWS, COLS>::getNumCols() const{
    return COLS;
}
 
template<typename DataType>
unsigned int Matrix<DataType, 0, 0>::getNumCols() const{
    return cols;
}
 
inline unsigned int Matrix<std::complex<double>, 0, 0>::getNumCols() const{
    return cols;
}
 
template<typename DataType>
inline const Matrix<DataType, 0, 0> Matrix<DataType, 0, 0>::operator*(
    const Matrix<DataType, 0, 0> &rhs
) const{
    TBTKAssert(
        cols == rhs.rows,
        "Matrix::operator*()",
        "Incompatible matrix dimensions.",
        "The matrix dimensions are " << rows << "x" << cols << " and "
        << rhs.rows << "x" << rhs.cols << "\n"
    );
 
    Matrix<DataType> result(rows, rhs.cols);
    for(unsigned int row = 0; row < rows; row++){
        for(unsigned int col = 0; col < rhs.cols; col++){
            result.at(row, col) = 0.;
 
            for(unsigned int n = 0; n < cols; n++){
                result.at(row, col)
                    += at(row, n)*rhs.at(n, col);
            }
        }
    }
 
    return result;
}
 
inline const Matrix<std::complex<double>, 0, 0> Matrix<std::complex<double>, 0, 0>::operator*(
    const Matrix<std::complex<double>, 0, 0> &rhs
) const{
    TBTKAssert(
        cols == rhs.rows,
        "Matrix::operator*()",
        "Incompatible matrix dimensions.",
        "The matrix dimensions are " << rows << "x" << cols << " and "
        << rhs.rows << "x" << rhs.cols << "\n"
    );
 
    Matrix<std::complex<double>> result(rows, rhs.cols);
    for(unsigned int row = 0; row < rows; row++){
        for(unsigned int col = 0; col < rhs.cols; col++){
            result.at(row, col) = 0.;
 
            for(unsigned int n = 0; n < cols; n++){
                result.at(row, col)
                    += at(row, n)*rhs.at(n, col);
            }
        }
    }
 
    return result;
}
 
extern "C"{
    void zgetrf_(
        int *M,
        int *N,
        std::complex<double> *A,
        int *lda,
        int *ipiv,
        int *info
    );
    void zgetri_(
        int *N,
        std::complex<double> *A,
        int *lda,
        int *ipiv,
        std::complex<double> *work,
        int *lwork,
        int *info
    );
};
 
inline void Matrix<std::complex<double>, 0, 0>::invert(){
    TBTKAssert(
        rows == cols,
        "Matrix::invert()",
        "Invalid matrix dimension. Only square matrices can be"
        << " inverted, but the matrix has size " << rows << "x" << cols
        << "\n",
        ""
    );
 
    int *ipiv = new int[std::min(rows, cols)];
    int lwork = rows*cols;
    std::complex<double> *work = new std::complex<double>[lwork];
    int info;
 
    zgetrf_((int*)&rows, (int*)&cols, data, (int*)&rows, ipiv, &info);
 
    if(info < 0){
        TBTKExit(
            "Matrix::invert()",
            "Argument '" << -info << "' to zgetrf_() is invlid.",
            "This should never happen, contact the developer."
        );
    }
    else if(info > 0){
        TBTKExit(
            "Matrix::invert()",
            "Unable to invert matrix since it is signular.",
            ""
        );
    }
 
    zgetri_((int*)&rows, data, (int*)&rows, ipiv, work, &lwork, &info);
    TBTKAssert(
        info == 0,
        "Matrix::invert()",
        "Inversion failed with error code 'INFO = " << info << "'.",
        "See the documentation for the lapack function zgetri_() for"
        << " further information."
    );
 
    delete [] ipiv;
    delete [] work;
}
 
inline std::complex<double> Matrix<std::complex<double>, 0, 0>::determinant(){
    TBTKAssert(
        rows == cols,
        "Matrix::determinant()",
        "Invalid matrix dimension. The determinant can only be"
        << " calculated for square matrices, but the matrix has size "
        << rows << "x" << cols << "\n",
        ""
    );
 
    std::complex<double> *copy = new std::complex<double>[rows*cols];
    for(unsigned int n = 0; n < rows*cols; n++)
        copy[n] = data[n];
 
    int *ipiv = new int[std::min(rows, cols)];
//  int lwork = rows*cols;
//  std::complex<double> *work = new std::complex<double>[lwork];
    int info;
 
    zgetrf_((int*)&rows, (int*)&cols, copy, (int*)&rows, ipiv, &info);
 
    if(info < 0){
        TBTKExit(
            "Matrix::determinant()",
            "Argument '" << -info << "' to zgetrf_() is invlid.",
            "This should never happen, contact the developer."
        );
    }
    else if(info > 0){
        TBTKExit(
            "Matrix::determinant()",
            "Unable to invert matrix since it is signular.",
            ""
        );
    }
 
    std::complex<double> det = 1.;
    for(unsigned int n = 0; n < rows; n++){
        Streams::out << ipiv[n] << "\n";
        if(ipiv[n]-1 == (int)n)
            det *= copy[rows*n + n];
        else
            det *= -copy[rows*n + n];
    }
 
    delete [] copy;
    delete [] ipiv;
 
    return det;
}
 
};  //End namespace TBTK
 
#endif