DenseMatrix.h

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/**
 *  @file DenseMatrix.h
 *  Headers for the DenseMatrix object, which deals with dense rectangular matrices and
 *  description of the numerics groupings of objects
 *  (see @ref numerics and @link Cantera::DenseMatrix DenseMatrix @endlink) .
 */
 
// This file is part of Cantera. See License.txt in the top-level directory or
// at https://cantera.org/license.txt for license and copyright information.
 
#ifndef CT_DENSEMATRIX_H
#define CT_DENSEMATRIX_H
 
#include "cantera/base/ct_defs.h"
#include "cantera/base/ctexceptions.h"
#include "cantera/base/Array.h"
 
namespace Cantera
{
/**
 * @defgroup numerics  Numerical Utilities
 *
 * @details %Cantera contains some capabilities for solving nonlinear equations and
 * integrating both ODE and DAE equation systems in time.
 */
 
/**
 * @defgroup matrices  Matrix Handling
 * Classes and methods implementing matrix operations.
 * @ingroup numerics
 */
 
//! A class for full (non-sparse) matrices with Fortran-compatible data storage,
//! which adds matrix operations to class Array2D.
/*!
 * The dense matrix class adds matrix operations onto the Array2D class. These
 * matrix operations are carried out by the appropriate BLAS and LAPACK routines
 *
 * @ingroup matrices
 */
class DenseMatrix : public Array2D
{
public:
    //! Default Constructor
    DenseMatrix() = default;
 
    //! Constructor.
    /*!
     * Create an @c n by @c m matrix, and initialize all elements to @c v.
     *
     * @param n  New number of rows
     * @param m  New number of columns
     * @param v  Default fill value. defaults to zero.
     */
    DenseMatrix(size_t n, size_t m, double v = 0.0);
 
    DenseMatrix(const DenseMatrix& y);
    DenseMatrix& operator=(const DenseMatrix& y);
 
    //! Resize the matrix
    /*!
     * Resize the matrix to n rows by m cols.
     *
     * @param n  New number of rows
     * @param m  New number of columns
     * @param v  Default fill value. defaults to zero.
     */
    void resize(size_t n, size_t m, double v=0.0) override;
 
    virtual double* const* colPts();
 
    //! Return a const vector of const pointers to the columns
    /*!
     * Note, the Jacobian can not be altered by this routine, and therefore the
     * member function is const.
     *
     * @returns a vector of pointers to the top of the columns of the matrices.
     */
    const double* const* const_colPts() const;
 
    virtual void mult(const double* b, double* prod) const;
 
    //! Multiply A*B and write result to @c prod.
    /*!
     * Take this matrix to be of size NxM.
     * @param[in]  b     DenseMatrix B of size MxP
     * @param[out] prod  DenseMatrix prod size NxP
     */
    virtual void mult(const DenseMatrix& b, DenseMatrix& prod) const;
 
    //! Left-multiply the matrix by transpose(b), and write the result to prod.
    /*!
     * @param b    left multiply by this vector. The length must be equal to n
     *             the number of rows in the matrix.
     * @param prod  Resulting vector. This is of length m, the number of columns
     *              in the matrix
     */
    virtual void leftMult(const double* const b, double* const prod) const;
 
    //! Return a changeable value of the pivot vector
    /*!
     * @returns a reference to the pivot vector as a vector<int>
     */
    vector<int>& ipiv();
 
    //! Return a changeable value of the pivot vector
    /*!
     *  @returns a reference to the pivot vector as a vector<int>
     */
    const vector<int>& ipiv() const {
        return m_ipiv;
    }
 
protected:
    //! Vector of pivots. Length is equal to the max of m and n.
    vector<int> m_ipiv;
 
    //! Vector of column pointers
    vector<double*> m_colPts;
};
 
 
//! Solve Ax = b. Array b is overwritten on exit with x.
/*!
 * The solve function uses the LAPACK routine dgetrf to invert the m xy n matrix.
 *
 * The factorization has the form
 *
 *     A = P * L * U
 *
 * where P is a permutation matrix, L is lower triangular with unit diagonal
 * elements (lower trapezoidal if m > n), and U is upper triangular (upper
 * trapezoidal if m < n).
 *
 * The system is then solved using the LAPACK routine dgetrs
 *
 * @param A    Dense matrix to be factored
 * @param b    RHS(s) to be solved.
 * @param nrhs Number of right hand sides to solve
 * @param ldb  Leading dimension of b, if nrhs > 1
 */
void solve(DenseMatrix& A, double* b, size_t nrhs=1, size_t ldb=0);
 
//! Solve Ax = b for multiple right-hand-side vectors.
/*!
 * @param A   Dense matrix to be factored
 * @param b   Dense matrix of RHS's. Each column is a RHS
 */
void solve(DenseMatrix& A, DenseMatrix& b);
 
//! Multiply @c A*b and return the result in @c prod. Uses BLAS routine DGEMV.
/*!
 * @f[
 *     prod_i = sum^N_{j = 1}{A_{ij} b_j}
 * @f]
 *
 * @param[in]  A     Dense Matrix A with M rows and N columns
 * @param[in]  b     vector b with length N
 * @param[out] prod  vector prod length = M
 */
void multiply(const DenseMatrix& A, const double* const b, double* const prod);
 
//! Multiply @c A*b and add it to the result in @c prod. Uses BLAS routine DGEMV.
/*!
 * @f[
 *     prod_i += sum^N_{j = 1}{A_{ij} b_j}
 * @f]
 *
 * @param[in]  A     Dense Matrix A with M rows and N columns
 * @param[in]  b     vector b with length N
 * @param[out] prod  vector prod length = M
 */
void increment(const DenseMatrix& A, const double* const b, double* const prod);
 
//! invert A. A is overwritten with A^-1.
/*!
 *  @param A   Invert the matrix A and store it back in place
 *  @param nn  Size of A. This defaults to -1, which means that the number of
 *             rows is used as the default size of n
 */
void invert(DenseMatrix& A, size_t nn=npos);
 
}
 
#endif