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) .
 */

// Copyright 2001  California Institute of Technology


#ifndef CT_DENSEMATRIX_H
#define CT_DENSEMATRIX_H

#include "cantera/base/ct_defs.h"
#include "cantera/base/Array.h"

namespace Cantera
{
/**
 * @defgroup numerics  Numerical Utilities within Cantera
 *
 *  Cantera contains some capabilities for solving nonlinear equations and
 *  integrating both ODE and DAE equation systems in time. This section describes these
 *  capabilities.
 *
 */


//! Exception thrown when an LAPACK error is encountered associated with inverting or solving a matrix
/*!
 *  A named error condition is used so that the calling code may differentiate this type of error
 *  from other error conditions.
 */
class CELapackError : public CanteraError
{
public:

    //! Constructor passes through to main Cantera error handler
    /*!
     *  @param routine  Name of calling routine
     *  @param msg      Informative message
     */
    CELapackError(const std::string& routine, const std::string& msg) :
        CanteraError(routine + " LAPACK ERROR", msg) {
    }

};

//!  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
 *
 *  Error handling from BLAS and LAPACK are handled via the following formulation.
 *  Depending on a variable, a singular matrix or other terminal error condition from
 *  LAPACK is handled by either throwing an exception of type, CELapackError, or by
 *  returning the error code condition to the calling routine.
 *
 *  The int variable,  m_useReturnErrorCode, determines which method is used.
 *  The default value of zero means that an exception is thrown. A value of 1
 *  means that a return code is used.
 *
 *  Reporting of these LAPACK error conditions is handled by the class variable
 *  m_printLevel. The default is for no reporting. If m_printLevel is nonzero,
 *  the error condition is reported to Cantera's log file.
 *
 *  @ingroup numerics
 */
class DenseMatrix : public Array2D
{
public:
    //! Default Constructor
    DenseMatrix();

    //! 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, doublereal v = 0.0);

    //! Copy constructor
    /*!
     *   @param y Object to be copied
     */
    DenseMatrix(const DenseMatrix& y);

    //! Assignment operator
    /*!
     *   @param y Object to be copied
     */
    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, doublereal v = 0.0);

    virtual doublereal*   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.
     *
     *   @return returns a vector of pointers to the top of the columns
     *           of the matrices.
     */
    const doublereal* const* const_colPts() const;

    virtual void mult(const double* b, double* prod) const;

    //! Multiply A*B and write result to \c prod.
    /*!
     *  @param    b     input      DenseMatrix B of size NxN
     *  @param    prod  output     output DenseMatrix prod size NxN
     */
    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
    /*!
     *  @return  Returns a reference to the pivot vector as a vector_int
     */
    vector_int& ipiv();

    //! Return a changeable value of the pivot vector
    /*!
     *  @return  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
    std::vector<doublereal*> m_colPts;

public:
    //! Error Handling Flag
    /*!
     *  The default is to set this to 0. In this case, if a factorization is requested and can't be achieved,
     *  a CESingularMatrix exception is triggered. No return code is used, because an exception is thrown.
     *  If this is set to 1, then an exception is not thrown. Routines return with an error code, that is up
     *  to the calling routine to handle correctly. Negative return codes always throw an exception.
     */
    int m_useReturnErrorCode;

    //! Print Level
    /*!
     *  Printing is done to the log file using the routine writelogf().
     *
     *  Level of printing that is carried out. Only error conditions are printed out, if this value is nonzero.
     */
    int m_printLevel;

    //  Listing of friend functions which are defined below

    friend int solve(DenseMatrix& A, double* b);
    friend int solve(DenseMatrix& A, DenseMatrix& b);
    friend int invert(DenseMatrix& A, int nn);
};


//! Solve Ax = b. Array b is overwritten on exit with x.
/*!
 *   The solve class 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 to be solved.
 */
int solve(DenseMatrix& A, double* b);

//!  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
 */
int 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    A     input      Dense Matrix A with M rows and N columns
 *  @param    b     input      vector b with length N
 *  @param    prod  output     output 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    A     input      Dense Matrix A with M rows and N columns
 *  @param    b     input      vector b with length N
 *  @param    prod  output     output 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
 */
int invert(DenseMatrix& A, size_t nn=npos);

}

#endif