gctl/lib/maths/linear_algebra.h

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 * Geophysical Computational Tools & Library (GCTL)
 *
 * Copyright (c) 2023  Yi Zhang (yizhang-geo@zju.edu.cn)
 *
 * GCTL is distributed under a dual licensing scheme. You can redistribute 
 * it and/or modify it under the terms of the GNU Lesser General Public 
 * License as published by the Free Software Foundation, either version 2 
 * of the License, or (at your option) any later version. You should have 
 * received a copy of the GNU Lesser General Public License along with this 
 * program. If not, see <http://www.gnu.org/licenses/>.
 * 
 * If the terms and conditions of the LGPL v.2. would prevent you from using 
 * the GCTL, please consider the option to obtain a commercial license for a 
 * fee. These licenses are offered by the GCTL's original author. As a rule, 
 * licenses are provided "as-is", unlimited in time for a one time fee. Please 
 * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
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 ******************************************************/

#ifndef _GCTL_LINEAR_ALGEBRA_H
#define _GCTL_LINEAR_ALGEBRA_H

#include "../core.h"

#ifdef GCTL_OPENMP
#include "omp.h"
#endif // GCTL_OPENMP

#ifdef GCTL_OPENBLAS
#include "cblas.h"
#endif // GCTL_OPENBLAS

namespace gctl
{
    /**
     * @brief Set values of an array's members to a given value. x .= c.
     * 
     * @param x The input/output array.
     * @param c The input value.
     */
    void vecset(_1d_array &x, double c);

    /**
     * @brief Set values of an array's members to a given value. x .= c.
     * 
     * @param x The input/output array.
     * @param c The input value.
     */
    void vecset(_1cd_array &x, std::complex<double> c);
    
    /**
     * @brief Copy values of an array to another with conjugate values
     * 
     * @param x The input/output array.
     * @param c The input value.
     */
    void vecconj(_1cd_array &x, const _1cd_array &y);

    /**
     * @brief Copy values of an array to another. x = c.*y.
     * 
     * @param x The input/output array.
     * @param y The source array.
     * @param c Multiplier of the source array. The default value is 1.0.
     */
    void veccpy(_1d_array &x, const _1d_array &y, double c = 1.0);

    /**
     * @brief Copy values of an array to another. x = c.*y.
     * 
     * @param x The input/output array.
     * @param y The source array.
     * @param c Multiplier of the source array.
     */
    void veccpy(_1cd_array &x, const _1cd_array &y, std::complex<double> c);

    /**
     * @brief Calculate the sum of two input arrays. a = t.*b + p.*c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of b. The default value is 1.0.
     * @param p MUltiplier of c. The default value is 1.0.
     */
    void vecadd(_1d_array &a, const _1d_array &b, const _1d_array &c, double t = 1.0, double p = 1.0);

    /**
     * @brief Calculate the sum of two input arrays. a = t.*b + p.*c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of b.
     * @param p MUltiplier of c.
     */
    void vecadd(_1cd_array &a, const _1cd_array &b, const _1cd_array &c, std::complex<double> t, std::complex<double> p);

    /**
     * @brief Calculate the difference of two input arrays. a = t.*b - p.*c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of b. The default value is 1.0.
     * @param p MUltiplier of c. The default value is 1.0.
     */
    void vecdiff(_1d_array &a, const _1d_array &b, const _1d_array &c, double t = 1.0, double p = 1.0);

    /**
     * @brief Calculate the difference of two input arrays. a = t.*b - p.*c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of b. The default value is 1.0.
     * @param p MUltiplier of c. The default value is 1.0.
     */
    void vecdiff(_1cd_array &a, const _1cd_array &b, const _1cd_array &c, std::complex<double> t, std::complex<double> p);

    /**
     * @brief Calculate the element-wise products of the two input array. a = t.*b.*c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of the output array. The default value is 1.0.
     */
    void vecmul(_1d_array &a, const _1d_array &b, const _1d_array &c, double t = 1.0);

    /**
     * @brief Calculate the element-wise divisions of the two input array. a = t.*b./c.
     * 
     * @param a The output array.
     * @param b The input array.
     * @param c The input array.
     * @param t Multiplier of the output array. The default value is 1.0.
     */
    void vecdiv(_1d_array &a, const _1d_array &b, const _1d_array &c, double t = 1.0);
    
    /**
     * @brief Scale the input/output array. x = c.*x.
     * 
     * @param x The input/output array.
     * @param c The input value.
     */
    void vecscale(_1d_array &x, double c);

    /**
     * @brief Append the source array to the output array. x += c.*b.
     * 
     * @param x The input/output array.
     * @param b The input/source array.
     * @param c Multiplier of the output array. The default value is 1.0.
     */
    void vecapp(_1d_array &x, const _1d_array &b, double c = 1.0);

    /**
     * @brief Append the source array to the output array. x += c.*b.
     * 
     * @param x The input/output array.
     * @param b The input/source array.
     * @param c Multiplier of the output array.
     */
    void vecapp(_1cd_array &x, const _1cd_array &b, std::complex<double> c);

    /**
     * @brief Subtract the source array from the output array. x -= c.*b.
     * 
     * @param x The input/output array.
     * @param b The input/source array.
     * @param c Multiplier of the output array. The default value is 1.0.
     */
    void vecsub(_1d_array &x, const _1d_array &b, double c = 1.0);

    /**
     * @brief Subtract the source array from the output array. x -= c.*b.
     * 
     * @param x The input/output array.
     * @param b The input/source array.
     * @param c Multiplier of the output array.
     */
    void vecsub(_1cd_array &x, const _1cd_array &b, std::complex<double> c);

    /**
     * @brief Set lower bound of the input/output array. x = min(x, l).
     * 
     * @param x The input/output array.
     * @param l The lower bound array.
     */
    void vecbtm(_1d_array &x, const _1d_array &l);

    /**
     * @brief Set upper bound of the input/output array. x = max(x, h).
     * 
     * @param x The input/output array.
     * @param h The upper bound array.
     */
    void vectop(_1d_array &x, const _1d_array &h);

    /**
     * @brief Calculate the product of a matrix and a vector. r = m * v or r = m^T * v.
     * 
     * @param r The output array.
     * @param m The input matrix.
     * @param v The input vector.
     * @param trans Transports the input matrix or not.
     */
    void matvec(_1d_array &r, const _2d_matrix &m, const _1d_array &v, matrix_layout_e trans = NoTrans);
    
    /**
     * @brief Calculate the product of two matrixes. r = m * v, r = m^T * v, r = m * v^T or r = m^T * v^T.
     * 
     * @param r The output matrix.
     * @param m The input matrix.
     * @param v The input matrix.
     * @param m_trans Transports the m matrix or not.
     * @param v_trans Transports the v matrix or not.
     */
    void matmat(_2d_matrix &r, const _2d_matrix &m, const _2d_matrix &v, matrix_layout_e m_trans = NoTrans, matrix_layout_e v_trans = NoTrans);
    
    /**
     * @brief Append vectors to an exciting matrix. r += v in a row-wise or column-wise fashion.
     * 
     * @param r Input/Output matrix
     * @param v Input array
     * @param odr Calculating direction
     */
    void matapp(_2d_matrix &r, const _1d_array &v, matrix_order_e odr = RowMajor);
    
    /**
     * @brief Calculate the difference of two matrixes. r = m - v
     * 
     * @param r The output matrix.
     * @param m The input matrix.
     * @param v The input matrix.
     */
    void matdiff(_2d_matrix &r, const _2d_matrix &m, const _2d_matrix &v);

    /**
     * @brief Calculate the product of a matrix and a vector. r = m * v or r = m^T * v.
     * 
     * @param r The output array.
     * @param m The input matrix.
     * @param v The input vector.
     * @param trans Transports the input matrix or not.
     * @param conj Conjugates the input matrix or not.
     */
    void matvec(_1cd_array &r, const _2cd_matrix &m, const _1cd_array &v, matrix_layout_e trans = NoTrans, conjugate_type_e conj = NoConj);

    /**
     * @brief Generate a set of orthogonal arrays.
     * 
     * @param a The input random array.
     * @param e The output orthogonal arrays.
     * @param a_s Size of the orthogonal set.
     */
    void schmidt_orthogonal(const _1d_array &a, _1d_array &e, size_t a_s);
    
    /**
     * @brief Check validity of the input box arrays. h > l.
     * 
     * @param h The input upper bound array.
     * @param l The input lower bound array.
     * @return true The input box arrays are valid.
     * @return false The input box arrays are not valid.
     */
    bool veccheckbox(const _1d_array &h, const _1d_array &l);
    
    /**
     * @brief Check if elements of the input array are all positive.
     * 
     * @param a The input array.
     * @return true All elements are positive.
     * @return false Not all elements are positive.
     */
    bool veccheckpos(const _1d_array &a);

    /**
     * @brief Check if elements of the input array are valid.
     * 
     * @param a The input array.
     * @return true All elements are valid.
     * @return false Not all elements are valid.
     */
    bool vecvalid(const _1d_array &a);

    /**
     * @brief Check if elements of the input array are valid.
     * 
     * @param a The input array.
     * @return true All elements are valid.
     * @return false Not all elements are valid.
     */
    bool vecvalid(const _1cd_array &a);

    /**
     * @brief Calculate the dot product of two input arrays.
     * 
     * @param b The input array.
     * @param c The input array.
     * @return The dot product.
     */
    double vecdot(const _1d_array &b, const _1d_array &c);

    /**
     * @brief Calculate the dot product of two input arrays.
     * 
     * @param a The input array.
     * @param b The input array.
     * @return The dot product.
     */
    std::complex<double> vecdot(const _1cd_array &a, const _1cd_array &b);

    /**
     * @brief Calculate the inner product of two input arrays.
     * 
     * @param a The input array.
     * @param b The input array.
     * @return The dot product.
     */
    std::complex<double> vecinner(const _1cd_array &a, const _1cd_array &b);

    /**
     * @brief Calculate the running average value.
     * 
     * @param old_mean Old average value.
     * @param old_count Old calculating counts.
     * @param new_input New input value.
     * @return New average value.
     */
    double dynamic_average(double old_mean, size_t old_count, double new_input);

    /**
     * @brief Calculate the running standard deviation value.
     * 
     * @param old_stddev Old standard deviation value.
     * @param old_count Old calculating counts.
     * @param old_mean Old averaging value.
     * @param new_input New input value.
     * @param new_mean New output averaging value.
     * @return New standard deviation value.
     */
    double dynamic_stddev(double old_stddev, size_t old_count, double old_mean, double new_input, double &new_mean);
}

#endif // _GCTL_LINEAR_ALGEBRA_H