C 代码 将数据投影到有限元空间，包括最小二乘 数据的近似值.rar

# include <float.h> # include <math.h> # include <stdio.h> # include <stdlib.h> # include <string.h> # include <time.h> int main ( int argc, char *argv[] ); char ch_cap ( char ch ); int ch_eqi ( char ch1, char ch2 ); int ch_to_digit ( char ch ); double *fem1d_approximate ( int sample_node_num, int sample_value_dim, double sample_node_x[], double sample_value[], int fem_node_num, double fem_node_x[], int fem_element_order, int fem_element_num, int fem_value_dim, int fem_value_num ); int file_column_count ( char *input_filename ); int file_row_count ( char *input_filename ); int *i4mat_data_read ( char *input_filename, int m, int n ); void i4mat_header_read ( char *input_filename, int *m, int *n ); double piecewise_linear_product_quad ( double a, double b, int f_num, double f_x[], double f_v[], int g_num, double g_x[], double g_v[] ); double r8_min ( double x, double y ); int r83_np_fa ( int n, double a[] ); double *r83_np_sl ( int n, double a_lu[], double b[], int job ); double *r8mat_data_read ( char *input_filename, int m, int n ); void r8mat_header_read ( char *input_filename, int *m, int *n ); void r8mat_write ( char *output_filename, int m, int n, double table[] ); double *r8mat_zero_new ( int m, int n ); void r8vec_bracket3 ( int n, double t[], double tval, int *left ); int s_len_trim ( char *s ); int s_to_i4 ( char *s, int *last, int *error ); int s_to_i4vec ( char *s, int n, int ivec[] ); double s_to_r8 ( char *s, int *lchar, int *error ); int s_to_r8vec ( char *s, int n, double rvec[] ); int s_word_count ( char *s ); void timestamp ( ); /******************************************************************************/ int main ( int argc, char *argv[] ) /******************************************************************************/ /* Purpose: MAIN is the main program for FEM1D_PROJECT. Discussion: FEM1D_PROJECT reads files defining a sampling of a (scalar or vector) function of 1 argument, and a list of nodes and elements to use for a finite element representation of the data. It computes a set of finite element coefficients to be associated with the given finite element mesh, and writes that information to a file so that an FEM representation is formed by the node, element and value files. Usage: fem1d_project sample_prefix fem_prefix where 'sample_prefix' is the common prefix for the SAMPLE files: * sample_prefix_nodes.txt, the node coordinates where samples were taken, * sample_prefix_values.txt, the sample values. and 'fem_prefix' is the common prefix for the FEM files: * fem_prefix_nodes.txt, the node coordinates. * fem_prefix_elements.txt, the nodes that make up each element; * fem_prefix_values.txt, the values defined at each node. Licensing: This code is distributed under the GNU LGPL license. Modified: 25 July 2019 Author: John Burkardt */ { char fem_element_filename[255]; int *fem_element_node; int fem_element_num; int fem_element_order; int fem_node_dim; char fem_node_filename[255]; int fem_node_num; double *fem_node_x; char fem_prefix[255]; double *fem_value; int fem_value_dim; char fem_value_filename[255]; int fem_value_num; char sample_prefix[255]; int sample_node_dim; char sample_node_filename[255]; int sample_node_num; double *sample_node_x; int sample_value_dim; int sample_value_num; double *sample_value; char sample_value_filename[255]; timestamp ( ); printf ( "\n" ); printf ( "FEM1D_PROJECT\n" ); printf ( " C version.\n" ); printf ( "\n" ); printf ( " Read files defining a sampling of a function of 1 argument.\n" ); printf ( " Read files defining a finite element mesh.\n" ); printf ( " Project the sample data onto the mesh, and\n" ); printf ( " write a file of FEM coefficient values.\n" ); /* Get the number of command line arguments. */ if ( 1 < argc ) { strcpy ( sample_prefix, argv[1] ); } else { printf ( "\n" ); printf ( "Enter the sample file prefix:\n" ); scanf ( "%s", sample_prefix ); } if ( 2 < argc ) { strcpy ( fem_prefix, argv[2] ); } else { printf ( "\n" ); printf ( "Enter the FEM file prefix:\n" ); scanf ( "%s", fem_prefix ); } /* Create the filenames. */ strcpy ( sample_node_filename, sample_prefix ); strcat ( sample_node_filename, "_nodes.txt" ); strcpy ( sample_value_filename, sample_prefix ); strcat ( sample_value_filename, "_values.txt" ); strcpy ( fem_node_filename, fem_prefix ); strcat ( fem_node_filename, "_nodes.txt" ); strcpy ( fem_element_filename, fem_prefix ); strcat ( fem_element_filename, "_elements.txt" ); strcpy ( fem_value_filename, fem_prefix ); strcat ( fem_value_filename, "_values.txt" ); /* Read the SAMPLE data. */ r8mat_header_read ( sample_node_filename, &sample_node_dim, &sample_node_num ); sample_node_x = r8mat_data_read ( sample_node_filename, sample_node_dim, sample_node_num ); printf ( "\n" ); printf ( " Sample node spatial dimension is %d\n", sample_node_dim ); printf ( " Sample node number is %d\n", sample_node_num ); if ( sample_node_dim != 1 ) { printf ( "\n" ); printf ( "FEM1D_PROJECT - Fatal error!\n" ); printf ( " Spatial dimension of the sample nodes is not 1.\n" ); exit ( 1 ); } r8mat_header_read ( sample_value_filename, &sample_value_dim, &sample_value_num ); printf ( " The SAMPLE value dimension is %d\n", sample_value_dim ); printf ( " the SAMPLE value number is %d\n", sample_value_num ); if ( sample_value_num != sample_node_num ) { printf ( "\n" ); printf ( "FEM1D_PROJECT - Fatal error!\n" ); printf ( " Number of sample values and nodes differ.\n" ); exit ( 1 ); } sample_value = r8mat_data_read ( sample_value_filename, sample_value_dim, sample_value_num ); /* Read the FEM data. */ r8mat_header_read ( fem_node_filename, &fem_node_dim, &fem_node_num ); printf ( "\n" ); printf ( " The FEM node dimension is %d\n", fem_node_dim ); printf ( " The FEM node number is %d\n", fem_node_num ); if ( fem_node_dim != 1 ) { printf ( "\n" ); printf ( "FEM1D_PROJECT - Fatal error!\n" ); printf ( " Spatial dimension of the nodes is not 1.\n" ); exit ( 1 ); } fem_node_x = r8mat_data_read ( fem_node_filename, fem_node_dim, fem_node_num ); i4mat_header_read ( fem_element_filename, &fem_element_order, &fem_element_num ); printf ( " The FEM element order is %d\n", fem_element_order ); printf ( " The FEM element number is %d\n", fem_element_num ); fem_element_node = i4mat_data_read ( fem_element_filename, fem_element_order, fem_element_num ); /* Compute the FEM values. */ fem_value_dim = sample_value_dim; fem_value_num = fem_node_num; fem_value = fem1d_approximate ( sample_node_num, sample_value_dim, sample_node_x, sample_value, fem_node_num, fem_node_x, fem_element_order, fem_element_num, fem_value_dim, fem_value_num ); /* Write the FEM values. */ r8mat_write ( fem_value_filename, fem_value_dim, fem_value_num, fem_value ); printf ( "\n" ); printf ( " Projected FEM values written to \"%s\"\n", fem_value_filename ); /* Free memory. */ free ( fem_element_node ); free ( fem_node_x ); free ( fem_value ); free ( sample_node_x ); free ( sample_value ); /* Terminate. */ printf ( "\n" ); printf ( "FEM1D_PROJECT\n" ); printf ( " Normal end of execution.\n" ); printf ( "\n" ); timestamp ( ); return 0; } /******************************************************************************/ char ch_cap ( char ch ) /******************************************************************************/ /* Purpose: CH_CAP capitalizes a single character. Discussion: This routine should be equivalent to the library "toupper" function. Licensing: This code is distri