# include # include # include # include # include # include # include using namespace std; # include "test_int_2d.hpp" int main ( int argc, char *argv[] ); bool ch_eqi ( char ch1, char ch2 ); int ch_to_digit ( char ch ); double *dtable_data_read ( string input_filename, int m, int n ); void dtable_header_read ( string input_filename, int *m, int *n ); int file_column_count ( string input_filename ); int file_row_count ( string input_filename ); double r8vec_dot ( int n, double a1[], double a2[] ); char *s_cat ( char *s1, char *s2 ); int s_len_trim ( char *s ); int s_to_i4 ( char *s, int *last, bool *error ); double s_to_r8 ( char *s, int *lchar, bool *error ); bool s_to_r8vec ( char *s, int n, double rvec[] ); int s_word_count ( char *s ); //****************************************************************************80 int main ( int argc, char *argv[] ) //****************************************************************************80 // // Purpose: // // MAIN is the main program for QUADRATURE_TEST_2D. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 30 January 2009 // // Author: // // John Burkardt // { double *a; double *b; int dim; int dim_num; int dim_num2; double exact; double *f; int point; int point_num; int point_num2; string prefix; int problem; int problem_num; double quad_err; double quad_est; string quad_r_filename; string quad_w_filename; string quad_x_filename; double *r; double volume1; double volume2; double *w; double *x; double *x2; timestamp ( ); cout << "\n"; cout << "QUADRATURE_TEST_2D\n"; cout << " C++ version\n"; cout << "\n"; cout << " Compiled on " << __DATE__ << " at " << __TIME__ << ".\n"; cout << "\n"; cout << " Investigate the accuracy of a 2D quadrature\n"; cout << " rule by integrating test functions.\n"; // // Get the quadrature file root name: // if ( 1 < argc ) { prefix = argv[1]; } else { cout << "\n"; cout << "QUADRATURE_TEST:\n"; cout << " Enter the \"root\" name of the quadrature files.\n"; cin >> prefix; } // // Create the names of: // the quadrature X file; // the quadrature W file; // the quadrature R file. // quad_x_filename = prefix + "_x.txt"; quad_w_filename = prefix + "_w.txt"; quad_r_filename = prefix + "_r.txt"; // // Summarize the input. // cout << "\n"; cout << "QUADRATURE_TEST_2D: User input:\n"; cout << " Quadrature rule X file = \"" << quad_x_filename << "\".\n"; cout << " Quadrature rule W file = \"" << quad_w_filename << "\".\n"; cout << " Quadrature rule R file = \"" << quad_r_filename << "\".\n"; // // Read the X file. // dtable_header_read ( quad_x_filename, &dim_num, &point_num ); cout << "\n"; cout << " Spatial dimension = " << dim_num << "\n"; cout << " Number of points = " << point_num << "\n"; if ( dim_num != 2 ) { cerr << "\n"; cerr << "QUADRATURE_TEST_2D - Fatal error!\n"; cerr << " The X file seems to have spatial dimension = " << dim_num << "\n"; cerr << " This program requires a spatial dimension of 2.\n"; exit ( 1 ); } x = dtable_data_read ( quad_x_filename, dim_num, point_num ); // // Read the W file. // dtable_header_read ( quad_w_filename, &dim_num2, &point_num2 ); if ( dim_num2 != 1 ) { cout << "\n"; cout << "QUADRATURE_TEST_2D - Fatal error!\n"; cout << " The quadrature weight file should have exactly\n"; cout << " one value on each line.\n"; exit ( 1 ); } if ( point_num2 != point_num ) { cout << "\n"; cout << "QUADRATURE_TEST_2D - Fatal error!\n"; cout << " The quadrature weight file should have exactly\n"; cout << " the same number of lines as the abscissa file.\n"; exit ( 1 ); } w = dtable_data_read ( quad_w_filename, 1, point_num ); // // Read the R file. // dtable_header_read ( quad_r_filename, &dim_num2, &point_num2 ); if ( dim_num2 != dim_num ) { cout << "\n"; cout << "QUADRATURE_TEST_2D - Fatal error!\n"; cout << " The quadrature region file should have the same\n"; cout << " number of values on each line as the abscissa file\n"; cout << " does.\n"; exit ( 1 ); } if ( point_num2 != 2 ) { cout << "\n"; cout << "QUADRATURE_TEST_2D - Fatal error!\n"; cout << " The quadrature region file should have two lines.\n"; exit ( 1 ); } r = dtable_data_read ( quad_r_filename, dim_num, 2 ); // // Rescale the weights, and translate the abscissas. // volume1 = 1.0; for ( dim = 0; dim < dim_num; dim++ ) { volume1 = volume1 * ( r[dim+1*dim_num] - r[dim+0*dim_num] ); } volume1 = fabs ( volume1 ); problem_num = p00_problem_num ( ); a = new double[dim_num]; b = new double[dim_num]; f = new double[point_num]; x2 = new double[dim_num*point_num]; cout << "\n"; cout << " Prob Dim Points Approx Exact Error\n"; cout << "\n"; for ( problem = 1; problem <= problem_num; problem++ ) { exact = p00_exact ( problem ); p00_lim ( problem, a, b ); volume2 = 1.0; for ( dim = 0; dim < dim_num; dim++ ) { volume2 = volume2 * ( b[dim] - a[dim] ); } volume2 = fabs ( volume2 ); // // Map the abscissas to the [A,B] hypercube. // for ( point = 0; point < point_num; point++ ) { for ( dim = 0; dim < dim_num; dim++ ) { x2[dim+point*dim_num] = ( ( r[dim+1*dim_num] - x[dim+point*dim_num] ) * a[dim] + ( x[dim+point*dim_num] - r[dim+0*dim_num] ) * b[dim] ) / ( r[dim+1*dim_num] - r[dim+0*dim_num] ); } } // // Evaluate the function at the abscissas. // p00_fun ( problem, point_num, x2, f ); // // Compute the weighted estimate. // quad_est = r8vec_dot ( point_num, w, f ) * volume2 / volume1; quad_err = fabs ( quad_est - exact ); cout << " " << setw(4) << problem << " " << setw(4) << dim_num << " " << setw(10) << point_num << " " << setw(14) << quad_est << " " << setw(14) << exact << " " << setw(14) << quad_err << "\n"; } delete [] a; delete [] b; delete [] f; delete [] r; delete [] w; delete [] x; delete [] x2; cout << "\n"; cout << "QUADRATURE_2D_TEST:\n"; cout << " Normal end of execution.\n"; cout << "\n"; timestamp ( ); return 0; } //****************************************************************************80 bool ch_eqi ( char ch1, char ch2 ) //****************************************************************************80 // // Purpose: // // CH_EQI is true if two characters are equal, disregarding case. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 13 June 2003 // // Author: // // John Burkardt // // Parameters: // // Input, char CH1, CH2, the characters to compare. // // Output, bool CH_EQI, is true if the two characters are equal, // disregarding case. // { if ( 97 <= ch1 && ch1 <= 122 ) { ch1 = ch1 - 32; } if ( 97 <= ch2 && ch2 <= 122 ) { ch2 = ch2 - 32; } return ( ch1 == ch2 ); } //****************************************************************************80 int ch_to_digit ( char ch ) //****************************************************************************80 // // Purpose: // // CH_TO_DIGIT returns the integer value of a base 10 digit. // // Example: // // CH DIGIT // --- ----- // '0' 0 // '1' 1 // ... ... // '9' 9 // ' ' 0 // 'X' -1 // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 13 June 2003 // // Author: // // John Burkardt // // Parameters: // // Input, char CH, the decimal digit, '0' through '9' or blank are legal. // // Output, int CH_TO_DIGIT, the corresponding integer value. If the // character was 'illegal', then DIGIT is -1. // { int digit; if ( '0' <= ch && ch <= '9' ) { digit = ch - '0'; } else if ( ch == ' ' ) { digit = 0; } else { digit = -1; } return digit; } //****************************************************************************80 double *dtable_data_read ( string input_filename, int m, int n ) //****************************************************************************80 // // Purpose: // // DTABLE_DATA_READ reads the data from a DTABLE file. // // Discussion: // // The file is assumed to contain one record per line. // // Records beginning with the '#' character are comments, and are ignored. // Blank lines are also ignored. // // Each line that is not ignored is assumed to contain exactly (or at least) // M real numbers, representing the coordinates of a point. // // There are assumed to be exactly (or at least) N such records. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 27 January 2005 // // Author: // // John Burkardt // // Parameters: // // Input, string INPUT_FILENAME, the name of the input file. // // Input, int M, the number of spatial dimensions. // // Input, int N, the number of points. The program // will stop reading data once N values have been read. // // Output, double DTABLE_DATA_READ[M*N], the table data. // { bool error; ifstream input; int i; int j; char line[255]; double *table; double *x; input.open ( input_filename.c_str ( ) ); if ( !input ) { cout << "\n"; cout << "DTABLE_DATA_READ - Fatal error!\n"; cout << " Could not open the input file: \"" << input_filename << "\"\n"; return NULL; } table = new double[m*n]; x = new double[m]; j = 0; while ( j < n ) { input.getline ( line, sizeof ( line ) ); if ( input.eof ( ) ) { break; } if ( line[0] == '#' || s_len_trim ( line ) == 0 ) { continue; } error = s_to_r8vec ( line, m, x ); if ( error ) { continue; } for ( i = 0; i < m; i++ ) { table[i+j*m] = x[i]; } j = j + 1; } input.close ( ); delete [] x; return table; } //****************************************************************************80 void dtable_header_read ( string input_filename, int *m, int *n ) //****************************************************************************80 // // Purpose: // // DTABLE_HEADER_READ reads the header from a DTABLE file. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 04 June 2004 // // Author: // // John Burkardt // // Parameters: // // Input, string INPUT_FILENAME, the name of the input file. // // Output, int *M, the number of spatial dimensions. // // Output, int *N, the number of points. // { *m = file_column_count ( input_filename ); if ( *m <= 0 ) { cout << "\n"; cout << "DTABLE_HEADER_READ - Fatal error!\n"; cout << " FILE_COLUMN_COUNT failed.\n"; *n = -1; return; } *n = file_row_count ( input_filename ); if ( *n <= 0 ) { cout << "\n"; cout << "DTABLE_HEADER_READ - Fatal error!\n"; cout << " FILE_ROW_COUNT failed.\n"; return; } return; } //****************************************************************************80 int file_column_count ( string filename ) //****************************************************************************80 // // Purpose: // // FILE_COLUMN_COUNT counts the columns in the first line of a file. // // Discussion: // // The file is assumed to be a simple text file. // // Most lines of the file are presumed to consist of COLUMN_NUM words, separated // by spaces. There may also be some blank lines, and some comment lines, // which have a "#" in column 1. // // The routine tries to find the first non-comment non-blank line and // counts the number of words in that line. // // If all lines are blanks or comments, it goes back and tries to analyze // a comment line. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 30 January 2009 // // Author: // // John Burkardt // // Parameters: // // Input, string FILENAME, the name of the file. // // Output, int FILE_COLUMN_COUNT, the number of columns assumed // to be in the file. // { int column_num; ifstream input; bool got_one; char text[255]; // // Open the file. // input.open ( filename.c_str ( ) ); if ( !input ) { column_num = -1; cerr << "\n"; cerr << "FILE_COLUMN_COUNT - Fatal error!\n"; cerr << " Could not open the file:\n"; cerr << " \"" << filename << "\"\n"; return column_num; } // // Read one line, but skip blank lines and comment lines. // got_one = false; for ( ; ; ) { input.getline ( text, sizeof ( text ) ); if ( input.eof ( ) ) { break; } if ( s_len_trim ( text ) == 0 ) { continue; } if ( text[0] == '#' ) { continue; } got_one = true; break; } if ( !got_one ) { input.close ( ); input.open ( filename.c_str ( ) ); for ( ; ; ) { input.getline ( text, sizeof ( text ) ); if ( input.eof ( ) ) { break; } if ( s_len_trim ( text ) == 0 ) { continue; } got_one = true; break; } } input.close ( ); if ( !got_one ) { cerr << "\n"; cerr << "FILE_COLUMN_COUNT - Warning!\n"; cerr << " The file does not seem to contain any data.\n"; return -1; } column_num = s_word_count ( text ); return column_num; } //****************************************************************************80 int file_row_count ( string input_filename ) //****************************************************************************80 // // Purpose: // // FILE_ROW_COUNT counts the number of row records in a file. // // Discussion: // // It does not count lines that are blank, or that begin with a // comment symbol '#'. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 13 June 2003 // // Author: // // John Burkardt // // Parameters: // // Input, string INPUT_FILENAME, the name of the input file. // // Output, int FILE_ROW_COUNT, the number of rows found. // { int comment_num; ifstream input; char line[255]; int record_num; int row_num; row_num = 0; comment_num = 0; record_num = 0; input.open ( input_filename.c_str ( ) ); if ( !input ) { cout << "\n"; cout << "FILE_ROW_COUNT - Fatal error!\n"; cout << " Could not open the input file: \"" << input_filename << "\"\n"; return (-1); } for ( ; ; ) { input.getline ( line, sizeof ( line ) ); if ( input.eof ( ) ) { break; } record_num = record_num + 1; if ( line[0] == '#' ) { comment_num = comment_num + 1; continue; } if ( s_len_trim ( line ) == 0 ) { comment_num = comment_num + 1; continue; } row_num = row_num + 1; } input.close ( ); return row_num; } //****************************************************************************80 double r8vec_dot ( int n, double a1[], double a2[] ) //****************************************************************************80 // // Purpose: // // R8VEC_DOT computes the dot product of a pair of R8VEC's. // // Discussion: // // An R8VEC is a vector of R8's. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 03 July 2005 // // Author: // // John Burkardt // // Parameters: // // Input, int N, the number of entries in the vectors. // // Input, double A1[N], A2[N], the two vectors to be considered. // // Output, double R8VEC_DOT, the dot product of the vectors. // { int i; double value; value = 0.0; for ( i = 0; i < n; i++ ) { value = value + a1[i] * a2[i]; } return value; } //****************************************************************************80 int s_len_trim ( char *s ) //****************************************************************************80 // // Purpose: // // S_LEN_TRIM returns the length of a string to the last nonblank. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 26 April 2003 // // Author: // // John Burkardt // // Parameters: // // Input, char *S, a pointer to a string. // // Output, int S_LEN_TRIM, the length of the string to the last nonblank. // If S_LEN_TRIM is 0, then the string is entirely blank. // { int n; char *t; n = strlen ( s ); t = s + strlen ( s ) - 1; while ( 0 < n ) { if ( *t != ' ' ) { return n; } t--; n--; } return n; } //****************************************************************************80 int s_to_i4 ( char *s, int *last, bool *error ) //****************************************************************************80 // // Purpose: // // S_TO_I4 reads an I4 from a string. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 13 June 2003 // // Author: // // John Burkardt // // Parameters: // // Input, char *S, a string to be examined. // // Output, int *LAST, the last character of S used to make IVAL. // // Output, bool *ERROR is TRUE if an error occurred. // // Output, int *S_TO_I4, the integer value read from the string. // If the string is blank, then IVAL will be returned 0. // { char c; int i; int isgn; int istate; int ival; *error = false; istate = 0; isgn = 1; i = 0; ival = 0; while ( *s ) { c = s[i]; i = i + 1; // // Haven't read anything. // if ( istate == 0 ) { if ( c == ' ' ) { } else if ( c == '-' ) { istate = 1; isgn = -1; } else if ( c == '+' ) { istate = 1; isgn = + 1; } else if ( '0' <= c && c <= '9' ) { istate = 2; ival = c - '0'; } else { *error = true; return ival; } } // // Have read the sign, expecting digits. // else if ( istate == 1 ) { if ( c == ' ' ) { } else if ( '0' <= c && c <= '9' ) { istate = 2; ival = c - '0'; } else { *error = true; return ival; } } // // Have read at least one digit, expecting more. // else if ( istate == 2 ) { if ( '0' <= c && c <= '9' ) { ival = 10 * (ival) + c - '0'; } else { ival = isgn * ival; *last = i - 1; return ival; } } } // // If we read all the characters in the string, see if we're OK. // if ( istate == 2 ) { ival = isgn * ival; *last = s_len_trim ( s ); } else { *error = true; *last = 0; } return ival; } //****************************************************************************80 double s_to_r8 ( char *s, int *lchar, bool *error ) //****************************************************************************80 // // Purpose: // // S_TO_R8 reads an R8 value from a string. // // Discussion: // // We have had some trouble with input of the form 1.0E-312. // For now, let's assume anything less than 1.0E-20 is zero. // // This routine will read as many characters as possible until it reaches // the end of the string, or encounters a character which cannot be // part of the real number. // // Legal input is: // // 1 blanks, // 2 '+' or '-' sign, // 2.5 spaces // 3 integer part, // 4 decimal point, // 5 fraction part, // 6 'E' or 'e' or 'D' or 'd', exponent marker, // 7 exponent sign, // 8 exponent integer part, // 9 exponent decimal point, // 10 exponent fraction part, // 11 blanks, // 12 final comma or semicolon. // // with most quantities optional. // // Example: // // S R // // '1' 1.0 // ' 1 ' 1.0 // '1A' 1.0 // '12,34,56' 12.0 // ' 34 7' 34.0 // '-1E2ABCD' -100.0 // '-1X2ABCD' -1.0 // ' 2E-1' 0.2 // '23.45' 23.45 // '-4.2E+2' -420.0 // '17d2' 1700.0 // '-14e-2' -0.14 // 'e2' 100.0 // '-12.73e-9.23' -12.73 * 10.0**(-9.23) // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 24 June 2005 // // Author: // // John Burkardt // // Parameters: // // Input, char *S, the string containing the // data to be read. Reading will begin at position 1 and // terminate at the end of the string, or when no more // characters can be read to form a legal real. Blanks, // commas, or other nonnumeric data will, in particular, // cause the conversion to halt. // // Output, int *LCHAR, the number of characters read from // the string to form the number, including any terminating // characters such as a trailing comma or blanks. // // Output, bool *ERROR, is true if an error occurred. // // Output, double S_TO_R8, the value that was read from the string. // { char c; int ihave; int isgn; int iterm; int jbot; int jsgn; int jtop; int nchar; int ndig; double r; double rbot; double rexp; double rtop; char TAB = 9; nchar = s_len_trim ( s ); *error = false; r = 0.0; *lchar = -1; isgn = 1; rtop = 0.0; rbot = 1.0; jsgn = 1; jtop = 0; jbot = 1; ihave = 1; iterm = 0; for ( ; ; ) { c = s[*lchar+1]; *lchar = *lchar + 1; // // Blank or TAB character. // if ( c == ' ' || c == TAB ) { if ( ihave == 2 ) { } else if ( ihave == 6 || ihave == 7 ) { iterm = 1; } else if ( 1 < ihave ) { ihave = 11; } } // // Comma. // else if ( c == ',' || c == ';' ) { if ( ihave != 1 ) { iterm = 1; ihave = 12; *lchar = *lchar + 1; } } // // Minus sign. // else if ( c == '-' ) { if ( ihave == 1 ) { ihave = 2; isgn = -1; } else if ( ihave == 6 ) { ihave = 7; jsgn = -1; } else { iterm = 1; } } // // Plus sign. // else if ( c == '+' ) { if ( ihave == 1 ) { ihave = 2; } else if ( ihave == 6 ) { ihave = 7; } else { iterm = 1; } } // // Decimal point. // else if ( c == '.' ) { if ( ihave < 4 ) { ihave = 4; } else if ( 6 <= ihave && ihave <= 8 ) { ihave = 9; } else { iterm = 1; } } // // Exponent marker. // else if ( ch_eqi ( c, 'E' ) || ch_eqi ( c, 'D' ) ) { if ( ihave < 6 ) { ihave = 6; } else { iterm = 1; } } // // Digit. // else if ( ihave < 11 && '0' <= c && c <= '9' ) { if ( ihave <= 2 ) { ihave = 3; } else if ( ihave == 4 ) { ihave = 5; } else if ( ihave == 6 || ihave == 7 ) { ihave = 8; } else if ( ihave == 9 ) { ihave = 10; } ndig = ch_to_digit ( c ); if ( ihave == 3 ) { rtop = 10.0 * rtop + ( double ) ndig; } else if ( ihave == 5 ) { rtop = 10.0 * rtop + ( double ) ndig; rbot = 10.0 * rbot; } else if ( ihave == 8 ) { jtop = 10 * jtop + ndig; } else if ( ihave == 10 ) { jtop = 10 * jtop + ndig; jbot = 10 * jbot; } } // // Anything else is regarded as a terminator. // else { iterm = 1; } // // If we haven't seen a terminator, and we haven't examined the // entire string, go get the next character. // if ( iterm == 1 || nchar <= *lchar + 1 ) { break; } } // // If we haven't seen a terminator, and we have examined the // entire string, then we're done, and LCHAR is equal to NCHAR. // if ( iterm != 1 && (*lchar) + 1 == nchar ) { *lchar = nchar; } // // Number seems to have terminated. Have we got a legal number? // Not if we terminated in states 1, 2, 6 or 7! // if ( ihave == 1 || ihave == 2 || ihave == 6 || ihave == 7 ) { *error = true; return r; } // // Number seems OK. Form it. // // We have had some trouble with input of the form 1.0E-312. // For now, let's assume anything less than 1.0E-20 is zero. // if ( jtop == 0 ) { rexp = 1.0; } else { if ( jbot == 1 ) { if ( jsgn * jtop < -20 ) { rexp = 0.0; } else { rexp = pow ( ( double ) 10.0, ( double ) ( jsgn * jtop ) ); } } else { if ( jsgn * jtop < -20 * jbot ) { rexp = 0.0; } else { rexp = jsgn * jtop; rexp = rexp / jbot; rexp = pow ( ( double ) 10.0, ( double ) rexp ); } } } r = isgn * rexp * rtop / rbot; return r; } //****************************************************************************80 bool s_to_r8vec ( char *s, int n, double rvec[] ) //****************************************************************************80 // // Purpose: // // S_TO_R8VEC reads an R8VEC from a string. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 19 February 2001 // // Author: // // John Burkardt // // Parameters: // // Input, char *S, the string to be read. // // Input, int N, the number of values expected. // // Output, double RVEC[N], the values read from the string. // // Output, bool S_TO_R8VEC, is true if an error occurred. // { bool error; int i; int lchar; error = false; for ( i = 0; i < n; i++ ) { rvec[i] = s_to_r8 ( s, &lchar, &error ); if ( error ) { return error; } s = s + lchar; } return error; } //****************************************************************************80 int s_word_count ( char *s ) //****************************************************************************80 // // Purpose: // // S_WORD_COUNT counts the number of "words" in a string. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 30 January 2006 // // Author: // // John Burkardt // // Parameters: // // Input, char *S, the string to be examined. // // Output, int S_WORD_COUNT, the number of "words" in the string. // Words are presumed to be separated by one or more blanks. // { bool blank; int word_num; word_num = 0; blank = true; while ( *s ) { if ( *s == ' ' ) { blank = true; } else if ( blank ) { word_num = word_num + 1; blank = false; } (*s)++; } return word_num; }