# include # include # include # include # include "r8ncf.h" /******************************************************************************/ int i4_log_10 ( int i ) /******************************************************************************/ /* Purpose: I4_LOG_10 returns the integer part of the logarithm base 10 of an I4. Example: I I4_LOG_10 ----- -------- 0 0 1 0 2 0 9 0 10 1 11 1 99 1 100 2 101 2 999 2 1000 3 1001 3 9999 3 10000 4 Discussion: I4_LOG_10 ( I ) + 1 is the number of decimal digits in I. Licensing: This code is distributed under the MIT license. Modified: 23 October 2007 Author: John Burkardt Parameters: Input, int I, the number whose logarithm base 10 is desired. Output, int I4_LOG_10, the integer part of the logarithm base 10 of the absolute value of X. */ { int i_abs; int ten_pow; int value; if ( i == 0 ) { value = 0; } else { value = 0; ten_pow = 10; i_abs = abs ( i ); while ( ten_pow <= i_abs ) { value = value + 1; ten_pow = ten_pow * 10; } } return value; } /******************************************************************************/ int i4_max ( int i1, int i2 ) /******************************************************************************/ /* Purpose: I4_MAX returns the maximum of two I4's. Licensing: This code is distributed under the MIT license. Modified: 29 August 2006 Author: John Burkardt Parameters: Input, int I1, I2, are two integers to be compared. Output, int I4_MAX, the larger of I1 and I2. */ { int value; if ( i2 < i1 ) { value = i1; } else { value = i2; } return value; } /******************************************************************************/ int i4_min ( int i1, int i2 ) /******************************************************************************/ /* Purpose: I4_MIN returns the smaller of two I4's. Licensing: This code is distributed under the MIT license. Modified: 29 August 2006 Author: John Burkardt Parameters: Input, int I1, I2, two integers to be compared. Output, int I4_MIN, the smaller of I1 and I2. */ { int value; if ( i1 < i2 ) { value = i1; } else { value = i2; } return value; } /******************************************************************************/ int i4_power ( int i, int j ) /******************************************************************************/ /* Purpose: I4_POWER returns the value of I^J. Licensing: This code is distributed under the MIT license. Modified: 23 October 2007 Author: John Burkardt Parameters: Input, int I, J, the base and the power. J should be nonnegative. Output, int I4_POWER, the value of I^J. */ { int k; int value; if ( j < 0 ) { if ( i == 1 ) { value = 1; } else if ( i == 0 ) { fprintf ( stderr, "\n" ); fprintf ( stderr, "I4_POWER - Fatal error!\n" ); fprintf ( stderr, " I^J requested, with I = 0 and J negative.\n" ); exit ( 1 ); } else { value = 0; } } else if ( j == 0 ) { if ( i == 0 ) { fprintf ( stderr, "\n" ); fprintf ( stderr, "I4_POWER - Fatal error!\n" ); fprintf ( stderr, " I^J requested, with I = 0 and J = 0.\n" ); exit ( 1 ); } else { value = 1; } } else if ( j == 1 ) { value = i; } else { value = 1; for ( k = 1; k <= j; k++ ) { value = value * i; } } return value; } /******************************************************************************/ int *i4vec_zeros_new ( int n ) /******************************************************************************/ /* Purpose: I4VEC_ZEROS_NEW creates and zeroes an I4VEC. Discussion: An I4VEC is a vector of I4's. Licensing: This code is distributed under the MIT license. Modified: 05 September 2008 Author: John Burkardt Parameters: Input, int N, the number of entries in the vector. Output, int I4VEC_ZEROS_NEW[N], a vector of zeroes. */ { int *a; int i; a = ( int * ) malloc ( n * sizeof ( int ) ); for ( i = 0; i < n; i++ ) { a[i] = 0; } return a; } /******************************************************************************/ double r8_uniform_01 ( int *seed ) /******************************************************************************/ /* Purpose: R8_UNIFORM_01 returns a unit pseudorandom R8. Discussion: This routine implements the recursion seed = 16807 * seed mod ( 2^31 - 1 ) r8_uniform_01 = seed / ( 2^31 - 1 ) The integer arithmetic never requires more than 32 bits, including a sign bit. If the initial seed is 12345, then the first three computations are Input Output R8_UNIFORM_01 SEED SEED 12345 207482415 0.096616 207482415 1790989824 0.833995 1790989824 2035175616 0.947702 Licensing: This code is distributed under the MIT license. Modified: 11 August 2004 Author: John Burkardt Reference: Paul Bratley, Bennett Fox, Linus Schrage, A Guide to Simulation, Springer Verlag, pages 201-202, 1983. Pierre L'Ecuyer, Random Number Generation, in Handbook of Simulation edited by Jerry Banks, Wiley Interscience, page 95, 1998. Bennett Fox, Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators, ACM Transactions on Mathematical Software, Volume 12, Number 4, pages 362-376, 1986. P A Lewis, A S Goodman, J M Miller, A Pseudo-Random Number Generator for the System/360, IBM Systems Journal, Volume 8, pages 136-143, 1969. Parameters: Input/output, int *SEED, the "seed" value. Normally, this value should not be 0. On output, SEED has been updated. Output, double R8_UNIFORM_01, a new pseudorandom variate, strictly between 0 and 1. */ { int k; double r; if ( *seed == 0 ) { fprintf ( stderr, "\n" ); fprintf ( stderr, "R8_UNIFORM_01 - Fatal error!\n" ); fprintf ( stderr, " Input value of SEED = 0\n" ); exit ( 1 ); } k = *seed / 127773; *seed = 16807 * ( *seed - k * 127773 ) - k * 2836; if ( *seed < 0 ) { *seed = *seed + 2147483647; } r = ( ( double ) ( *seed ) ) * 4.656612875E-10; return r; } /******************************************************************************/ void r8ge_print ( int m, int n, double a[], char *title ) /******************************************************************************/ /* Purpose: R8GE_PRINT prints an R8GE matrix. Discussion: The R8GE storage format is used for a "general" M by N matrix. A physical storage space is made for each logical entry. The two dimensional logical array is mapped to a vector, in which storage is by columns. Licensing: This code is distributed under the MIT license. Modified: 28 February 2012 Author: John Burkardt Parameters: Input, int M, the number of rows of the matrix. M must be positive. Input, int N, the number of columns of the matrix. N must be positive. Input, double A[M*N], the R8GE matrix. Input, char *TITLE, a title. */ { r8ge_print_some ( m, n, a, 1, 1, m, n, title ); return; } /******************************************************************************/ void r8ge_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, int jhi, char *title ) /******************************************************************************/ /* Purpose: R8GE_PRINT_SOME prints some of an R8GE matrix. Discussion: The R8GE storage format is used for a "general" M by N matrix. A physical storage space is made for each logical entry. The two dimensional logical array is mapped to a vector, in which storage is by columns. Licensing: This code is distributed under the MIT license. Modified: 28 February 2012 Author: John Burkardt Parameters: Input, int M, the number of rows of the matrix. M must be positive. Input, int N, the number of columns of the matrix. N must be positive. Input, double A[M*N], the R8GE matrix. Input, int ILO, JLO, IHI, JHI, designate the first row and column, and the last row and column to be printed. Input, char *TITLE, a title. */ { # define INCX 5 int i; int i2hi; int i2lo; int j; int j2hi; int j2lo; printf ( "\n" ); printf ( "%s\n", title ); /* Print the columns of the matrix, in strips of 5. */ for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX ) { j2hi = j2lo + INCX - 1; j2hi = i4_min ( j2hi, n ); j2hi = i4_min ( j2hi, jhi ); printf ( "\n" ); /* For each column J in the current range... Write the header. */ printf ( " Col: " ); for ( j = j2lo; j <= j2hi; j++ ) { printf ( "%7d ", j ); } printf ( "\n" ); printf ( " Row\n" ); printf ( " ---\n" ); /* Determine the range of the rows in this strip. */ i2lo = i4_max ( ilo, 1 ); i2hi = i4_min ( ihi, m ); for ( i = i2lo; i <= i2hi; i++ ) { /* Print out (up to) 5 entries in row I, that lie in the current strip. */ printf ( "%5d ", i ); for ( j = j2lo; j <= j2hi; j++ ) { printf ( "%12g ", a[i-1+(j-1)*m] ); } printf ( "\n" ); } } return; # undef INCX } /******************************************************************************/ double *r8ncf_dif2 ( int m, int n, int nz_num, int rowcol[] ) /******************************************************************************/ /* Purpose: R8NCF_DIF2 sets up an R8NCF second difference matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 20 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Input, int ROWCOL[2,NZ_NUM], the coordinates of the nonzero entries. Output, double A[NZ_NUM], the matrix. */ { double *a; int i; int j; int k; a = r8vec_zeros_new ( nz_num ); for ( k = 0; k < nz_num; k++ ) { i = rowcol[0+k*2]; j = rowcol[1+k*2]; if ( j == i - 1 ) { a[k] = -1.0; } else if ( j == i ) { a[k] = 2.0; } else if ( j == i + 1 ) { a[k] = -1.0; } } return a; } /******************************************************************************/ int r8ncf_dif2_nz_num ( int m, int n ) /******************************************************************************/ /* Purpose: R8NCF_DIF2_NZ_NUM counts nonzeros in an R8NCF second difference matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 20 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Output, int NZ_NUM, the number of nonzero entries. */ { int nz_num; if ( m < n ) { nz_num = 3 * m - 1; } else if ( m == n ) { nz_num = 3 * n - 2; } else { nz_num = 3 * n - 1; } return nz_num; } /******************************************************************************/ int *r8ncf_dif2_rowcol ( int m, int n, int nz_num ) /******************************************************************************/ /* Purpose: R8NCF_DIF2_ROWCOL sets indexing for an R8NCF second difference matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 20 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Output, int ROWCOL[2*NZ_NUM], the coordinates of the nonzero entries. */ { int i; int j; int k; int *rowcol; rowcol = i4vec_zeros_new ( 2 * nz_num ); k = 0; for ( i = 0; i < m; i++ ) { j = i - 1; if ( 0 <= j && j < n ) { rowcol[0+k*2] = i; rowcol[1+k*2] = j; k = k + 1; } j = i; if ( j < n ) { rowcol[0+k*2] = i; rowcol[1+k*2] = j; k = k + 1; } j = i + 1; if ( j < n ) { rowcol[0+k*2] = i; rowcol[1+k*2] = j; k = k + 1; } } return rowcol; } /******************************************************************************/ double *r8ncf_indicator ( int m, int n, int nz_num, int rowcol[] ) /******************************************************************************/ /* Purpose: R8NCF_INDICATOR sets up an R8NCF indicator matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 20 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Input, int ROWCOL[2*NZ_NUM], the coordinates of the nonzero entries. Output, double A[NZ_NUM], the indicator matrix. */ { double *a; int fac; int i; int j; int k; a = r8vec_zeros_new ( nz_num ); fac = i4_power ( 10, i4_log_10 ( n ) + 1 ); for ( k = 0; k < nz_num; k++ ) { i = rowcol[0+k*2]; j = rowcol[1+k*2]; a[k] = ( double ) ( fac * ( i + 1 ) + ( j + 1 ) ); } return a; } /******************************************************************************/ double *r8ncf_mtv ( int m, int n, int nz_num, int rowcol[], double a[], double x[] ) /******************************************************************************/ /* Purpose: R8NCF_MTV multiplies an R8VEC times an R8NCF matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 21 July 2016 Author: John Burkardt Parameters: Input, int M, N, the order of the matrix. Input, int NZ_NUM, the number of nonzero elements in the matrix. Input, int ROWCOL[2*NZ_NUM], the row and column indices of the nonzero elements. Input, double A[NZ_NUM], the nonzero elements of the matrix. Input, double X[M], the vector to be multiplied by A'. Output, double R8NCF_MTV[N], the product A' * x. */ { double *b; int i; int j; int k; b = r8vec_zeros_new ( n ); for ( k = 0; k < nz_num; k++ ) { i = rowcol[0+k*2]; j = rowcol[1+k*2]; b[j] = b[j] + a[k] * x[i]; } return b; } /******************************************************************************/ double *r8ncf_mv ( int m, int n, int nz_num, int rowcol[], double a[], double x[] ) /******************************************************************************/ /* Purpose: R8NCF_MV multiplies an R8NCF matrix by an R8VEC. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 21 July 2016 Author: John Burkardt Parameters: Input, int M, N, the order of the matrix. Input, int NZ_NUM, the number of nonzero elements in the matrix. Input, int ROWCOL[2*NZ_NUM], the row and column indices of the nonzero elements. Input, double A[NZ_NUM], the nonzero elements of the matrix. Input, double X[N], the vector to be multiplied by A. Output, double R8NCF_MV[M], the product A * x. */ { double *b; int i; int j; int k; b = r8vec_zeros_new ( m ); for ( k = 0; k < nz_num; k++ ) { i = rowcol[0+k*2]; j = rowcol[1+k*2]; b[i] = b[i] + a[k] * x[j]; } return b; } /******************************************************************************/ void r8ncf_print ( int m, int n, int nz_num, int rowcol[], double a[], char *title ) /******************************************************************************/ /* Purpose: R8NCF_PRINT prints an R8NCF matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 14 February 2013 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns of the matrix. Input, int NZ_NUM, the number of nonzero elements in the matrix. Input, int ROWCOL[2*NZ_NUM], the row and column indices of the nonzero elements. Input, double A[NZ_NUM], the nonzero elements of the matrix. Input, char *TITLE, a title. */ { r8ncf_print_some ( m, n, nz_num, rowcol, a, 0, 0, m - 1, n - 1, title ); return; } /******************************************************************************/ void r8ncf_print_some ( int m, int n, int nz_num, int rowcol[], double a[], int ilo, int jlo, int ihi, int jhi, char *title ) /******************************************************************************/ /* Purpose: R8NCF_PRINT_SOME prints some of an R8NCF matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 14 February 2013 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns of the matrix. Input, int NZ_NUM, the number of nonzero elements in the matrix. Input, int ROWCOL[2*NZ_NUM], the row and column indices of the nonzero elements. Input, double A[NZ_NUM], the nonzero elements of the matrix. Input, int ILO, JLO, IHI, JHI, the first row and column, and the last row and column to be printed. Input, char *TITLE, a title. */ { # define INCX 5 double aij; int i; int i2hi; int i2lo; int j; int j2hi; int j2lo; int k; printf ( "\n" ); printf ( "%s\n", title ); /* Print the columns of the matrix, in strips of 5. */ for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX ) { j2hi = j2lo + INCX - 1; j2hi = i4_min ( j2hi, n - 1 ); j2hi = i4_min ( j2hi, jhi ); printf ( "\n" ); /* For each column J in the current range... Write the header. */ printf ( " Col: " ); for ( j = j2lo; j <= j2hi; j++ ) { printf ( "%7d ", j ); } printf ( "\n" ); printf ( " Row\n" ); printf ( " ---\n" ); /* Determine the range of the rows in this strip. */ i2lo = i4_max ( ilo, 0 ); i2hi = i4_min ( ihi, m - 1 ); for ( i = i2lo; i <= i2hi; i++ ) { printf ( "%5d ", i ); for ( j = j2lo; j <= j2hi; j++ ) { aij = 0.0; for ( k = 0; k < nz_num; k++ ) { if ( rowcol[0+k*2] == i && rowcol[1+k*2] == j ) { aij = a[k]; break; } } printf ( " %12g", aij ); } printf ( "\n" ); } } return; # undef INCX } /******************************************************************************/ double *r8ncf_random ( int m, int n, int nz_num, int rowcol[], int *seed ) /******************************************************************************/ /* Purpose: R8NCF_RANDOM randomizes an R8NCF matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 21 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Input, int ROWCOL[2*NZ_NUM], the coordinates of the nonzero entries. Input/output, int *SEED, a seed for the random number generator. Output, double R8NCF_RANDOM[NZ_NUM], the indicator matrix. */ { double *a; int k; a = r8vec_zeros_new ( nz_num ); for ( k = 0; k < nz_num; k++ ) { a[k] = r8_uniform_01 ( seed ); } return a; } /******************************************************************************/ double *r8ncf_to_r8ge ( int m, int n, int nz_num, int rowcol[], double a[] ) /******************************************************************************/ /* Purpose: R8NCF_TO_R8GE converts an R8NCF matrix to R8GE format. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 21 July 2016 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Input, int ROWCOL[2*NZ_NUM], the coordinates of the nonzero entries. Input, double A[NZ_NUM], the matrix. Output, double R8NCF_TO_R8GE[M*N], the R8GE matrix. */ { double *a_r8ge; int i; int j; int k; a_r8ge = r8vec_zeros_new ( m * n ); for ( k = 0; k < nz_num; k++ ) { i = rowcol[0+k*2]; j = rowcol[1+k*2]; a_r8ge[i+j*m] = a_r8ge[i+j*m] + a[k]; } return a_r8ge; } /******************************************************************************/ double *r8ncf_zeros ( int m, int n, int nz_num, int rowcol[] ) /******************************************************************************/ /* Purpose: R8NCF_ZEROS zeros an R8NCF indicator matrix. Discussion: The R8NCF storage format stores NZ_NUM, the number of nonzeros, a real array containing the nonzero values, a 2 by NZ_NUM integer array storing the row and column of each nonzero entry. The R8NCF format is used by NSPCG. NSPCG requires that the information for the diagonal entries of the matrix must come first. Licensing: This code is distributed under the MIT license. Modified: 18 August 2015 Author: John Burkardt Parameters: Input, int M, N, the number of rows and columns in the matrix. Input, int NZ_NUM, the number of nonzero entries. Input, int ROWCOL[2*NZ_NUM], the coordinates of the nonzero entries. Output, double R8NCF_ZEROS[NZ_NUM], the matrix. */ { double *a; a = r8vec_zeros_new ( nz_num ); return a; } /******************************************************************************/ double *r8vec_indicator1_new ( int n ) /******************************************************************************/ /* Purpose: R8VEC_INDICATOR1_NEW sets an R8VEC to the indicator1 vector {1,2,3...}. Licensing: This code is distributed under the MIT license. Modified: 26 August 2008 Author: John Burkardt Parameters: Input, int N, the number of elements of A. Output, double R8VEC_INDICATOR1_NEW[N], the array. */ { double *a; int i; a = r8vec_zeros_new ( n ); for ( i = 0; i <= n - 1; i++ ) { a[i] = ( double ) ( i + 1 ); } return a; } /******************************************************************************/ void r8vec_print ( int n, double a[], char *title ) /******************************************************************************/ /* Purpose: R8VEC_PRINT prints an R8VEC. Discussion: An R8VEC is a vector of R8's. Licensing: This code is distributed under the MIT license. Modified: 08 April 2009 Author: John Burkardt Parameters: Input, int N, the number of components of the vector. Input, double A[N], the vector to be printed. Input, char *TITLE, a title. */ { int i; printf ( "\n" ); printf ( "%s\n", title ); printf ( "\n" ); for ( i = 0; i < n; i++ ) { printf ( " %8d %14f\n", i, a[i] ); } return; } /******************************************************************************/ double *r8vec_zeros_new ( int n ) /******************************************************************************/ /* Purpose: R8VEC_ZEROS_NEW creates and zeroes an R8VEC. Discussion: An R8VEC is a vector of R8's. Licensing: This code is distributed under the MIT license. Modified: 25 March 2009 Author: John Burkardt Parameters: Input, int N, the number of entries in the vector. Output, double R8VEC_ZEROS_NEW[N], a vector of zeroes. */ { double *a; int i; a = ( double * ) malloc ( n * sizeof ( double ) ); for ( i = 0; i < n; i++ ) { a[i] = 0.0; } return a; }