# include # include # include # include # include "r8sr.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; } /******************************************************************************/ 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; 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 } /******************************************************************************/ void r8sr_dif2 ( int n, int *nz, int row[], int col[], double diag[], double off[] ) /******************************************************************************/ /* Purpose: R8SR_DIF2 sets up an R8SR second difference matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the entry in A(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Output, int *NZ, the number of offdiagonal nonzero elements in the matrix. NZ = 2 * N - 2. Output, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Output, int COL[NZ], contains the column index of the element in the corresponding position in A. Output, double DIAG[N], the diagonal elements of A. Output, double OFF[NZ], the off-diagonal elements of A. */ { int i; int nz2; for ( i = 0; i < n; i++ ) { diag[i] = - 2.0; } row[0] = 0; nz2 = 0; for ( i = 0; i < n; i++ ) { if ( i == 0 ) { col[nz2] = i + 1; off[nz2] = 1.0; nz2 = nz2 + 1; row[i+1] = row[i] + 1; } else if ( i < n - 1 ) { col[nz2] = i - 1; off[nz2] = 1.0; nz2 = nz2 + 1; col[nz2] = i + 1; off[nz2] = 1.0; nz2 = nz2 + 1; row[i+1] = row[i] + 2; } else { col[nz2] = i - 1; off[nz2] = 1.0; nz2 = nz2 + 1; row[i+1] = row[i] + 1; } } return; } /******************************************************************************/ void r8sr_indicator ( int n, int nz, int row[], int col[], double diag[], double off[] ) /******************************************************************************/ /* Purpose: R8SR_INDICATOR sets up an R8SR indicator matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Output, double DIAG[N], the diagonal elements of A. Output, double OFF[NZ], the off-diagonal elements of A. */ { int fac; int i; int j; int k; fac = i4_power ( 10, i4_log_10 ( n ) + 1 ); for ( i = 0; i < n; i++ ) { j = i; diag[i] = ( double ) ( fac * ( i + 1 ) + ( j + 1 ) ); for ( k = row[i]; k <= row[i+1] - 1; k++ ) { j = col[k]; off[k] = ( double ) ( fac * ( i + 1 ) + ( j + 1 ) ); } } return; } /******************************************************************************/ double *r8sr_mtv ( int n, int nz, int row[], int col[], double diag[], double off[], double x[] ) /******************************************************************************/ /* Purpose: R8SR_MTV multiplies a vector times an R8SR matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 17 February 2013 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Input, double DIAG[N], the diagonal elements of A. Input, double OFF[NZ], the off-diagonal elements of A. Input, double X[N], the vector to be multiplies by A. Output, double R8SR_MTV[N], the product A' * X. */ { double *b; int i; int j; int k; b = ( double * ) malloc ( n * sizeof ( double ) ); for ( i = 0; i < n; i++ ) { b[i] = diag[i] * x[i]; } for ( i = 0; i < n; i++ ) { for ( k = row[i]; k <= row[i+1] - 1; k++ ) { j = col[k]; b[j] = b[j] + off[k] * x[i]; } } return b; } /******************************************************************************/ double *r8sr_mv ( int n, int nz, int row[], int col[], double diag[], double off[], double x[] ) /******************************************************************************/ /* Purpose: R8SR_MV multiplies an R8SR matrix times a vector. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 17 February 2013 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Input, double DIAG[N], the diagonal elements of A. Input, double OFF[NZ], the off-diagonal elements of A. Input, double X[N], the vector to be multiplied by A. Output, double R8SR_MV[N], the product A * X. */ { double *b; int i; int j; int k; b = ( double * ) malloc ( n * sizeof ( double ) ); for ( i = 0; i < n; i++ ) { b[i] = diag[i] * x[i]; } for ( i = 0; i < n; i++ ) { for ( k = row[i]; k <= row[i+1] - 1; k++ ) { j = col[k]; b[i] = b[i] + off[k] * x[j]; } } return b; } /******************************************************************************/ void r8sr_print ( int n, int nz, int row[], int col[], double diag[], double off[], char *title ) /******************************************************************************/ /* Purpose: R8SR_PRINT prints an R8SR matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the entry in A(J). Licensing: This code is distributed under the MIT license. Modified: 17 February 2013 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Input, double DIAG[N], the diagonal elements of A. Input, double OFF[NZ], the off-diagonal elements of A. Input, char *TITLE, a title. */ { r8sr_print_some ( n, nz, row, col, diag, off, 0, 0, n - 1, n - 1, title ); return; } /******************************************************************************/ void r8sr_print_some ( int n, int nz, int row[], int col[], double diag[], double off[], int ilo, int jlo, int ihi, int jhi, char *title ) /******************************************************************************/ /* Purpose: R8SR_PRINT_SOME prints some of an R8SR matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the entry in A(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Input, double DIAG[N], the diagonal elements of A. Input, double OFF[NZ], the off-diagonal elements of A. 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" ); 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, n - 1 ); for ( i = i2lo; i <= i2hi; i++ ) { printf ( "%6d ", i ); /* Print out (up to) 5 entries in row I, that lie in the current strip. */ for ( j = j2lo; j <= j2hi; j++ ) { aij = 0.0; if ( j == i ) { aij = diag[i]; } else { for ( k = row[i]; k <= row[i+1] - 1; k++ ) { if ( j == col[k] ) { aij = off[k]; } } } printf ( "%12g ", aij ); } printf ( "\n" ); } } return; # undef INCX } /******************************************************************************/ void r8sr_random ( int n, int nz, int row[], int col[], double diag[], double off[], int *seed ) /******************************************************************************/ /* Purpose: R8SR_RANDOM randomizes an R8SR matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Output, double DIAG[N], the diagonal elements of A. Output, double OFF[NZ], the off-diagonal elements of A. Input/output, int *SEED, a seed for the random number generator. */ { int i; int j; for ( i = 0; i < n; i++ ) { diag[i] = r8_uniform_01 ( seed ); for ( j = row[i]; j <= row[i+1] - 1; j++ ) { off[j] = r8_uniform_01 ( seed ); } } return; } /******************************************************************************/ double *r8sr_to_r8ge ( int n, int nz, int row[], int col[], double diag[], double off[] ) /******************************************************************************/ /* Purpose: R8SR_TO_R8GE converts an R8SR matrix to an R8GE matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Input, double DIAG[N], the diagonal elements of A. Input, double OFF[NZ], the off-diagonal elements of A. Output, double R8SR_TO_R8GE[N*N], the R8GE matrix. */ { double *b; int i; int j; b = ( double * ) malloc ( n * n * sizeof ( double ) ); for ( j = 0; j < n; j++ ) { for ( i = 0; i < n; i++ ) { b[i+j*n] = 0.0; } } for ( i = 0; i < n; i++ ) { b[i+i*n] = diag[i]; } for ( i = 0; i < n; i++ ) { for ( j = row[i]; j <= row[i+1] - 1; j++ ) { b[i+col[j]*n] = off[j]; } } return b; } /******************************************************************************/ void r8sr_zeros ( int n, int nz, int row[], int col[], double diag[], double off[] ) /******************************************************************************/ /* Purpose: R8SR_ZEROS zeros an R8SR matrix. Discussion: The R8SR storage format stores the diagonal of a sparse matrix in DIAG. The off-diagonal entries of row I are stored in entries ROW(I) through ROW(I+1)-1 of OFF. COL(J) records the column index of the the entry stored in OFF(J). Licensing: This code is distributed under the MIT license. Modified: 12 June 2016 Author: John Burkardt Parameters: Input, int N, the order of the matrix. Input, int NZ, the number of offdiagonal nonzero elements in A. Input, int ROW[N+1]. The nonzero offdiagonal elements of row I of A are contained in A(ROW(I)) through A(ROW(I+1)-1). Input, int COL[NZ], contains the column index of the element in the corresponding position in A. Output, double DIAG[N], the diagonal elements of A. Output, double OFF[NZ], the off-diagonal elements of A. */ { int i; int j; for ( i = 0; i < n; i++ ) { diag[i] = 0.0; for ( j = row[i]; j <= row[i+1] - 1; j++ ) { off[j] = 0.0; } } return; } /******************************************************************************/ 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; }