# include # include # include # include # include # include "r8bto.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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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; } /******************************************************************************/ double *r8bto_dif2 ( int m, int l ) /******************************************************************************/ /* Purpose: R8BTO_DIF2 sets up an R8BTO second difference matrix. Discussion: To get the second difference matrix, it is assumed that M will be 1! The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Example: M = 2, L = 3 1 2 | 3 4 | 5 6 5 5 | 6 6 | 7 7 ----+-----+----- 7 8 | 1 2 | 3 4 8 8 | 5 5 | 6 6 ----+-----+----- 9 0 | 7 8 | 1 2 9 9 | 8 8 | 5 5 X = (/ 1, 2, 3, 4, 5, 6 /) B = (/ 91, 134, 73, 125, 97, 129 /) Licensing: This code is distributed under the GNU LGPL license. Modified: 05 July 2016 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Output, double R8BTO_INDICATOR[M*M*(2*L-1)], the R8BTO matrix. */ { double *a; int i; int i2; int j; int j2; int k; double value; a = r8vec_zeros_new ( m * m * ( 2 * l - 1 ) ); /* Blocks 1 to L form the first row. */ j = 0; for ( k = 1; k <= l; k++ ) { if ( k == 1 ) { value = 2.0; } else if ( k == 2 ) { value = -1.0; } else { value = 0.0; } for ( j2 = 1; j2 <= m; j2++ ) { j = j + 1; for ( i = 1; i <= m; i++ ) { a[i-1+(j2-1)*m+(k-1)*m*m] = value; } } } /* Blocks L+1 through 2*L-1 form the remainder of the first column. */ i = m; for ( k = l + 1; k <= 2 * l - 1; k++ ) { if ( k == l + 1 ) { value = -1.0; } else { value = 0.0; } for ( i2 = 1; i2 <= m; i2++ ) { i = i + 1; for ( j = 1; j <= m; j++ ) { a[i2-1+(j-1)*m+(k-1)*m*m] = value; } } } return a; } /******************************************************************************/ double *r8bto_indicator ( int m, int l ) /******************************************************************************/ /* Purpose: R8BTO_INDICATOR sets up an R8BTO indicator matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Example: M = 2, L = 3 1 2 | 3 4 | 5 6 5 5 | 6 6 | 7 7 ----+-----+----- 7 8 | 1 2 | 3 4 8 8 | 5 5 | 6 6 ----+-----+----- 9 0 | 7 8 | 1 2 9 9 | 8 8 | 5 5 X = (/ 1, 2, 3, 4, 5, 6 /) B = (/ 91, 134, 73, 125, 97, 129 /) Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Output, double R8BTO_INDICATOR[M*M*(2*L-1)], the R8BTO matrix. */ { double *a; int fac; int i; int i2; int j; int j2; int k; a = r8vec_zeros_new ( m * m * ( 2 * l - 1 ) ); fac = i4_power ( 10, i4_log_10 ( m * l ) + 1 ); /* Blocks 1 to L form the first row. */ j = 0; for ( k = 1; k <= l; k++ ) { for ( j2 = 1; j2 <= m; j2++ ) { j = j + 1; for ( i = 1; i <= m; i++ ) { a[i-1+(j2-1)*m+(k-1)*m*m] = ( double ) ( fac * i + j ); } } } /* Blocks L+1 through 2*L-1 form the remainder of the first column. */ i = m; for ( k = l + 1; k <= 2 * l - 1; k++ ) { for ( i2 = 1; i2 <= m; i2++ ) { i = i + 1; for ( j = 1; j <= m; j++ ) { a[i2-1+(j-1)*m+(k-1)*m*m] = ( double ) ( fac * i + j ); } } } return a; } /******************************************************************************/ double *r8bto_mtv ( int m, int l, double a[], double x[] ) /******************************************************************************/ /* Purpose: R8BTO_MTV multiplies a vector times an R8BTO matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Example: M = 2, L = 3 1 2 | 3 4 | 5 6 5 5 | 6 6 | 7 7 ----+-----+----- 7 8 | 1 2 | 3 4 8 8 | 5 5 | 6 6 ----+-----+----- 9 0 | 7 8 | 1 2 9 9 | 8 8 | 5 5 X = (/ 1, 2, 3, 4, 5, 6 /) B = (/ 163, 122, 121, 130, 87, 96 /) Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Input, double A[M*M*(2*L-1)], the R8BTO matrix. Input, double X[M*L], the vector to be multiplied. Output, double R8BTO_MTV[M*L], the product X * A. */ { double *b; int i; int i2; int j; int k; b = r8vec_zeros_new ( m * l ); /* Construct the right hand side by blocks. */ for ( j = 1; j <= l; j++ ) { for ( k = 1; k <= j; k++ ) { for ( i = 1; i <= m; i++ ) { for ( i2 = 1; i2 <= m; i2++ ) { b[i-1+(j-1)*m] = b[i-1+(j-1)*m] + a[i2-1+(i-1)*m+(j-k)*m*m] * x[i2-1+(k-1)*m]; } } } for ( k = j + 1; k <= l; k++ ) { for ( i = 1; i <= m; i++ ) { for ( i2 = 1; i2 <= m; i2++ ) { b[i-1+(j-1)*m] = b[i-1+(j-1)*m] + a[i2-1+(i-1)*m+(l+k-j-1)*m*m] * x[i2-1+(k-1)*m]; } } } } return b; } /******************************************************************************/ double *r8bto_mv ( int m, int l, double a[], double x[] ) /******************************************************************************/ /* Purpose: R8BTO_MV multiplies an R8BTO matrix times a vector. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Example: M = 2, L = 3 1 2 | 3 4 | 5 6 5 5 | 6 6 | 7 7 ----+-----+----- 7 8 | 1 2 | 3 4 8 8 | 5 5 | 6 6 ----+-----+----- 9 0 | 7 8 | 1 2 9 9 | 8 8 | 5 5 X = (/ 1, 2, 3, 4, 5, 6 /) B = (/ 91, 134, 73, 125, 79, 138 /) Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Input, double A[M*M*(2*L-1)], the R8BTO matrix. Input, double X[M*L], the vector to be multiplied. Output, double R8BTO_MV[M*L], the product A * X. */ { double *b; int i; int i2; int j; int k; b = r8vec_zeros_new ( m * l ); /* Construct the right hand side by blocks. */ for ( j = 0; j < l; j++ ) { for ( k = 0; k <= j - 1; k++ ) { for ( i = 0; i < m; i++ ) { for ( i2 = 0; i2 < m; i2++ ) { b[i+j*m] = b[i+j*m] + a[i+i2*m+(l+j-k-1)*m*m] * x[i2+k*m]; } } } for ( k = j; k < l; k++ ) { for ( i = 0; i < m; i++ ) { for ( i2 = 0; i2 < m; i2++ ) { b[i+j*m] = b[i+j*m] + a[i+i2*m+(k-j)*m*m] * x[i2+k*m]; } } } } return b; } /******************************************************************************/ void r8bto_print ( int m, int l, double a[], char *title ) /******************************************************************************/ /* Purpose: R8BTO_PRINT prints an R8BTO matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Input, double A[M*M*(2*L-1)], the R8BTO matrix. Input, char *TITLE, a title. */ { r8bto_print_some ( m, l, a, 1, 1, m*l, m*l, title ); return; } /******************************************************************************/ void r8bto_print_some ( int m, int l, double a[], int ilo, int jlo, int ihi, int jhi, char *title ) /******************************************************************************/ /* Purpose: R8BTO_PRINT_SOME prints some of an R8BTO matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Input, double A[M*M*(2*L-1)], the R8BTO 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 i1; int i2; int i3hi; int i3lo; int inc; int j; int j1; int j2; int j3hi; int j3lo; int n; n = m * l; printf ( "\n" ); printf ( "%s\n", title ); /* Print the columns of the matrix, in strips of 5. */ for ( j3lo = jlo; j3lo <= jhi; j3lo = j3lo + INCX ) { j3hi = j3lo + INCX - 1; j3hi = i4_min ( j3hi, n ); j3hi = i4_min ( j3hi, jhi ); inc = j3hi + 1 - j3lo; printf ( "\n" ); printf ( " Col: " ); for ( j = j3lo; j <= j3hi; j++ ) { printf ( "%7d ", j ); } printf ( "\n" ); printf ( " Row\n" ); printf ( " ---\n" ); /* Determine the range of the rows in this strip. */ i3lo = i4_max ( ilo, 1 ); i3hi = i4_min ( ihi, n ); for ( i = i3lo; i <= i3hi; i++ ) { printf ( "%4d ", i ); /* Print out (up to) 5 entries in row I, that lie in the current strip. */ for ( j = j3lo; j <= j3lo + inc - 1; j++ ) { /* i = M * ( i1 - 1 ) + i2 j = M * ( j1 - 1 ) + j2 */ i1 = ( i - 1 ) / m + 1; i2 = i - m * ( i1 - 1 ); j1 = ( j - 1 ) / m + 1; j2 = j - m * ( j1 - 1 ); if ( i1 <= j1 ) { printf ( "%12g ", a[i2-1+(j2-1)*m+(j1-i1)*m*m] ); } else { printf ( "%12g ", a[i2-1+(j2-1)*m+(l-1+i1-j1)*m*m] ); } } printf ( "\n" ); } } return; # undef INCX } /******************************************************************************/ double *r8bto_random ( int m, int l, int *seed ) /******************************************************************************/ /* Purpose: R8BTO_RANDOM randomizes an R8BTO matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Input/output, int *SEED, a seed for the random number generator. Output, double R8BTO_RANDOM[M*M*(2*L-1)], the R8BTO matrix. */ { double *a; int i; int j; int k; a = r8vec_zeros_new ( m * m * ( 2 * l - 1 ) ); for ( i = 0; i < m; i++ ) { for ( j = 0; j < m; j++ ) { for ( k = 0; k < 2 * l - 1; k++ ) { a[i+j*m+k*m*m] = r8_uniform_01 ( seed ); } } } return a; } /******************************************************************************/ double *r8bto_to_r8ge ( int m, int l, double a[] ) /******************************************************************************/ /* Purpose: R8BTO_TO_R8GE copies an R8BTO matrix to an R8GE matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the R8BTO matrix. Input, int L, the number of blocks in a row or column of the R8BTO matrix. Input, double A[M*M*(2*L-1)], the R8BTO matrix. Output, double R8BTO_TO_R8GE[(M*L)*(M*L)], the R8GE matrix. */ { double *b; int i; int i1; int i2; int j; int j1; int j2; int n; n = m * l; b = r8vec_zeros_new ( n * n ); for ( i = 1; i <= n; i++ ) { i1 = ( i - 1 ) / m + 1; i2 = i - m * ( i1 - 1 ); for ( j = 1; j <= n; j++ ) { j1 = ( j - 1 ) / m + 1; j2 = j - m * ( j1 - 1 ); if ( i1 <= j1 ) { b[i-1+(j-1)*n] = a[i2-1+(j2-1)*m+(j1-i1)*m*m]; } else { b[i-1+(j-1)*n] = a[i2-1+(j2-1)*m+(l+i1-j1-1)*m*m]; } } } return b; } /******************************************************************************/ double *r8bto_zeros ( int m, int l ) /******************************************************************************/ /* Purpose: R8BTO_ZEROS zeros an R8BTO matrix. Discussion: The R8BTO storage format is for a block Toeplitz matrix. The matrix can be regarded as an L by L array of blocks, each of size M by M. The full matrix has order N = M * L. The L by L matrix is Toeplitz, that is, along its diagonal, the blocks repeat. Storage for the matrix consists of the L blocks of the first row, followed by the L-1 blocks of the first column (skipping the first row). These items are stored in the natural way in an (M,M,2*L-1) array. Licensing: This code is distributed under the GNU LGPL license. Modified: 20 January 2013 Author: John Burkardt Parameters: Input, int M, the order of the blocks of the matrix A. Input, int L, the number of blocks in a row or column of A. Output, double R8BTO_ZEROS[M*M*(2*L-1)], the R8BTO matrix. */ { double *a; a = r8vec_zeros_new ( m * m * ( 2 * l - 1 ) ); return a; } /******************************************************************************/ int r8ge_fa ( int n, double a[], int pivot[] ) /******************************************************************************/ /* Purpose: R8GE_FA performs a LINPACK-style PLU factorization 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. R8GE_FA is a simplified version of the LINPACK routine SGEFA. The two dimensional array is stored by columns in a one dimensional array. Licensing: This code is distributed under the GNU LGPL license. Modified: 10 February 2012 Author: John Burkardt Reference: Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart, LINPACK User's Guide, SIAM, 1979, ISBN13: 978-0-898711-72-1, LC: QA214.L56. Parameters: Input, int N, the order of the matrix. N must be positive. Input/output, double A[N*N], the matrix to be factored. On output, A contains an upper triangular matrix and the multipliers which were used to obtain it. The factorization can be written A = L * U, where L is a product of permutation and unit lower triangular matrices and U is upper triangular. Output, int PIVOT[N], a vector of pivot indices. Output, int R8GE_FA, singularity flag. 0, no singularity detected. nonzero, the factorization failed on the INFO-th step. */ { int i; int j; int k; int l; double t; for ( k = 1; k <= n - 1; k++ ) { /* Find L, the index of the pivot row. */ l = k; for ( i = k + 1; i <= n; i++ ) { if ( fabs ( a[l-1+(k-1)*n] ) < fabs ( a[i-1+(k-1)*n] ) ) { l = i; } } pivot[k-1] = l; /* If the pivot index is zero, the algorithm has failed. */ if ( a[l-1+(k-1)*n] == 0.0 ) { fprintf ( stderr, "\n" ); fprintf ( stderr, "R8GE_FA - Fatal error!\n" ); fprintf ( stderr, " Zero pivot on step %d\n", k ); exit ( 1 ); } /* Interchange rows L and K if necessary. */ if ( l != k ) { t = a[l-1+(k-1)*n]; a[l-1+(k-1)*n] = a[k-1+(k-1)*n]; a[k-1+(k-1)*n] = t; } /* Normalize the values that lie below the pivot entry A(K,K). */ for ( i = k + 1; i <= n; i++ ) { a[i-1+(k-1)*n] = - a[i-1+(k-1)*n] / a[k-1+(k-1)*n]; } /* Row elimination with column indexing. */ for ( j = k + 1; j <= n; j++ ) { if ( l != k ) { t = a[l-1+(j-1)*n]; a[l-1+(j-1)*n] = a[k-1+(j-1)*n]; a[k-1+(j-1)*n] = t; } for ( i = k + 1; i <= n; i++ ) { a[i-1+(j-1)*n] = a[i-1+(j-1)*n] + a[i-1+(k-1)*n] * a[k-1+(j-1)*n]; } } } pivot[n-1] = n; if ( a[n-1+(n-1)*n] == 0.0 ) { fprintf ( stderr, "\n" ); fprintf ( stderr, "R8GE_FA - Fatal error!\n" ); fprintf ( stderr, " Zero pivot on step %d\n", n ); exit ( 1 ); } return 0; } /******************************************************************************/ double *r8ge_indicator ( int m, int n ) /******************************************************************************/ /* Purpose: R8GE_INDICATOR sets up an R8GE indicator 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 GNU LGPL license. Modified: 25 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. Output, double R8GE_INDICATOR[M*N], the R8GE matrix. */ { double *a; int fac; int i; int j; a = r8vec_zeros_new ( m * n ); fac = i4_power ( 10, i4_log_10 ( n ) + 1 ); for ( i = 1; i <= m; i++ ) { for ( j = 1; j <= n; j++ ) { a[i-1+(j-1)*m] = ( double ) ( fac * i + j ); } } return a; } /******************************************************************************/ 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 GNU LGPL 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 GNU LGPL 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 *r8ge_sl_new ( int n, double a_lu[], int pivot[], double b[], int job ) /******************************************************************************/ /* Purpose: R8GE_SL_NEW solves an R8GE system factored by R8GE_FA. 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. R8GE_SL_NEW is a simplified version of the LINPACK routine SGESL. Licensing: This code is distributed under the GNU LGPL license. Modified: 06 March 2012 Author: John Burkardt Parameters: Input, int N, the order of the matrix. N must be positive. Input, double A_LU[N*N], the LU factors from R8GE_FA. Input, int PIVOT[N], the pivot vector from R8GE_FA. Input, double B[N], the right hand side vector. Input, int JOB, specifies the operation. 0, solve A * x = b. nonzero, solve A' * x = b. Output, double R8GE_SL_NEW[N], the solution vector. */ { int i; int k; int l; double t; double *x; x = r8vec_zeros_new ( n ); for ( i = 0; i < n; i++ ) { x[i] = b[i]; } /* Solve A * x = b. */ if ( job == 0 ) { /* Solve PL * Y = B. */ for ( k = 1; k <= n - 1; k++ ) { l = pivot[k-1]; if ( l != k ) { t = x[l-1]; x[l-1] = x[k-1]; x[k-1] = t; } for ( i = k + 1; i <= n; i++ ) { x[i-1] = x[i-1] + a_lu[i-1+(k-1)*n] * x[k-1]; } } /* Solve U * X = Y. */ for ( k = n; 1 <= k; k-- ) { x[k-1] = x[k-1] / a_lu[k-1+(k-1)*n]; for ( i = 1; i <= k - 1; i++ ) { x[i-1] = x[i-1] - a_lu[i-1+(k-1)*n] * x[k-1]; } } } /* Solve A' * X = B. */ else { /* Solve U' * Y = B. */ for ( k = 1; k <= n; k++ ) { t = 0.0; for ( i = 1; i <= k - 1; i++ ) { t = t + x[i-1] * a_lu[i-1+(k-1)*n]; } x[k-1] = ( x[k-1] - t ) / a_lu[k-1+(k-1)*n]; } /* Solve ( PL )' * X = Y. */ for ( k = n - 1; 1 <= k; k-- ) { t = 0.0; for ( i = k + 1; i <= n; i++ ) { t = t + x[i-1] * a_lu[i-1+(k-1)*n]; } x[k-1] = x[k-1] + t; l = pivot[k-1]; if ( l != k ) { t = x[l-1]; x[l-1] = x[k-1]; x[k-1] = t; } } } return x; } /******************************************************************************/ 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 GNU LGPL 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 = ( double * ) malloc ( n * sizeof ( double ) ); 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 GNU LGPL 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 GNU LGPL 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; } /******************************************************************************/ void timestamp ( ) /******************************************************************************/ /* Purpose: TIMESTAMP prints the current YMDHMS date as a time stamp. Example: 31 May 2001 09:45:54 AM Licensing: This code is distributed under the GNU LGPL license. Modified: 24 September 2003 Author: John Burkardt Parameters: None */ { # define TIME_SIZE 40 static char time_buffer[TIME_SIZE]; const struct tm *tm; time_t now; now = time ( NULL ); tm = localtime ( &now ); strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm ); printf ( "%s\n", time_buffer ); return; # undef TIME_SIZE }