function i4_log_10 ( i ) !*****************************************************************************80 ! !! 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: ! ! 08 June 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer I, the number whose logarithm base 10 ! is desired. ! ! Output, integer I4_LOG_10, the integer part of the ! logarithm base 10 of the absolute value of X. ! implicit none integer i integer i_abs integer i4_log_10 integer ten_pow if ( i == 0 ) then i4_log_10 = 0 else i4_log_10 = 0 ten_pow = 10 i_abs = abs ( i ) do while ( ten_pow <= i_abs ) i4_log_10 = i4_log_10 + 1 ten_pow = ten_pow * 10 end do end if return end function r8_uniform_01 ( seed ) !*****************************************************************************80 ! !! R8_UNIFORM_01 returns a unit pseudorandom R8. ! ! Discussion: ! ! An R8 is a real ( kind = rk ) value. ! ! For now, the input quantity SEED is an integer variable. ! ! 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: ! ! 05 July 2006 ! ! 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. ! ! Peter Lewis, Allen Goodman, James Miller ! A Pseudo-Random Number Generator for the System/360, ! IBM Systems Journal, ! Volume 8, pages 136-143, 1969. ! ! Parameters: ! ! Input/output, integer SEED, the "seed" value, ! which should NOT be 0. On output, SEED has been updated. ! ! Output, real ( kind = rk ) R8_UNIFORM_01, a new pseudorandom variate, ! strictly between 0 and 1. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer k real ( kind = rk ) r8_uniform_01 integer seed if ( seed == 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8_UNIFORM_01 - Fatal error!' write ( *, '(a)' ) ' Input value of SEED = 0.' stop 1 end if k = seed / 127773 seed = 16807 * ( seed - k * 127773 ) - k * 2836 if ( seed < 0 ) then seed = seed + 2147483647 end if ! ! Although SEED can be represented exactly as a 32 bit integer, ! it generally cannot be represented exactly as a 32 bit real number! ! r8_uniform_01 = real ( seed, kind = rk ) * 4.656612875D-10 return end subroutine r8ge_print ( m, n, a, title ) !*****************************************************************************80 ! !! R8GE_PRINT prints an R8GE matrix. ! ! Discussion: ! ! The R8GE storage format is used for a general M by N matrix. A storage ! space is made for each entry. The two dimensional logical ! array can be thought of as a vector of M*N entries, starting with ! the M entries in the column 1, then the M entries in column 2 ! and so on. Considered as a vector, the entry A(I,J) is then stored ! in vector location I+(J-1)*M. ! ! R8GE storage is used by LINPACK and LAPACK. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 07 May 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, the number of rows of the matrix. ! M must be positive. ! ! Input, integer N, the number of columns of the matrix. ! N must be positive. ! ! Input, real ( kind = rk ) A(M,N), the R8GE matrix. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n real ( kind = rk ) a(m,n) character ( len = * ) title call r8ge_print_some ( m, n, a, 1, 1, m, n, title ) return end subroutine r8ge_print_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! R8GE_PRINT_SOME prints some of an R8GE matrix. ! ! Discussion: ! ! The R8GE storage format is used for a general M by N matrix. A storage ! space is made for each entry. The two dimensional logical ! array can be thought of as a vector of M*N entries, starting with ! the M entries in the column 1, then the M entries in column 2 ! and so on. Considered as a vector, the entry A(I,J) is then stored ! in vector location I+(J-1)*M. ! ! R8GE storage is used by LINPACK and LAPACK. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 March 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, the number of rows of the matrix. ! M must be positive. ! ! Input, integer N, the number of columns of the matrix. ! N must be positive. ! ! Input, real ( kind = rk ) A(M,N), the R8GE matrix. ! ! Input, integer ILO, JLO, IHI, JHI, the first row and ! column, and the last row and column to be printed. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: incx = 5 integer m integer n real ( kind = rk ) a(m,n) character ( len = 14 ) ctemp(incx) integer i integer i2hi integer i2lo integer ihi integer ilo integer inc integer j integer j2 integer j2hi integer j2lo integer jhi integer jlo character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) ! ! Print the columns of the matrix, in strips of 5. ! do j2lo = jlo, jhi, incx j2hi = j2lo + incx - 1 j2hi = min ( j2hi, n ) j2hi = min ( j2hi, jhi ) inc = j2hi + 1 - j2lo write ( *, '(a)' ) ' ' do j = j2lo, j2hi j2 = j + 1 - j2lo write ( ctemp(j2), '(i7,7x)' ) j end do write ( *, '('' Col: '',5a14)' ) ( ctemp(j2), j2 = 1, inc ) write ( *, '(a)' ) ' Row' write ( *, '(a)' ) ' ---' ! ! Determine the range of the rows in this strip. ! i2lo = max ( ilo, 1 ) i2hi = min ( ihi, m ) do i = i2lo, i2hi ! ! Print out (up to) 5 entries in row I, that lie in the current strip. ! do j2 = 1, inc j = j2lo - 1 + j2 write ( ctemp(j2), '(g14.6)' ) a(i,j) end do write ( *, '(i5,1x,5a14)' ) i, ( ctemp(j2), j2 = 1, inc ) end do end do return end subroutine r8pbl_dif2 ( n, ml, a ) !*****************************************************************************80 ! !! R8PBL_DIF2 returns the DIF2 matrix in R8PBL format. ! ! Example: ! ! N = 5 ! ! 2 -1 . . . ! -1 2 -1 . . ! . -1 2 -1 . ! . . -1 2 -1 ! . . . -1 2 ! ! Properties: ! ! A is banded, with bandwidth 3. ! ! A is tridiagonal. ! ! Because A is tridiagonal, it has property A (bipartite). ! ! A is a special case of the TRIS or tridiagonal scalar matrix. ! ! A is integral, therefore det ( A ) is integral, and ! det ( A ) * inverse ( A ) is integral. ! ! A is Toeplitz: constant along diagonals. ! ! A is symmetric: A' = A. ! ! Because A is symmetric, it is normal. ! ! Because A is normal, it is diagonalizable. ! ! A is persymmetric: A(I,J) = A(N+1-J,N+1-I). ! ! A is positive definite. ! ! A is an M matrix. ! ! A is weakly diagonally dominant, but not strictly diagonally dominant. ! ! A has an LU factorization A = L * U, without pivoting. ! ! The matrix L is lower bidiagonal with subdiagonal elements: ! ! L(I+1,I) = -I/(I+1) ! ! The matrix U is upper bidiagonal, with diagonal elements ! ! U(I,I) = (I+1)/I ! ! and superdiagonal elements which are all -1. ! ! A has a Cholesky factorization A = L * L', with L lower bidiagonal. ! ! L(I,I) = sqrt ( (I+1) / I ) ! L(I,I-1) = -sqrt ( (I-1) / I ) ! ! The eigenvalues are ! ! LAMBDA(I) = 2 + 2 * COS(I*PI/(N+1)) ! = 4 SIN^2(I*PI/(2*N+2)) ! ! The corresponding eigenvector X(I) has entries ! ! X(I)(J) = sqrt(2/(N+1)) * sin ( I*J*PI/(N+1) ). ! ! Simple linear systems: ! ! x = (1,1,1,...,1,1), A*x=(1,0,0,...,0,1) ! ! x = (1,2,3,...,n-1,n), A*x=(0,0,0,...,0,n+1) ! ! det ( A ) = N + 1. ! ! The value of the determinant can be seen by induction, ! and expanding the determinant across the first row: ! ! det ( A(N) ) = 2 * det ( A(N-1) ) - (-1) * (-1) * det ( A(N-2) ) ! = 2 * N - (N-1) ! = N + 1 ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 05 June 2016 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Robert Gregory, David Karney, ! A Collection of Matrices for Testing Computational Algorithms, ! Wiley, 1969, ! ISBN: 0882756494, ! LC: QA263.68 ! ! Morris Newman, John Todd, ! Example A8, ! The evaluation of matrix inversion programs, ! Journal of the Society for Industrial and Applied Mathematics, ! Volume 6, Number 4, pages 466-476, 1958. ! ! John Todd, ! Basic Numerical Mathematics, ! Volume 2: Numerical Algebra, ! Birkhauser, 1980, ! ISBN: 0817608117, ! LC: QA297.T58. ! ! Joan Westlake, ! A Handbook of Numerical Matrix Inversion and Solution of ! Linear Equations, ! John Wiley, 1968, ! ISBN13: 978-0471936756, ! LC: QA263.W47. ! ! Parameters: ! ! Input, integer N, the number of rows and columns. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Output, real ( kind = rk ) A(ML+1,N), the matrix. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) a(1:ml+1,1:n) = 0.0D+00 a(1,1:n) = +2.0D+00 a(2,1:n-1) = -1.0D+00 return end subroutine r8pbl_indicator ( n, ml, a ) !*****************************************************************************80 ! !! R8PBL_INDICATOR sets up an R8PBL indicator matrix. ! ! Discussion: ! ! The "indicator matrix" simply has a value like I*10+J at every ! entry of a dense matrix, or at every entry of a compressed storage ! matrix for which storage is allocated. ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 13 January 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Output, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) integer fac integer i integer i4_log_10 integer j fac = 10 ** ( i4_log_10 ( n ) + 1 ) ! ! Zero out the "junk" entries. ! do j = n + 1 - ml, n do i = n + 1, j + ml a(i-j+1,j) = 0.0D+00 end do end do ! ! Set the meaningful values. ! do i = 1, n do j = max ( 1, i - ml ), i a(i-j+1,j) = real ( fac * i + j, kind = rk ) end do end do return end subroutine r8pbl_mv ( n, ml, a, x, b ) !*****************************************************************************80 ! !! R8PBL_MV multiplies an R8PBL matrix by an R8VEC. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 01 July 2016 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Input, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! ! Input, real ( kind = rk ) X(N), the vector to be multiplied by A. ! ! Output, real ( kind = rk ) B(N), the result vector A * x. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) real ( kind = rk ) aij real ( kind = rk ) b(n) integer i integer j integer k real ( kind = rk ) x(n) ! ! Multiply X by the diagonal of the matrix. ! b(1:n) = a(1,1:n) * x(1:n) ! ! Multiply X by the subdiagonals of the matrix. ! do k = 1, ml do j = 1, n - k i = j + k aij = a(k+1,j) b(i) = b(i) + aij * x(j) b(j) = b(j) + aij * x(i) end do end do return end subroutine r8pbl_print ( n, ml, a, title ) !*****************************************************************************80 ! !! R8PBL_PRINT prints an R8PBL matrix. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 03 May 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Input, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) character ( len = * ) title call r8pbl_print_some ( n, ml, a, 1, 1, n, n, title ) return end subroutine r8pbl_print_some ( n, ml, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! R8PBL_PRINT_SOME prints some of an R8PBL matrix. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 03 May 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Input, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! ! Input, integer ILO, JLO, IHI, JHI, the first row and ! column, and the last row and column to be printed. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: incx = 5 integer ml integer n real ( kind = rk ) a(ml+1,n) real ( kind = rk ) aij character ( len = 14 ) ctemp(incx) integer i integer i2hi integer i2lo integer ihi integer ilo integer inc integer j integer j2 integer j2hi integer j2lo integer jhi integer jlo character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) ! ! Print the columns of the matrix, in strips of 5. ! do j2lo = jlo, jhi, incx j2hi = j2lo + incx - 1 j2hi = min ( j2hi, n ) j2hi = min ( j2hi, jhi ) inc = j2hi + 1 - j2lo write ( *, '(a)' ) ' ' do j = j2lo, j2hi j2 = j + 1 - j2lo write ( ctemp(j2), '(i7,7x)' ) j end do write ( *, '(a,5a14)' ) ' Col: ', ( ctemp(j2), j2 = 1, inc ) write ( *, '(a)' ) ' Row' write ( *, '(a)' ) ' ---' ! ! Determine the range of the rows in this strip. ! i2lo = max ( ilo, 1 ) i2lo = max ( i2lo, j2lo - ml ) i2hi = min ( ihi, n ) i2hi = min ( i2hi, j2hi + ml ) do i = i2lo, i2hi ! ! Print out (up to) 5 entries in row I, that lie in the current strip. ! do j2 = 1, inc j = j2lo - 1 + j2 if ( i <= j .and. j <= i + ml ) then aij = a(j-i+1,i) else if ( j <= i .and. i <= j + ml ) then aij = a(i-j+1,j) else aij = 0.0D+00 end if if ( ml < i - j .or. ml < j - i ) then ctemp(j2) = ' ' else write ( ctemp(j2), '(g14.6)' ) aij end if end do write ( *, '(i5,1x,5a14)' ) i, ( ctemp(j2), j2 = 1, inc ) end do end do return end subroutine r8pbl_random ( n, ml, seed, a ) !*****************************************************************************80 ! !! R8PBL_RANDOM randomizes an R8PBL matrix. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! The matrix returned will be positive definite, but of limited ! randomness. The off diagonal elements are random values between ! 0 and 1, and the diagonal element of each row is selected to ! ensure strict diagonal dominance. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 October 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Input/output, integer SEED, a seed for the random number ! generator. ! ! Output, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) real ( kind = rk ) r8_uniform_01 integer i integer j integer jhi integer jlo real ( kind = rk ) r integer seed real ( kind = rk ) sum2 ! ! Zero out the "junk" entries. ! do j = n + 1 - ml, n a(2+n-j:ml+1,j) = 0.0D+00 end do ! ! Set the off diagonal values. ! do i = 1, n do j = max ( 1, i - ml ), i - 1 a(i-j+1,j) = r8_uniform_01 ( seed ) end do end do ! ! Set the diagonal values. ! do i = 1, n sum2 = 0.0D+00 jlo = max ( 1, i - ml ) do j = jlo, i - 1 sum2 = sum2 + abs ( a(i-j+1,j) ) end do jhi = min ( i + ml, n ) do j = i + 1, jhi sum2 = sum2 + abs ( a(j-i+1,i) ) end do r = r8_uniform_01 ( seed ) a(1,i) = ( 1.0D+00 + r ) * ( sum2 + 0.01D+00 ) end do return end subroutine r8pbl_to_r8ge ( n, ml, a, b ) !*****************************************************************************80 ! !! R8PBL_TO_R8GE copies an R8PBL matrix to an R8GE matrix. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! The R8GE storage format is used for a general M by N matrix. A storage ! space is made for each entry. The two dimensional logical ! array can be thought of as a vector of M*N entries, starting with ! the M entries in the column 1, then the M entries in column 2 ! and so on. Considered as a vector, the entry A(I,J) is then stored ! in vector location I+(J-1)*M. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 September 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrices. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Input, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! ! Output, real ( kind = rk ) B(N,N), the R8GE matrix. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) real ( kind = rk ) b(n,n) integer i integer j do i = 1, n do j = 1, n if ( i <= j .and. j <= i + ml ) then b(i,j) = a(j-i+1,i) else if ( i - ml <= j .and. j < i ) then b(i,j) = a(i-j+1,j) else b(i,j) = 0.0D+00 end if end do end do return end subroutine r8pbl_zeros ( n, ml, a ) !*****************************************************************************80 ! !! R8PBL_ZEROS zeroes an R8PBL matrix. ! ! Discussion: ! ! The R8PBL storage format is for a symmetric positive definite band matrix. ! ! To save storage, only the diagonal and lower triangle of A is stored, ! in a compact diagonal format that preserves columns. ! ! The diagonal is stored in row 1 of the array. ! The first subdiagonal in row 2, columns 1 through ML. ! The second subdiagonal in row 3, columns 1 through ML-1. ! The ML-th subdiagonal in row ML+1, columns 1 through 1. ! ! The matrix returned will be positive definite, but of limited ! randomness. The off diagonal elements are random values between ! 0 and 1, and the diagonal element of each row is selected to ! ensure strict diagonal dominance. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 26 January 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the order of the matrix. ! ! Input, integer ML, the number of subdiagonals in the matrix. ! ML must be at least 0 and no more than N-1. ! ! Output, real ( kind = rk ) A(ML+1,N), the R8PBL matrix. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer ml integer n real ( kind = rk ) a(ml+1,n) a(1:ml+1,1:n) = 0.0D+00 return end subroutine r8vec_indicator1 ( n, a ) !*****************************************************************************80 ! !! R8VEC_INDICATOR1 sets an R8VEC to the indicator1 vector. ! ! Discussion: ! ! A(1:N) = (/ 1 : N /) ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 06 September 2006 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the number of elements of A. ! ! Output, real ( kind = rk ) A(N), the array to be initialized. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) integer i do i = 1, n a(i) = real ( i, kind = rk ) end do return end subroutine r8vec_print ( n, a, title ) !*****************************************************************************80 ! !! R8VEC_PRINT prints an R8VEC. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 16 December 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer N, the number of components of the vector. ! ! Input, real ( kind = rk ) A(N), the vector to be printed. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a(n) integer i character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) write ( *, '(a)' ) ' ' do i = 1, n write ( *, '(i8,g14.6)' ) i, a(i) end do return end