program main !*****************************************************************************80 ! !! MAIN is the main program for TET_MESH_QUAD. ! ! Discussion: ! ! TET_MESH_QUAD estimates the integral of a scalar or vector function ! over a region defined by a tetrahedral mesh, using only the values of ! the function at the nodes of the tet mesh. ! ! Usage: ! ! tet_mesh_quad prefix ! ! where ! ! * 'prefix'_nodes.txt contains the node coordinates; ! * 'prefix'_elements.txt contains the element definitions. ! * 'prefix'_values.txt contains the function component values at each node. ! ! The program will compute and print the values of QUAD. ! QUAD will be a scalar or vector of numbers, containing the estimates ! for the integral of each component of the function over the tet mesh. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 20 December 2012 ! ! Author: ! ! John Burkardt ! ! Local: ! ! Local, integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM), ! lists the nodes that make up each element. ! ! Local, integer ELEMENT_NUM, the number of elements. ! ! Local, integer ELEMENT_ORDER, the order of the elements, ! either 4 or 10. ! ! Local, integer NODE_DIM, the spatial dimension. ! ! Local, integer NODE_NUM, the number of nodes. ! ! Local, real ( kind = rk ) NODE_XYZ(DIM_NUM,NODE_NUM), the point set. ! ! Local, real ( kind = rk ) VALUE(VALUE_DIM,VALUE_NUM), the VALUE_DIM ! components of a vector function evaluated at each of the NODE_NUM nodes. ! ! Local, integer VALUE_DIM, the number of components of the ! function. ! ! Local, integer VALUE_NUM, the number of points at which ! function values were supplied. This must be equal to NODE_NUM. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer arg_num character ( len = 255 ) element_filename integer, allocatable :: element_node(:,:) integer element_num integer element_order integer iarg integer iargc integer node_dim character ( len = 255 ) node_filename integer node_num real ( kind = rk ), allocatable :: node_xyz(:,:) character ( len = 255 ) prefix real ( kind = rk ), allocatable :: quad(:) integer value_dim character ( len = 255 ) value_filename integer value_num real ( kind = rk ), allocatable :: value(:,:) real ( kind = rk ), allocatable :: volume(:) write ( *, '(a)' ) ' ' call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD:' write ( *, '(a)' ) ' FORTRAN90 version:' write ( *, '(a)' ) & ' Estimate an integral over a region defined by a tetrahedral mesh.' ! ! Get the number of command line arguments. ! arg_num = iargc ( ) ! ! Argument 1 is the common filename prefix. ! if ( 1 <= arg_num ) then iarg = 1 call getarg ( iarg, prefix ) else write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD:' write ( *, '(a)' ) ' Please enter the filename prefix.' read ( *, '(a)' ) prefix end if ! ! Create the filenames. ! node_filename = trim ( prefix ) // '_nodes.txt' element_filename = trim ( prefix ) // '_elements.txt' value_filename = trim ( prefix ) // '_values.txt' ! ! Read the node data. ! call r8mat_header_read ( node_filename, node_dim, node_num ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the header of "' & // trim ( node_filename ) //'".' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Spatial dimension NODE_DIM = ', node_dim write ( *, '(a,i8)' ) ' Number of points NODE_NUM = ', node_num if ( node_dim /= 3 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD - Fatal error!' write ( *, '(a)' ) ' Dataset must have spatial dimension 3.' stop end if allocate ( node_xyz(1:node_dim,1:node_num) ) call r8mat_data_read ( node_filename, node_dim, node_num, node_xyz ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the data in "' & // trim ( node_filename ) //'".' call r8mat_transpose_print_some ( node_dim, node_num, node_xyz, 1, 1, & node_dim, 5, ' First 5 nodes:' ) ! ! Read the element data. ! call i4mat_header_read ( element_filename, element_order, & element_num ) if ( element_order /= 4 .and. element_order /= 10 ) then write ( *, * ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD - Fatal error!' write ( *, '(a)' ) ' Data is not for a 4-node or 10-node tet mesh.' stop end if write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the header of "' & // trim ( element_filename ) //'".' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Tetrahedron order = ', element_order write ( *, '(a,i8)' ) ' Number of elements ELEMENT_NUM = ', element_num allocate ( element_node(1:element_order,1:element_num) ) call i4mat_data_read ( element_filename, element_order, & element_num, element_node ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the data in "' & // trim ( element_filename ) //'".' call i4mat_transpose_print_some ( element_order, element_num, & element_node, 1, 1, element_order, 5, ' First 5 tetrahedrons:' ) ! ! Read the value data. ! call r8mat_header_read ( value_filename, value_dim, value_num ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the header of "' & // trim ( value_filename ) //'".' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Value dimension VALUE_DIM = ', value_dim write ( *, '(a,i8)' ) ' Number of values VALUE_NUM = ', value_num if ( value_num /= node_num ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD - Fatal error!' write ( *, '(a)' ) ' Number of values must equal number of nodes.' stop end if allocate ( value(1:value_dim,1:value_num) ) call r8mat_data_read ( value_filename, value_dim, value_num, value ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the data in "' & // trim ( value_filename ) //'".' call r8mat_transpose_print_some ( value_dim, value_num, value, 1, 1, & value_dim, 5, ' First 5 values:' ) ! ! Detect and correct 0-based indexing. ! call mesh_base_one ( node_num, element_order, element_num, element_node ) ! ! Compute the tetrahedron volumes. ! allocate ( volume(1:element_num) ) volume(1:element_num) = ( 1.0D+00 / 6.0D+00 ) * abs ( & ( node_xyz(1,element_node(2,1:element_num)) & - node_xyz(1,element_node(1,1:element_num)) ) & * ( ( node_xyz(2,element_node(3,1:element_num)) & - node_xyz(2,element_node(1,1:element_num)) ) & * ( node_xyz(3,element_node(4,1:element_num)) & - node_xyz(3,element_node(1,1:element_num)) ) & - ( node_xyz(3,element_node(3,1:element_num)) & - node_xyz(3,element_node(1,1:element_num)) ) & * ( node_xyz(2,element_node(4,1:element_num)) & - node_xyz(2,element_node(1,1:element_num)) ) ) & + ( node_xyz(2,element_node(2,1:element_num)) & - node_xyz(2,element_node(1,1:element_num)) ) & * ( ( node_xyz(3,element_node(3,1:element_num)) & - node_xyz(3,element_node(1,1:element_num)) ) & * ( node_xyz(1,element_node(4,1:element_num)) & - node_xyz(1,element_node(1,1:element_num)) ) & - ( node_xyz(1,element_node(3,1:element_num)) & - node_xyz(1,element_node(1,1:element_num)) ) & * ( node_xyz(3,element_node(4,1:element_num)) & - node_xyz(3,element_node(1,1:element_num)) ) ) & + ( node_xyz(3,element_node(2,1:element_num)) & - node_xyz(3,element_node(1,1:element_num)) ) & * ( ( node_xyz(1,element_node(3,1:element_num)) & - node_xyz(1,element_node(1,1:element_num)) ) & * ( node_xyz(2,element_node(4,1:element_num)) & - node_xyz(2,element_node(1,1:element_num)) ) & - ( node_xyz(2,element_node(3,1:element_num)) & - node_xyz(2,element_node(1,1:element_num)) ) & * ( node_xyz(1,element_node(4,1:element_num)) & - node_xyz(1,element_node(1,1:element_num)) ) ) ) ! ! Compute the integral estimate. ! allocate ( quad(1:value_dim) ) quad(1:value_dim) = matmul ( & ( value(1:value_dim,element_node(1,1:element_num)) & + value(1:value_dim,element_node(2,1:element_num)) & + value(1:value_dim,element_node(3,1:element_num)) & + value(1:value_dim,element_node(4,1:element_num)) ), & volume(1:element_num) ) / 4.0D+00 write ( *, '(a)' ) ' ' write ( *, '(a,g14.6)' ) & ' Tetrahedral mesh volume is ', sum ( volume(1:element_num) ) call r8vec_print ( value_dim, quad, ' Integral estimates:' ) ! ! Free memory. ! deallocate ( element_node ) deallocate ( node_xyz ) deallocate ( quad ) deallocate ( value ) deallocate ( volume ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TET_MESH_QUAD:' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop end subroutine ch_cap ( c ) !*****************************************************************************80 ! !! CH_CAP capitalizes a single character. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 July 1998 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character C, the character to capitalize. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character c integer itemp itemp = ichar ( c ) if ( 97 <= itemp .and. itemp <= 122 ) then c = char ( itemp - 32 ) end if return end function ch_eqi ( c1, c2 ) !*****************************************************************************80 ! !! CH_EQI is a case insensitive comparison of two characters for equality. ! ! Example: ! ! CH_EQI ( 'A', 'a' ) is .TRUE. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 July 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C1, C2, the characters to compare. ! ! Output, logical CH_EQI, the result of the comparison. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) logical ch_eqi character c1 character c1_cap character c2 character c2_cap c1_cap = c1 c2_cap = c2 call ch_cap ( c1_cap ) call ch_cap ( c2_cap ) if ( c1_cap == c2_cap ) then ch_eqi = .true. else ch_eqi = .false. end if return end subroutine ch_to_digit ( c, digit ) !*****************************************************************************80 ! !! CH_TO_DIGIT returns the integer value of a base 10 digit. ! ! Example: ! ! C DIGIT ! --- ----- ! '0' 0 ! '1' 1 ! ... ... ! '9' 9 ! ' ' 0 ! 'X' -1 ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 04 August 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C, the decimal digit, '0' through '9' or blank ! are legal. ! ! Output, integer DIGIT, the corresponding integer value. ! If C was 'illegal', then DIGIT is -1. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character c integer digit if ( lge ( c, '0' ) .and. lle ( c, '9' ) ) then digit = ichar ( c ) - 48 else if ( c == ' ' ) then digit = 0 else digit = -1 end if return end subroutine file_column_count ( input_filename, column_num ) !*****************************************************************************80 ! !! FILE_COLUMN_COUNT counts the number of columns in the first line of a file. ! ! Discussion: ! ! The file is assumed to be a simple text file. ! ! Most lines of the file is presumed to consist of COLUMN_NUM words, ! separated by spaces. There may also be some blank lines, and some ! comment lines, ! which have a "#" in column 1. ! ! The routine tries to find the first non-comment non-blank line and ! counts the number of words in that line. ! ! If all lines are blanks or comments, it goes back and tries to analyze ! a comment line. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 June 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the file. ! ! Output, integer COLUMN_NUM, the number of columns in the file. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer column_num logical got_one character ( len = * ) input_filename integer input_status integer input_unit character ( len = 255 ) line ! ! Open the file. ! call get_unit ( input_unit ) open ( unit = input_unit, file = input_filename, status = 'old', & form = 'formatted', access = 'sequential', iostat = input_status ) if ( input_status /= 0 ) then column_num = -1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_COLUMN_COUNT - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' & // trim ( input_filename ) // '" on unit ', input_unit return end if ! ! Read one line, but skip blank lines and comment lines. ! got_one = .false. do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then exit end if if ( len_trim ( line ) == 0 ) then cycle end if if ( line(1:1) == '#' ) then cycle end if got_one = .true. exit end do if ( .not. got_one ) then rewind ( input_unit ) do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then exit end if if ( len_trim ( line ) == 0 ) then cycle end if got_one = .true. exit end do end if close ( unit = input_unit ) if ( .not. got_one ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_COLUMN_COUNT - Warning!' write ( *, '(a)' ) ' The file does not seem to contain any data.' column_num = -1 return end if call s_word_count ( line, column_num ) return end subroutine file_row_count ( input_filename, row_num ) !*****************************************************************************80 ! !! FILE_ROW_COUNT counts the number of row records in a file. ! ! Discussion: ! ! It does not count lines that are blank, or that begin with a ! comment symbol '#'. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 06 March 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer ROW_NUM, the number of rows found. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer bad_num integer comment_num integer ierror character ( len = * ) input_filename integer input_status integer input_unit character ( len = 255 ) line integer record_num integer row_num call get_unit ( input_unit ) open ( unit = input_unit, file = input_filename, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then row_num = -1; ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_ROW_COUNT - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_filename ) // '" on unit ', input_unit stop end if comment_num = 0 row_num = 0 record_num = 0 bad_num = 0 do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then ierror = record_num exit end if record_num = record_num + 1 if ( line(1:1) == '#' ) then comment_num = comment_num + 1 cycle end if if ( len_trim ( line ) == 0 ) then comment_num = comment_num + 1 cycle end if row_num = row_num + 1 end do close ( unit = input_unit ) return end subroutine get_unit ( iunit ) !*****************************************************************************80 ! !! GET_UNIT returns a free FORTRAN unit number. ! ! Discussion: ! ! A "free" FORTRAN unit number is a value between 1 and 99 which ! is not currently associated with an I/O device. A free FORTRAN unit ! number is needed in order to open a file with the OPEN command. ! ! If IUNIT = 0, then no free FORTRAN unit could be found, although ! all 99 units were checked (except for units 5, 6 and 9, which ! are commonly reserved for console I/O). ! ! Otherwise, IUNIT is a value between 1 and 99, representing a ! free FORTRAN unit. Note that GET_UNIT assumes that units 5 and 6 ! are special, and will never return those values. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 26 October 2008 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer IUNIT, the free unit number. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer i integer ios integer iunit logical lopen iunit = 0 do i = 1, 99 if ( i /= 5 .and. i /= 6 .and. i /= 9 ) then inquire ( unit = i, opened = lopen, iostat = ios ) if ( ios == 0 ) then if ( .not. lopen ) then iunit = i return end if end if end if end do return end subroutine i4mat_data_read ( input_filename, m, n, table ) !*****************************************************************************80 ! !! I4MAT_DATA_READ reads data from an I4MAT file. ! ! Discussion: ! ! The file may contain more than N points, but this routine ! will return after reading N points. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 27 January 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Input, integer M, the spatial dimension. ! ! Input, integer N, the number of points. ! ! Output, integer TABLE(M,N), the table data. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer ierror character ( len = * ) input_filename integer input_status integer input_unit integer j character ( len = 255 ) line integer table(m,n) integer x(m) ierror = 0 call get_unit ( input_unit ) open ( unit = input_unit, file = input_filename, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_DATA_READ - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_filename ) // '" on unit ', input_unit stop end if j = 0 do while ( j < n ) read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then ierror = 2 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_DATA_READ - Fatal error!' write ( *, '(a)' ) ' Error while reading lines of data.' write ( *, '(a,i8)' ) ' Number of values expected per line M = ', m write ( *, '(a,i8)' ) ' Number of data lines read, J = ', j write ( *, '(a,i8)' ) ' Number of data lines needed, N = ', n stop end if if ( line(1:1) == '#' .or. len_trim ( line ) == 0 ) then cycle end if call s_to_i4vec ( line, m, x, ierror ) if ( ierror /= 0 ) then cycle end if j = j + 1 table(1:m,j) = x(1:m) end do close ( unit = input_unit ) return end subroutine i4mat_header_read ( input_filename, m, n ) !*****************************************************************************80 ! !! I4MAT_HEADER_READ reads the header from an I4MAT. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 04 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer M, spatial dimension. ! ! Output, integer N, the number of points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character ( len = * ) input_filename integer m integer n call file_column_count ( input_filename, m ) if ( m <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data columns in' write ( *, '(a)' ) ' the file "' // trim ( input_filename ) // '".' stop end if call file_row_count ( input_filename, n ) if ( n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data rows in' write ( *, '(a)' ) ' the file "' // trim ( input_filename ) // '".' stop end if return end subroutine i4mat_transpose_print ( m, n, a, title ) !*****************************************************************************80 ! !! I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed. ! ! Discussion: ! ! An I4MAT is a rectangular array of I4 values. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 December 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, integer A(M,N), an M by N matrix to be printed. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer a(m,n) character ( len = * ) title call i4mat_transpose_print_some ( m, n, a, 1, 1, m, n, title ) return end subroutine i4mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT. ! ! Discussion: ! ! An I4MAT is a rectangular array of I4 values. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 10 September 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, integer A(M,N), an M by N matrix to be printed. ! ! Input, integer ILO, JLO, the first row and column to print. ! ! Input, integer IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, a title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: incx = 10 integer m integer n integer a(m,n) character ( len = 8 ) ctemp(incx) integer i integer i2 integer i2hi integer i2lo integer ihi integer ilo integer inc integer j integer j2hi integer j2lo integer jhi integer jlo character ( len = * ) title write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) do i2lo = max ( ilo, 1 ), min ( ihi, m ), incx i2hi = i2lo + incx - 1 i2hi = min ( i2hi, m ) i2hi = min ( i2hi, ihi ) inc = i2hi + 1 - i2lo write ( *, '(a)' ) ' ' do i = i2lo, i2hi i2 = i + 1 - i2lo write ( ctemp(i2), '(i8)' ) i end do write ( *, '('' Row '',10a8)' ) ctemp(1:inc) write ( *, '(a)' ) ' Col' write ( *, '(a)' ) ' ' j2lo = max ( jlo, 1 ) j2hi = min ( jhi, n ) do j = j2lo, j2hi do i2 = 1, inc i = i2lo - 1 + i2 write ( ctemp(i2), '(i8)' ) a(i,j) end do write ( *, '(i5,1x,10a8)' ) j, ( ctemp(i), i = 1, inc ) end do end do return end subroutine mesh_base_one ( node_num, element_order, element_num, element_node ) !*****************************************************************************80 ! !! MESH_BASE_ONE ensures that the element definition is one-based. ! ! Discussion: ! ! The ELEMENT_NODE array contains nodes indices that form elements. ! The convention for node indexing might start at 0 or at 1. ! Since a FORTRAN90 program will naturally assume a 1-based indexing, it is ! necessary to check a given element definition and, if it is actually ! 0-based, to convert it. ! ! This function attempts to detect 9-based node indexing and correct it. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 02 October 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, int NODE_NUM, the number of nodes. ! ! Input, int ELEMENT_ORDER, the order of the elements. ! ! Input, int ELEMENT_NUM, the number of elements. ! ! Input/output, int ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM), the element ! definitions. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer element_num integer element_order integer element_node(element_order,element_num) integer node_max integer node_min integer node_num node_min = node_num + 1 node_max = -1 node_min = minval ( element_node(1:element_order,1:element_num) ) node_max = maxval ( element_node(1:element_order,1:element_num) ) if ( node_min == 0 .and. node_max == node_num - 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' )'MESH_BASE_ONE:' write ( *, '(a)' )' The element indexing appears to be 0-based!' write ( *, '(a)' )' This will be converted to 1-based.' element_node(1:element_order,1:element_num) = & element_node(1:element_order,1:element_num) + 1 else if ( node_min == 1 .and. node_max == node_num ) then write ( *, '(a)' ) ' ' write ( *, '(a)' )'MESH_BASE_ONE:' write ( *, '(a)' )' The element indexing appears to be 1-based!' write ( *, '(a)' )' No conversion is necessary.' else write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'MESH_BASE_ONE - Warning!' write ( *, '(a)' ) ' The element indexing is not of a recognized type.' write ( *, '(a,i8)' ) ' NODE_MIN = ', node_min write ( *, '(a,i8)' ) ' NODE_MAX = ', node_max write ( *, '(a,i8)' ) ' NODE_NUM = ', node_num end if return end subroutine r8mat_data_read ( input_filename, m, n, table ) !*****************************************************************************80 ! !! R8MAT_DATA_READ reads data from an R8MAT file. ! ! Discussion: ! ! The file may contain more than N points, but this routine will ! return after reading N of them. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 October 2008 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Input, integer M, the spatial dimension. ! ! Input, integer N, the number of points. ! ! Output, real ( kind = rk ) TABLE(M,N), the table data. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer ierror character ( len = * ) input_filename integer input_status integer input_unit integer j character ( len = 255 ) line real ( kind = rk ) table(m,n) real ( kind = rk ) x(m) ierror = 0 call get_unit ( input_unit ) open ( unit = input_unit, file = input_filename, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_DATA_READ - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_filename ) // '" on unit ', input_unit stop end if j = 0 do while ( j < n ) read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_DATA_READ - Fatal error!' write ( *, '(a)' ) ' Error while reading lines of data.' write ( *, '(a,i8)' ) ' Number of values expected per line M = ', m write ( *, '(a,i8)' ) ' Number of data lines read, J = ', j write ( *, '(a,i8)' ) ' Number of data lines needed, N = ', n stop end if if ( line(1:1) == '#' .or. len_trim ( line ) == 0 ) then cycle end if call s_to_r8vec ( line, m, x, ierror ) if ( ierror /= 0 ) then cycle end if j = j + 1 table(1:m,j) = x(1:m) end do close ( unit = input_unit ) return end subroutine r8mat_header_read ( input_filename, m, n ) !*****************************************************************************80 ! !! R8MAT_HEADER_READ reads the header from an R8MAT file. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer M, spatial dimension. ! ! Output, integer N, the number of points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character ( len = * ) input_filename integer m integer n call file_column_count ( input_filename, m ) if ( m <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data columns in' write ( *, '(a)' ) ' the file "' // trim ( input_filename ) // '".' stop end if call file_row_count ( input_filename, n ) if ( n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data rows in' write ( *, '(a)' ) ' the file "' // trim ( input_filename ) // '".' stop end if return end subroutine r8mat_transpose_print ( m, n, a, title ) !*****************************************************************************80 ! !! R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, real ( kind = rk ) A(M,N), an M by N matrix to be printed. ! ! Input, character ( len = * ) TITLE, an optional title. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n real ( kind = rk ) a(m,n) character ( len = * ) title call r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title ) return end subroutine r8mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT transposed. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, N, the number of rows and columns. ! ! Input, real ( kind = rk ) A(M,N), an M by N matrix to be printed. ! ! Input, integer ILO, JLO, the first row and column to print. ! ! Input, integer IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, an optional 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 i2 integer i2hi integer i2lo integer ihi integer ilo integer inc integer j integer j2hi integer j2lo integer jhi integer jlo character ( len = * ) title if ( 0 < len_trim ( title ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) trim ( title ) end if do i2lo = max ( ilo, 1 ), min ( ihi, m ), incx i2hi = i2lo + incx - 1 i2hi = min ( i2hi, m ) i2hi = min ( i2hi, ihi ) inc = i2hi + 1 - i2lo write ( *, '(a)' ) ' ' do i = i2lo, i2hi i2 = i + 1 - i2lo write ( ctemp(i2), '(i8,6x)') i end do write ( *, '('' Row'',5a14)' ) ctemp(1:inc) write ( *, '(a)' ) ' Col' j2lo = max ( jlo, 1 ) j2hi = min ( jhi, n ) do j = j2lo, j2hi do i2 = 1, inc i = i2lo - 1 + i2 write ( ctemp(i2), '(g14.6)' ) a(i,j) end do write ( *, '(2x,i8,5a14)' ) j, ( ctemp(i), i = 1, inc ) end do end do return end subroutine r8vec_print ( n, a, title ) !*****************************************************************************80 ! !! R8VEC_PRINT prints an R8VEC. ! ! Discussion: ! ! An R8VEC is a vector of R8's. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 22 August 2000 ! ! 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 ( *, '(2x,i8,2x,g16.8)' ) i, a(i) end do return end subroutine s_to_i4 ( s, ival, ierror, length ) !*****************************************************************************80 ! !! S_TO_I4 reads an I4 from a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 28 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, a string to be examined. ! ! Output, integer IVAL, the integer value read from the string. ! If the string is blank, then IVAL will be returned 0. ! ! Output, integer IERROR, an error flag. ! 0, no error. ! 1, an error occurred. ! ! Output, integer LENGTH, the number of characters of S ! used to make IVAL. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character c integer i integer ierror integer isgn integer istate integer ival integer length character ( len = * ) s ierror = 0 istate = 0 isgn = 1 ival = 0 do i = 1, len_trim ( s ) c = s(i:i) ! ! Haven't read anything. ! if ( istate == 0 ) then if ( c == ' ' ) then else if ( c == '-' ) then istate = 1 isgn = -1 else if ( c == '+' ) then istate = 1 isgn = + 1 else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read the sign, expecting digits. ! else if ( istate == 1 ) then if ( c == ' ' ) then else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read at least one digit, expecting more. ! else if ( istate == 2 ) then if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then ival = 10 * ival + ichar ( c ) - ichar ( '0' ) else ival = isgn * ival length = i - 1 return end if end if end do ! ! If we read all the characters in the string, see if we're OK. ! if ( istate == 2 ) then ival = isgn * ival length = len_trim ( s ) else ierror = 1 length = 0 end if return end subroutine s_to_i4vec ( s, n, ivec, ierror ) !*****************************************************************************80 ! !! S_TO_I4VEC reads an I4VEC from a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 08 October 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer N, the number of values expected. ! ! Output, integer IVEC(N), the values read from the string. ! ! Output, integer IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n integer i integer ierror integer ilo integer ivec(n) integer length character ( len = * ) s i = 0 ierror = 0 ilo = 1 do while ( i < n ) i = i + 1 call s_to_i4 ( s(ilo:), ivec(i), ierror, length ) if ( ierror /= 0 ) then ierror = -i exit end if ilo = ilo + length end do return end subroutine s_to_r8 ( s, dval, ierror, length ) !*****************************************************************************80 ! !! S_TO_R8 reads an R8 from a string. ! ! Discussion: ! ! The routine will read as many characters as possible until it reaches ! the end of the string, or encounters a character which cannot be ! part of the number. ! ! Legal input is: ! ! 1 blanks, ! 2 '+' or '-' sign, ! 2.5 blanks ! 3 integer part, ! 4 decimal point, ! 5 fraction part, ! 6 'E' or 'e' or 'D' or 'd', exponent marker, ! 7 exponent sign, ! 8 exponent integer part, ! 9 exponent decimal point, ! 10 exponent fraction part, ! 11 blanks, ! 12 final comma or semicolon, ! ! with most quantities optional. ! ! Example: ! ! S DVAL ! ! '1' 1.0 ! ' 1 ' 1.0 ! '1A' 1.0 ! '12,34,56' 12.0 ! ' 34 7' 34.0 ! '-1E2ABCD' -100.0 ! '-1X2ABCD' -1.0 ! ' 2E-1' 0.2 ! '23.45' 23.45 ! '-4.2E+2' -420.0 ! '17d2' 1700.0 ! '-14e-2' -0.14 ! 'e2' 100.0 ! '-12.73e-9.23' -12.73 * 10.0^(-9.23) ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string containing the ! data to be read. Reading will begin at position 1 and ! terminate at the end of the string, or when no more ! characters can be read to form a legal real. Blanks, ! commas, or other nonnumeric data will, in particular, ! cause the conversion to halt. ! ! Output, real ( kind = rk ) DVAL, the value read from the string. ! ! Output, integer IERROR, error flag. ! 0, no errors occurred. ! 1, 2, 6 or 7, the input number was garbled. The ! value of IERROR is the last type of input successfully ! read. For instance, 1 means initial blanks, 2 means ! a plus or minus sign, and so on. ! ! Output, integer LENGTH, the number of characters read ! to form the number, including any terminating ! characters such as a trailing comma or blanks. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character c logical ch_eqi real ( kind = rk ) dval integer ierror integer ihave integer isgn integer iterm integer jbot integer jsgn integer jtop integer length integer nchar integer ndig real ( kind = rk ) rbot real ( kind = rk ) rexp real ( kind = rk ) rtop character ( len = * ) s nchar = len_trim ( s ) ierror = 0 dval = 0.0D+00 length = -1 isgn = 1 rtop = 0 rbot = 1 jsgn = 1 jtop = 0 jbot = 1 ihave = 1 iterm = 0 do length = length + 1 if ( nchar < length+1 ) then exit end if c = s(length+1:length+1) ! ! Blank character. ! if ( c == ' ' ) then if ( ihave == 2 ) then else if ( ihave == 6 .or. ihave == 7 ) then iterm = 1 else if ( 1 < ihave ) then ihave = 11 end if ! ! Comma. ! else if ( c == ',' .or. c == ';' ) then if ( ihave /= 1 ) then iterm = 1 ihave = 12 length = length + 1 end if ! ! Minus sign. ! else if ( c == '-' ) then if ( ihave == 1 ) then ihave = 2 isgn = -1 else if ( ihave == 6 ) then ihave = 7 jsgn = -1 else iterm = 1 end if ! ! Plus sign. ! else if ( c == '+' ) then if ( ihave == 1 ) then ihave = 2 else if ( ihave == 6 ) then ihave = 7 else iterm = 1 end if ! ! Decimal point. ! else if ( c == '.' ) then if ( ihave < 4 ) then ihave = 4 else if ( 6 <= ihave .and. ihave <= 8 ) then ihave = 9 else iterm = 1 end if ! ! Scientific notation exponent marker. ! else if ( ch_eqi ( c, 'E' ) .or. ch_eqi ( c, 'D' ) ) then if ( ihave < 6 ) then ihave = 6 else iterm = 1 end if ! ! Digit. ! else if ( ihave < 11 .and. lle ( '0', c ) .and. lle ( c, '9' ) ) then if ( ihave <= 2 ) then ihave = 3 else if ( ihave == 4 ) then ihave = 5 else if ( ihave == 6 .or. ihave == 7 ) then ihave = 8 else if ( ihave == 9 ) then ihave = 10 end if call ch_to_digit ( c, ndig ) if ( ihave == 3 ) then rtop = 10.0D+00 * rtop + real ( ndig, kind = rk ) else if ( ihave == 5 ) then rtop = 10.0D+00 * rtop + real ( ndig, kind = rk ) rbot = 10.0D+00 * rbot else if ( ihave == 8 ) then jtop = 10 * jtop + ndig else if ( ihave == 10 ) then jtop = 10 * jtop + ndig jbot = 10 * jbot end if ! ! Anything else is regarded as a terminator. ! else iterm = 1 end if ! ! If we haven't seen a terminator, and we haven't examined the ! entire string, go get the next character. ! if ( iterm == 1 ) then exit end if end do ! ! If we haven't seen a terminator, and we have examined the ! entire string, then we're done, and LENGTH is equal to NCHAR. ! if ( iterm /= 1 .and. length+1 == nchar ) then length = nchar end if ! ! Number seems to have terminated. Have we got a legal number? ! Not if we terminated in states 1, 2, 6 or 7! ! if ( ihave == 1 .or. ihave == 2 .or. ihave == 6 .or. ihave == 7 ) then ierror = ihave write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'S_TO_R8 - Serious error!' write ( *, '(a)' ) ' Illegal or nonnumeric input:' write ( *, '(a)' ) ' ' // trim ( s ) return end if ! ! Number seems OK. Form it. ! if ( jtop == 0 ) then rexp = 1.0D+00 else if ( jbot == 1 ) then rexp = 10.0D+00 ** ( jsgn * jtop ) else rexp = 10.0D+00 ** ( real ( jsgn * jtop, kind = rk ) & / real ( jbot, kind = rk ) ) end if end if dval = real ( isgn, kind = rk ) * rexp * rtop / rbot return end subroutine s_to_r8vec ( s, n, rvec, ierror ) !*****************************************************************************80 ! !! S_TO_R8VEC reads an R8VEC from a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer N, the number of values expected. ! ! Output, real ( kind = rk ) RVEC(N), the values read from the string. ! ! Output, integer IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n integer i integer ierror integer ilo integer lchar real ( kind = rk ) rvec(n) character ( len = * ) s i = 0 ierror = 0 ilo = 1 do while ( i < n ) i = i + 1 call s_to_r8 ( s(ilo:), rvec(i), ierror, lchar ) if ( ierror /= 0 ) then ierror = -i exit end if ilo = ilo + lchar end do return end subroutine s_word_count ( s, nword ) !*****************************************************************************80 ! !! S_WORD_COUNT counts the number of "words" in a string. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 April 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be examined. ! ! Output, integer NWORD, the number of "words" in the string. ! Words are presumed to be separated by one or more blanks. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) logical blank integer i integer lens integer nword character ( len = * ) s nword = 0 lens = len ( s ) if ( lens <= 0 ) then return end if blank = .true. do i = 1, lens if ( s(i:i) == ' ' ) then blank = .true. else if ( blank ) then nword = nword + 1 blank = .false. end if end do return end subroutine timestamp ( ) !*****************************************************************************80 ! !! TIMESTAMP prints the current YMDHMS date as a time stamp. ! ! Example: ! ! 31 May 2001 9:45:54.872 AM ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 May 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character ( len = 8 ) ampm integer d integer h integer m integer mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer n integer s integer values(8) integer y call date_and_time ( values = values ) y = values(1) m = values(2) d = values(3) h = values(5) n = values(6) s = values(7) mm = values(8) if ( h < 12 ) then ampm = 'AM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Noon' else ampm = 'PM' end if else h = h - 12 if ( h < 12 ) then ampm = 'PM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Midnight' else ampm = 'AM' end if end if end if write ( *, '(i2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) & d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm ) return end