program main !*****************************************************************************80 ! !! MAIN is the main program for TRIANGULATION_CORNER. ! ! Discussion: ! ! TRIANGULATION_TRIANGLE_CORNER tries to alter a triangular mesh in ! cases where two sides of a triangle lie on the boundary. ! ! The program reads the node and triangle data, computes the triangle ! neighbor information, and writes it to a file. ! ! Usage: ! ! triangulation_corner prefix ! ! where 'prefix' is the common filename prefix: ! ! * prefix_nodes.txt contains the node coordinates, ! * prefix_elements.txtcontains the element definitions. ! * prefix_corner_nodes.txt will contain the revised node coordinates, ! * prefix_corner_elements.txt will contain the revised element definitions. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 03 October 2009 ! ! Author: ! ! John Burkardt ! implicit none real ( kind = 8 ) area integer ( kind = 4 ) arg_num logical, parameter :: debug = .false. integer ( kind = 4 ) dim_num integer ( kind = 4 ) i integer ( kind = 4 ) i4_wrap integer ( kind = 4 ) iarg integer ( kind = 4 ) iargc character ( len = 255 ) :: node_filename = ' ' character ( len = 255 ) :: element_filename = ' ' integer ( kind = 4 ) j integer ( kind = 4 ) j1 integer ( kind = 4 ) j2 integer ( kind = 4 ) j3 integer ( kind = 4 ) j4 integer ( kind = 4 ) n1_index integer ( kind = 4 ) n2_index integer ( kind = 4 ) n3_index integer ( kind = 4 ) negative integer ( kind = 4 ) negative_total(0:3) integer ( kind = 4 ) neighbor integer ( kind = 4 ) node integer ( kind = 4 ) node_num real ( kind = 8 ), allocatable, dimension ( :, : ) :: node_xy integer ( kind = 4 ) node1 integer ( kind = 4 ) node2 integer ( kind = 4 ) node3 character ( len = 255 ) :: node_corner_filename = ' ' character ( len = 255 ) :: element_corner_filename = ' ' character ( len = 255 ) prefix integer ( kind = 4 ) t1_to_t2 integer ( kind = 4 ) t2_to_t1 real ( kind = 8 ) t3(2,3) integer ( kind = 4 ) triangle integer ( kind = 4 ) triangle1 integer ( kind = 4 ) triangle2 integer ( kind = 4 ), allocatable, dimension ( :, : ) :: triangle_neighbor integer ( kind = 4 ), allocatable, dimension ( :, : ) :: triangle_node integer ( kind = 4 ) triangle_num integer ( kind = 4 ) triangle_order call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' ' write ( *, '(a)' ) & ' Read a node file of NODE_NUM point coordinates in 2 dimensions.' write ( *, '(a)' ) ' Read an associated triangle file of ' write ( *, '(a)' ) ' TRIANGLE_NUM triangles, listing 3 or 6 node indices.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) & ' Any triangle which has exactly two sides on the boundary' write ( *, '(a)' ) ' is a corner triangle.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' If there are any corner triangles this program tries to' write ( *, '(a)' ) ' eliminate them.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The "repaired" triangle file is written out.' ! ! 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)' ) 'TRIANGULATION_CORNER:' 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' node_corner_filename = trim ( prefix ) // '_corner_nodes.txt' element_corner_filename = trim ( prefix ) // '_corner_elements.txt' ! ! Read the node data. ! call r8mat_header_read ( node_filename, dim_num, node_num ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the header of "' & // trim ( node_filename ) //'".' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Spatial dimension DIM_NUM = ', dim_num write ( *, '(a,i8)' ) ' Number of nodes NODE_NUM = ', node_num allocate ( node_xy(1:dim_num,1:node_num) ) call r8mat_data_read ( node_filename, dim_num, node_num, node_xy ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the data in "' & // trim ( node_filename ) //'".' call r8mat_transpose_print_some ( dim_num, node_num, node_xy, 1, 1, & dim_num, 5, ' Coordinates of first 5 nodes:' ) ! ! Read the element data. ! call i4mat_header_read ( element_filename, triangle_order, & triangle_num ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the header of "' & // trim ( element_filename ) //'".' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Triangle order TRIANGLE_ORDER = ', triangle_order write ( *, '(a,i8)' ) ' Number of triangles TRIANGLE_NUM = ', triangle_num if ( triangle_order /= 3 .and. triangle_order /= 6 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER - Fatal error!' write ( *, '(a)' ) ' This program can only handle triangulations' write ( *, '(a)' ) ' of orders 3 and 6.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The input triangulation seems to have' write ( *, '(a,i8)' ) ' order = ', triangle_order stop end if allocate ( triangle_node(1:triangle_order,1:triangle_num) ) call i4mat_data_read ( element_filename, triangle_order, & triangle_num, triangle_node ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Read the data in "' & // trim ( element_filename ) //'".' call i4mat_transpose_print_some ( triangle_order, triangle_num, & triangle_node, 1, 1, triangle_order, 5, ' First 5 triangles:' ) ! ! Detect and correct zero-based indexing. ! call mesh_base_one ( node_num, triangle_order, triangle_num, triangle_node ) ! ! Create the triangle neighbor array. ! allocate ( triangle_neighbor(1:3,1:triangle_num) ) if ( triangle_order == 3 ) then call triangulation_order3_neighbor_triangles ( triangle_num, & triangle_node, triangle_neighbor ) else if ( triangle_order == 6 ) then call triangulation_order6_neighbor_triangles ( triangle_num, & triangle_node, triangle_neighbor ) end if ! ! Examine the triangle neighbor array. ! negative_total(0:3) = 0 do triangle = 1, triangle_num negative = 0 do neighbor = 1, 3 if ( triangle_neighbor(neighbor,triangle) < 0 ) then negative = negative + 1 end if end do negative_total(negative) = negative_total(negative) + 1 end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Number of boundary sides Number of triangles' write ( *, '(a)' ) ' ' do i = 0, 3 write ( *, '(12x,i8,12x,i8)' ) i, negative_total(i) end do ! ! Try to patch problems. For now, assume order 3 triangulation. ! if ( 0 < negative_total(3) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER - Fatal error!' write ( *, '(a)' ) ' There is at least one triangle with all sides' write ( *, '(a)' ) ' on the boundary.' stop else if ( 0 == negative_total(2) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' write ( *, '(a)' ) ' No corner triangles were found.' write ( *, '(a)' ) ' No corrections need to be made.' else ! ! We need the triangles to be oriented properly. ! negative = 0 do triangle = 1, triangle_num t3(1:2,1:3) = node_xy(1:2,triangle_node(1:3,triangle)) call triangle_area_2d ( t3, area ) if ( area < 0.0D+00 ) then negative = negative + 1 node = triangle_node(2,triangle) triangle_node(2,triangle) = triangle_node(3,triangle) triangle_node(3,triangle) = node if ( triangle_order == 6 ) then node = triangle_node(4,triangle) triangle_node(4,triangle) = triangle_node(6,triangle) triangle_node(6,triangle) = node end if neighbor = triangle_neighbor(1,triangle) triangle_neighbor(1,triangle) = triangle_neighbor(3,triangle) triangle_neighbor(3,triangle) = neighbor end if end do if ( 0 < negative ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' write ( *, '(a,i8,a)' ) ' Reoriented ', negative, ' triangles.' write ( *, '(a)' ) ' ' else write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' write ( *, '(a)' ) ' Triangles were already properly oriented.' write ( *, '(a)' ) ' ' end if ! ! Now consider each triangle that has exactly two boundary sides. ! do triangle1 = 1, triangle_num negative = 0 do neighbor = 1, 3 if ( triangle_neighbor(neighbor,triangle1) < 0 ) then negative = negative + 1 end if end do if ( negative == 2 ) then triangle2 = -1 do neighbor = 1, 3 if ( 0 < triangle_neighbor(neighbor,triangle1) ) then triangle2 = triangle_neighbor(neighbor,triangle1) t1_to_t2 = neighbor end if end do write ( *, '(a,i8,a,i8)' ) & ' Adjusting triangle ', triangle1, ' using triangle ', triangle2 t2_to_t1 = -1 do neighbor = 1, 3 if ( triangle_neighbor(neighbor,triangle2) == triangle1 ) then t2_to_t1 = neighbor end if end do if ( debug ) then write ( *, * ) ' ' write ( *, * ) ' Before:' write ( *, * ) ' T1 = ', triangle_node(1:triangle_order,triangle1) write ( *, * ) ' N1 = ', triangle_neighbor(1:3,triangle1) write ( *, * ) ' T2 = ', triangle_node(1:triangle_order,triangle2) write ( *, * ) ' N2 = ', triangle_neighbor(1:3,triangle2) end if n1_index = t1_to_t2 - 1 n1_index = i4_wrap ( n1_index, 1, 3 ) node = triangle_node(n1_index,triangle1) n1_index = t1_to_t2 + 1 n1_index = i4_wrap ( n1_index, 1, 3 ) n2_index = t2_to_t1 - 1 n2_index = i4_wrap ( n2_index, 1, 3 ) triangle_node(n1_index,triangle1) = triangle_node(n2_index,triangle2) n1_index = t1_to_t2 - 1 n1_index = i4_wrap ( n1_index, 1, 3 ) n2_index = t2_to_t1 + 1 n2_index = i4_wrap ( n2_index, 1, 3 ) triangle_node(n2_index,triangle2) = node if ( triangle_order == 6 ) then ! ! Adjust coordinates of the new midside node. ! j1 = t1_to_t2 - 1 j1 = i4_wrap ( j1, 1, 3 ) j2 = t1_to_t2 + 3 j2 = i4_wrap ( j2, 4, 6 ) j3 = t2_to_t1 - 1 j3 = i4_wrap ( j3, 1, 3 ) node1 = triangle_node(j1,triangle1) node2 = triangle_node(j2,triangle1) node3 = triangle_node(j3,triangle2) node_xy(1,node2) = 0.5D+00 * ( node_xy(1,node1) + node_xy(1,node3) ) node_xy(2,node2) = 0.5D+00 * ( node_xy(2,node1) + node_xy(2,node3) ) ! ! Update the triangle array. ! j1 = t1_to_t2 + 4 j1 = i4_wrap ( j1, 4, 6 ) j2 = t1_to_t2 + 3 j2 = i4_wrap ( j2, 4, 6 ) j3 = t2_to_t1 + 4 j3 = i4_wrap ( j3, 4, 6 ) j4 = t2_to_t1 + 3 j4 = i4_wrap ( j4, 4, 6 ) node = triangle_node(j1,triangle1) triangle_node(j1,triangle1) = triangle_node(j2,triangle1) triangle_node(j2,triangle1) = triangle_node(j3,triangle2) triangle_node(j3,triangle2) = triangle_node(j4,triangle2) triangle_node(j4,triangle2) = node end if ! ! Update the neighbor array. ! n2_index = t2_to_t1 + 1 n2_index = i4_wrap ( n2_index, 1, 3 ) triangle = triangle_neighbor(n2_index,triangle2) triangle_neighbor(n2_index,triangle2) = triangle1 triangle_neighbor(t2_to_t1,triangle2) = -1 n1_index = t1_to_t2 + 1 n1_index = i4_wrap ( n1_index, 1, 3 ) triangle_neighbor(n1_index,triangle1) = triangle2 triangle_neighbor(t1_to_t2,triangle1) = triangle if ( debug ) then write ( *, * ) ' ' write ( *, * ) ' After:' write ( *, * ) ' T1 = ', triangle_node(1:triangle_order,triangle1) write ( *, * ) ' N1 = ', triangle_neighbor(1:3,triangle1) write ( *, * ) ' T2 = ', triangle_node(1:triangle_order,triangle2) write ( *, * ) ' N2 = ', triangle_neighbor(1:3,triangle2) write ( *, * ) ' ' end if end if end do ! ! Write out the corrected triangle file. ! call i4mat_write ( element_corner_filename, triangle_order, & triangle_num, triangle_node ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' write ( *, '(a)' ) ' New triangle file with repaired corners written to ' write ( *, '(a)' ) ' "' // trim ( element_corner_filename ) //'".' ! ! Write out the corrected node coordinate file. ! This may only differ from the input node file if the elements are quadratic. ! call r8mat_write ( node_corner_filename, dim_num, node_num, node_xy ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' write ( *, '(a)' ) ' New node coordinate file with adjusted midside nodes' write ( *, '(a)' ) ' written to "' // trim ( node_corner_filename ) //'".' end if ! ! Free memory. ! deallocate ( node_xy ) deallocate ( triangle_neighbor ) deallocate ( triangle_node ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_CORNER:' 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 GNU LGPL license. ! ! Modified: ! ! 19 July 1998 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character C, the character to capitalize. ! implicit none character c integer ( kind = 4 ) 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 GNU LGPL 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 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 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 GNU LGPL license. ! ! Modified: ! ! 04 August 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C, the decimal digit, '0' through '9' or blank ! are legal. ! ! Output, integer ( kind = 4 ) DIGIT, the corresponding value. If C was ! 'illegal', then DIGIT is -1. ! implicit none character c integer ( kind = 4 ) 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 GNU LGPL license. ! ! Modified: ! ! 21 June 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the file. ! ! Output, integer ( kind = 4 ) COLUMN_NUM, the number of columns in the file. ! implicit none integer ( kind = 4 ) column_num logical got_one character ( len = * ) input_filename integer ( kind = 4 ) input_status integer ( kind = 4 ) 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)' ) ' Could not open the file:' write ( *, '(a)' ) ' ' // trim ( input_filename ) 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 GNU LGPL license. ! ! Modified: ! ! 06 March 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer ( kind = 4 ) ROW_NUM, the number of rows found. ! implicit none integer ( kind = 4 ) bad_num integer ( kind = 4 ) comment_num integer ( kind = 4 ) ierror character ( len = * ) input_filename integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit character ( len = 255 ) line integer ( kind = 4 ) record_num integer ( kind = 4 ) 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)' ) ' Could not open the input file: ' // & trim ( input_filename ) 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 GNU LGPL license. ! ! Modified: ! ! 18 September 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer ( kind = 4 ) IUNIT, the free unit number. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ) ios integer ( kind = 4 ) 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 function i4_modp ( i, j ) !*****************************************************************************80 ! !! I4_MODP returns the nonnegative remainder of I4 division. ! ! Discussion: ! ! If ! NREM = I4_MODP ( I, J ) ! NMULT = ( I - NREM ) / J ! then ! I = J * NMULT + NREM ! where NREM is always nonnegative. ! ! The MOD function computes a result with the same sign as the ! quantity being divided. Thus, suppose you had an angle A, ! and you wanted to ensure that it was between 0 and 360. ! Then mod(A,360) would do, if A was positive, but if A ! was negative, your result would be between -360 and 0. ! ! On the other hand, I4_MODP(A,360) is between 0 and 360, always. ! ! An I4 is an integer ( kind = 4 ) value. ! ! Example: ! ! I J MOD I4_MODP Factorization ! ! 107 50 7 7 107 = 2 * 50 + 7 ! 107 -50 7 7 107 = -2 * -50 + 7 ! -107 50 -7 43 -107 = -3 * 50 + 43 ! -107 -50 -7 43 -107 = 3 * -50 + 43 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 02 March 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) I, the number to be divided. ! ! Input, integer ( kind = 4 ) J, the number that divides I. ! ! Output, integer ( kind = 4 ) I4_MODP, the nonnegative remainder when I is ! divided by J. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ) i4_modp integer ( kind = 4 ) j integer ( kind = 4 ) value if ( j == 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4_MODP - Fatal error!' write ( *, '(a,i8)' ) ' Illegal divisor J = ', j stop end if value = mod ( i, j ) if ( value < 0 ) then value = value + abs ( j ) end if i4_modp = value return end function i4_wrap ( ival, ilo, ihi ) !*****************************************************************************80 ! !! I4_WRAP forces an I4 to lie between given limits by wrapping. ! ! Discussion: ! ! An I4 is an integer ( kind = 4 ) value. ! ! There appears to be a bug in the GFORTRAN compiler which can lead to ! erroneous results when the first argument of I4_WRAP is an expression. ! In particular: ! ! do i = 1, 3 ! if ( test ) then ! i4 = i4_wrap ( i + 1, 1, 3 ) ! end if ! end do ! ! was, when I = 3, returning I4 = 3. So I had to replace this with ! ! do i = 1, 3 ! if ( test ) then ! i4 = i + 1 ! i4 = i4_wrap ( i4, 1, 3 ) ! end if ! end do ! ! Example: ! ! ILO = 4, IHI = 8 ! ! I Value ! ! -2 8 ! -1 4 ! 0 5 ! 1 6 ! 2 7 ! 3 8 ! 4 4 ! 5 5 ! 6 6 ! 7 7 ! 8 8 ! 9 4 ! 10 5 ! 11 6 ! 12 7 ! 13 8 ! 14 4 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 19 August 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) IVAL, a value. ! ! Input, integer ( kind = 4 ) ILO, IHI, the desired bounds. ! ! Output, integer ( kind = 4 ) I4_WRAP, a "wrapped" version of the value. ! implicit none integer ( kind = 4 ) i4_modp integer ( kind = 4 ) i4_wrap integer ( kind = 4 ) ihi integer ( kind = 4 ) ilo integer ( kind = 4 ) ival integer ( kind = 4 ) jhi integer ( kind = 4 ) jlo integer ( kind = 4 ) value integer ( kind = 4 ) wide jlo = min ( ilo, ihi ) jhi = max ( ilo, ihi ) wide = jhi - jlo + 1 if ( wide == 1 ) then value = jlo else value = jlo + i4_modp ( ival - jlo, wide ) end if i4_wrap = value 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 GNU LGPL license. ! ! Modified: ! ! 27 January 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Output, integer ( kind = 4 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) ierror character ( len = * ) input_filename integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit integer ( kind = 4 ) j character ( len = 255 ) line integer ( kind = 4 ) table(m,n) integer ( kind = 4 ) 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 GNU LGPL license. ! ! Modified: ! ! 04 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer ( kind = 4 ) M, spatial dimension. ! ! Output, integer ( kind = 4 ) N, the number of points. ! implicit none character ( len = * ) input_filename integer ( kind = 4 ) m integer ( kind = 4 ) 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_some ( m, n, a, ilo, jlo, ihi, jhi, title ) !*****************************************************************************80 ! !! I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 February 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input, integer ( kind = 4 ) A(M,N), an M by N matrix to be printed. ! ! Input, integer ( kind = 4 ) ILO, JLO, the first row and column to print. ! ! Input, integer ( kind = 4 ) IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, an optional title. ! implicit none integer ( kind = 4 ), parameter :: incx = 10 integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) character ( len = 7 ) ctemp(incx) integer ( kind = 4 ) i integer ( kind = 4 ) i2 integer ( kind = 4 ) i2hi integer ( kind = 4 ) i2lo integer ( kind = 4 ) ihi integer ( kind = 4 ) ilo integer ( kind = 4 ) inc integer ( kind = 4 ) j integer ( kind = 4 ) j2hi integer ( kind = 4 ) j2lo integer ( kind = 4 ) jhi integer ( kind = 4 ) 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), '(i7)') i end do write ( *, '('' Row '',10a7)' ) 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), '(i7)' ) a(i,j) end do write ( *, '(i5,1x,10a7)' ) j, ( ctemp(i), i = 1, inc ) end do end do return end subroutine i4mat_write ( output_filename, m, n, table ) !*****************************************************************************80 ! !! I4MAT_WRITE writes an I4MAT file. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 31 May 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) OUTPUT_FILENAME, the output file name. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Input, integer ( kind = 4 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) j character ( len = * ) output_filename integer ( kind = 4 ) output_status integer ( kind = 4 ) output_unit character ( len = 30 ) string integer ( kind = 4 ) table(m,n) ! ! Open the file. ! call get_unit ( output_unit ) open ( unit = output_unit, file = output_filename, & status = 'replace', iostat = output_status ) if ( output_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_WRITE - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the output file "' // & trim ( output_filename ) // '" on unit ', output_unit output_unit = -1 stop end if ! ! Create a format string. ! write ( string, '(a1,i8,a4)' ) '(', m, 'i10)' ! ! Write the data. ! do j = 1, n write ( output_unit, string ) table(1:m,j) end do ! ! Close the file. ! close ( unit = output_unit ) return end subroutine i4row_compare ( m, n, a, i, j, isgn ) !*****************************************************************************80 ! !! I4ROW_COMPARE compares two rows of an I4ROW. ! ! Example: ! ! Input: ! ! M = 3, N = 4, I = 2, J = 3 ! ! A = ( ! 1 2 3 4 ! 5 6 7 8 ! 9 10 11 12 ) ! ! Output: ! ! ISGN = -1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 14 November 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input, integer ( kind = 4 ) A(M,N), an array of M rows of vectors ! of length N. ! ! Input, integer ( kind = 4 ) I, J, the rows to be compared. ! I and J must be between 1 and M. ! ! Output, integer ( kind = 4 ) ISGN, the results of the comparison: ! -1, row I < row J, ! 0, row I = row J, ! +1, row J < row I. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) i integer ( kind = 4 ) isgn integer ( kind = 4 ) j integer ( kind = 4 ) k ! ! Check that I and J are legal. ! if ( i < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_COMPARE - Fatal error!' write ( *, '(a)' ) ' Row index I is less than 1.' write ( *, '(a,i8)' ) ' I = ', i stop else if ( m < i ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_COMPARE - Fatal error!' write ( *, '(a)' ) ' Row index I is out of bounds.' write ( *, '(a,i8)' ) ' I = ', i write ( *, '(a,i8)' ) ' Maximum legal value is M = ', m stop end if if ( j < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_COMPARE - Fatal error!' write ( *, '(a)' ) ' Row index J is less than 1.' write ( *, '(a,i8)' ) ' J = ', j stop else if ( m < j ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_COMPARE - Fatal error!' write ( *, '(a)' ) ' Row index J is out of bounds.' write ( *, '(a,i8)' ) ' J = ', j write ( *, '(a,i8)' ) ' Maximum legal value is M = ', m stop end if isgn = 0 if ( i == j ) then return end if k = 1 do while ( k <= n ) if ( a(i,k) < a(j,k) ) then isgn = -1 return else if ( a(j,k) < a(i,k) ) then isgn = +1 return end if k = k + 1 end do return end subroutine i4row_sort_a ( m, n, a ) !*****************************************************************************80 ! !! I4ROW_SORT_A ascending sorts the rows of an I4ROW. ! ! Discussion: ! ! In lexicographic order, the statement "X < Y", applied to two ! vectors X and Y of length M, means that there is some index I, with ! 1 <= I <= M, with the property that ! ! X(J) = Y(J) for J < I, ! and ! X(I) < Y(I). ! ! In other words, X is less than Y if, at the first index where they ! differ, the X value is less than the Y value. ! ! Example: ! ! Input: ! ! M = 5, N = 3 ! ! A = ! 3 2 1 ! 2 4 3 ! 3 1 8 ! 2 4 2 ! 1 9 9 ! ! Output: ! ! A = ! 1 9 9 ! 2 4 2 ! 2 4 3 ! 3 1 8 ! 3 2 1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 25 September 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, the number of rows of A. ! ! Input, integer ( kind = 4 ) N, the number of columns of A. ! ! Input/output, integer ( kind = 4 ) A(M,N). ! On input, the array of M rows of N-vectors. ! On output, the rows of A have been sorted in ascending ! lexicographic order. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) i integer ( kind = 4 ) indx integer ( kind = 4 ) isgn integer ( kind = 4 ) j if ( m <= 1 ) then return end if if ( n <= 0 ) then return end if ! ! Initialize. ! i = 0 indx = 0 isgn = 0 j = 0 ! ! Call the external heap sorter. ! do call sort_heap_external ( m, indx, i, j, isgn ) ! ! Interchange the I and J objects. ! if ( 0 < indx ) then call i4row_swap ( m, n, a, i, j ) ! ! Compare the I and J objects. ! else if ( indx < 0 ) then call i4row_compare ( m, n, a, i, j, isgn ) else if ( indx == 0 ) then exit end if end do return end subroutine i4row_swap ( m, n, a, irow1, irow2 ) !*****************************************************************************80 ! !! I4ROW_SWAP swaps two rows of an I4ROW. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 April 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input/output, integer ( kind = 4 ) A(M,N), an array of data. ! ! Input, integer ( kind = 4 ) IROW1, IROW2, the two rows to swap. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) irow1 integer ( kind = 4 ) irow2 integer ( kind = 4 ) row(n) ! ! Check. ! if ( irow1 < 1 .or. m < irow1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_SWAP - Fatal error!' write ( *, '(a)' ) ' IROW1 is out of range.' stop end if if ( irow2 < 1 .or. m < irow2 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4ROW_SWAP - Fatal error!' write ( *, '(a)' ) ' IROW2 is out of range.' stop end if if ( irow1 == irow2 ) then return end if row(1:n) = a(irow1,1:n) a(irow1,1:n) = a(irow2,1:n) a(irow2,1:n) = row(1:n) 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 GNU LGPL 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 ( kind = 4 ) element_num integer ( kind = 4 ) element_order integer ( kind = 4 ) element integer ( kind = 4 ) element_node(element_order,element_num) integer ( kind = 4 ) node integer ( kind = 4 ) node_max integer ( kind = 4 ) node_min integer ( kind = 4 ) node_num integer ( kind = 4 ) order 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 GNU LGPL license. ! ! Modified: ! ! 18 October 2008 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Output, real ( kind = 8 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) ierror character ( len = * ) input_filename integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit integer ( kind = 4 ) j character ( len = 255 ) line real ( kind = 8 ) table(m,n) real ( kind = 8 ) 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 GNU LGPL license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILENAME, the name of the input file. ! ! Output, integer ( kind = 4 ) M, spatial dimension. ! ! Output, integer ( kind = 4 ) N, the number of points. ! implicit none character ( len = * ) input_filename integer ( kind = 4 ) m integer ( kind = 4 ) 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_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 GNU LGPL license. ! ! Modified: ! ! 14 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input, real ( kind = 8 ) A(M,N), an M by N matrix to be printed. ! ! Input, integer ( kind = 4 ) ILO, JLO, the first row and column to print. ! ! Input, integer ( kind = 4 ) IHI, JHI, the last row and column to print. ! ! Input, character ( len = * ) TITLE, an optional title. ! implicit none integer ( kind = 4 ), parameter :: incx = 5 integer ( kind = 4 ) m integer ( kind = 4 ) n real ( kind = 8 ) a(m,n) character ( len = 14 ) ctemp(incx) integer ( kind = 4 ) i integer ( kind = 4 ) i2 integer ( kind = 4 ) i2hi integer ( kind = 4 ) i2lo integer ( kind = 4 ) ihi integer ( kind = 4 ) ilo integer ( kind = 4 ) inc integer ( kind = 4 ) j integer ( kind = 4 ) j2hi integer ( kind = 4 ) j2lo integer ( kind = 4 ) jhi integer ( kind = 4 ) 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), '(i7,7x)') i end do write ( *, '('' Row '',5a14)' ) 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), '(g14.6)' ) a(i,j) end do write ( *, '(i5,1x,5a14)' ) j, ( ctemp(i), i = 1, inc ) end do end do return end subroutine r8mat_write ( output_filename, m, n, table ) !*****************************************************************************80 ! !! R8MAT_WRITE writes an R8MAT file. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 31 May 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) OUTPUT_FILENAME, the output file name. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Input, real ( kind = 8 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) j character ( len = * ) output_filename integer ( kind = 4 ) output_status integer ( kind = 4 ) output_unit character ( len = 30 ) string real ( kind = 8 ) table(m,n) ! ! Open the file. ! call get_unit ( output_unit ) open ( unit = output_unit, file = output_filename, & status = 'replace', iostat = output_status ) if ( output_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_WRITE - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the output file "' // & trim ( output_filename ) // '" on unit ', output_unit output_unit = -1 stop end if ! ! Create a format string. ! ! For greater precision in the output file, try: ! ! '(', m, 'g', 24, '.', 16, ')' ! write ( string, '(a1,i8,a1,i8,a1,i8,a1)' ) '(', m, 'g', 14, '.', 6, ')' ! ! Write the data. ! do j = 1, n write ( output_unit, string ) table(1:m,j) end do ! ! Close the file. ! close ( unit = output_unit ) 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 GNU LGPL license. ! ! Modified: ! ! 28 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, a string to be examined. ! ! Output, integer ( kind = 4 ) IVAL, the value read from the string. ! If the string is blank, then IVAL will be returned 0. ! ! Output, integer ( kind = 4 ) IERROR, an error flag. ! 0, no error. ! 1, an error occurred. ! ! Output, integer ( kind = 4 ) LENGTH, the number of characters of S used. ! implicit none character c integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) isgn integer ( kind = 4 ) istate integer ( kind = 4 ) ival integer ( kind = 4 ) 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 GNU LGPL license. ! ! Modified: ! ! 08 October 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer ( kind = 4 ) N, the number of values expected. ! ! Output, integer ( kind = 4 ) IVEC(N), the values read from the string. ! ! Output, integer ( kind = 4 ) IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) ilo integer ( kind = 4 ) ivec(n) integer ( kind = 4 ) 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 ( kind = 4 ) part, ! 4 decimal point, ! 5 fraction part, ! 6 'E' or 'e' or 'D' or 'd', exponent marker, ! 7 exponent sign, ! 8 exponent integer ( kind = 4 ) 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 GNU LGPL 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 = 8 ) DVAL, the value read from the string. ! ! Output, integer ( kind = 4 ) 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 ( kind = 4 ) LENGTH, the number of characters read ! to form the number, including any terminating ! characters such as a trailing comma or blanks. ! implicit none logical ch_eqi character c real ( kind = 8 ) dval integer ( kind = 4 ) ierror integer ( kind = 4 ) ihave integer ( kind = 4 ) isgn integer ( kind = 4 ) iterm integer ( kind = 4 ) jbot integer ( kind = 4 ) jsgn integer ( kind = 4 ) jtop integer ( kind = 4 ) length integer ( kind = 4 ) nchar integer ( kind = 4 ) ndig real ( kind = 8 ) rbot real ( kind = 8 ) rexp real ( kind = 8 ) 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 = 8 ) else if ( ihave == 5 ) then rtop = 10.0D+00 * rtop + real ( ndig, kind = 8 ) 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 = 8 ) & / real ( jbot, kind = 8 ) ) end if end if dval = real ( isgn, kind = 8 ) * 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 GNU LGPL license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer ( kind = 4 ) N, the number of values expected. ! ! Output, real ( kind = 8 ) RVEC(N), the values read from the string. ! ! Output, integer ( kind = 4 ) IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) ilo integer ( kind = 4 ) lchar real ( kind = 8 ) 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 GNU LGPL license. ! ! Modified: ! ! 14 April 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be examined. ! ! Output, integer ( kind = 4 ) NWORD, the number of "words" in the string. ! Words are presumed to be separated by one or more blanks. ! implicit none logical blank integer ( kind = 4 ) i integer ( kind = 4 ) lens integer ( kind = 4 ) 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 sort_heap_external ( n, indx, i, j, isgn ) !*****************************************************************************80 ! !! SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order. ! ! Discussion: ! ! The actual list of data is not passed to the routine. Hence this ! routine may be used to sort integer ( kind = 4 )s, reals, numbers, names, ! dates, shoe sizes, and so on. After each call, the routine asks ! the user to compare or interchange two items, until a special ! return value signals that the sorting is completed. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 05 February 2004 ! ! Reference: ! ! Albert Nijenhuis and Herbert Wilf, ! Combinatorial Algorithms, ! Academic Press, 1978, second edition, ! ISBN 0-12-519260-6. ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the number of items to be sorted. ! ! Input/output, integer ( kind = 4 ) INDX, the main communication signal. ! ! The user must set INDX to 0 before the first call. ! Thereafter, the user should not change the value of INDX until ! the sorting is done. ! ! On return, if INDX is ! ! greater than 0, ! * interchange items I and J; ! * call again. ! ! less than 0, ! * compare items I and J; ! * set ISGN = -1 if I < J, ISGN = +1 if J < I; ! * call again. ! ! equal to 0, the sorting is done. ! ! Output, integer ( kind = 4 ) I, J, the indices of two items. ! On return with INDX positive, elements I and J should be interchanged. ! On return with INDX negative, elements I and J should be compared, and ! the result reported in ISGN on the next call. ! ! Input, integer ( kind = 4 ) ISGN, results of comparison of elements ! I and J. ! (Used only when the previous call returned INDX less than 0). ! ISGN <= 0 means I is less than or equal to J; ! 0 <= ISGN means I is greater than or equal to J. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ), save :: i_save = 0 integer ( kind = 4 ) indx integer ( kind = 4 ) isgn integer ( kind = 4 ) j integer ( kind = 4 ), save :: j_save = 0 integer ( kind = 4 ), save :: k = 0 integer ( kind = 4 ), save :: k1 = 0 integer ( kind = 4 ) n integer ( kind = 4 ), save :: n1 = 0 ! ! INDX = 0: This is the first call. ! if ( indx == 0 ) then i_save = 0 j_save = 0 k = n / 2 k1 = k n1 = n ! ! INDX < 0: The user is returning the results of a comparison. ! else if ( indx < 0 ) then if ( indx == -2 ) then if ( isgn < 0 ) then i_save = i_save + 1 end if j_save = k1 k1 = i_save indx = -1 i = i_save j = j_save return end if if ( 0 < isgn ) then indx = 2 i = i_save j = j_save return end if if ( k <= 1 ) then if ( n1 == 1 ) then i_save = 0 j_save = 0 indx = 0 else i_save = n1 n1 = n1 - 1 j_save = 1 indx = 1 end if i = i_save j = j_save return end if k = k - 1 k1 = k ! ! 0 < INDX, the user was asked to make an interchange. ! else if ( indx == 1 ) then k1 = k end if do i_save = 2 * k1 if ( i_save == n1 ) then j_save = k1 k1 = i_save indx = -1 i = i_save j = j_save return else if ( i_save <= n1 ) then j_save = i_save + 1 indx = -2 i = i_save j = j_save return end if if ( k <= 1 ) then exit end if k = k - 1 k1 = k end do if ( n1 == 1 ) then i_save = 0 j_save = 0 indx = 0 i = i_save j = j_save else i_save = n1 n1 = n1 - 1 j_save = 1 indx = 1 i = i_save j = j_save end if 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 GNU LGPL license. ! ! Modified: ! ! 18 May 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none character ( len = 8 ) ampm integer ( kind = 4 ) d integer ( kind = 4 ) h integer ( kind = 4 ) m integer ( kind = 4 ) mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer ( kind = 4 ) n integer ( kind = 4 ) s integer ( kind = 4 ) values(8) integer ( kind = 4 ) 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 subroutine triangle_area_2d ( t, area ) !*****************************************************************************80 ! !! TRIANGLE_AREA_2D computes the area of a triangle in 2D. ! ! Discussion: ! ! If the triangle's vertices are given in counterclockwise order, ! the area will be positive. If the triangle's vertices are given ! in clockwise order, the area will be negative! ! ! An earlier version of this routine always returned the absolute ! value of the computed area. I am convinced now that that is ! a less useful result! For instance, by returning the signed ! area of a triangle, it is possible to easily compute the area ! of a nonconvex polygon as the sum of the (possibly negative) ! areas of triangles formed by node 1 and successive pairs of vertices. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 17 October 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, real ( kind = 8 ) T(2,3), the triangle vertices. ! ! Output, real ( kind = 8 ) AREA, the area of the triangle. ! implicit none integer ( kind = 4 ), parameter :: dim_num = 2 real ( kind = 8 ) area real ( kind = 8 ) t(dim_num,3) area = 0.5D+00 * ( & t(1,1) * ( t(2,2) - t(2,3) ) & + t(1,2) * ( t(2,3) - t(2,1) ) & + t(1,3) * ( t(2,1) - t(2,2) ) ) return end subroutine triangulation_order3_neighbor_triangles ( triangle_num, tri_vert, & tri_nabe ) !*****************************************************************************80 ! !! TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors. ! ! Discussion: ! ! A triangulation of a set of nodes can be completely described by ! the coordinates of the nodes, and the list of nodes that make up ! each triangle. However, in some cases, it is necessary to know ! triangle adjacency information, that is, which triangle, if any, ! is adjacent to a given triangle on a particular side. ! ! This routine creates a data structure recording this information. ! ! The primary amount of work occurs in sorting a list of 3 * TRIANGLE_NUM ! data items. ! ! Example: ! ! The input information from TRI_VERT: ! ! Triangle Nodes ! -------- --------------- ! 1 3 4 1 ! 2 3 1 2 ! 3 3 2 8 ! 4 2 1 5 ! 5 8 2 13 ! 6 8 13 9 ! 7 3 8 9 ! 8 13 2 5 ! 9 9 13 7 ! 10 7 13 5 ! 11 6 7 5 ! 12 9 7 6 ! 13 10 9 6 ! 14 6 5 12 ! 15 11 6 12 ! 16 10 6 11 ! ! The output information in TRI_NABE: ! ! Triangle Neighboring Triangles ! -------- --------------------- ! ! 1 -1 -1 2 ! 2 1 4 3 ! 3 2 5 7 ! 4 2 -1 8 ! 5 3 8 6 ! 6 5 9 7 ! 7 3 6 -1 ! 8 5 4 10 ! 9 6 10 12 ! 10 9 8 11 ! 11 12 10 14 ! 12 9 11 13 ! 13 -1 12 16 ! 14 11 -1 15 ! 15 16 14 -1 ! 16 13 15 -1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 17 July 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) TRIANGLE_NUM, the number of triangles. ! ! Input, integer ( kind = 4 ) TRI_VERT(3,TRIANGLE_NUM), the nodes that make ! up each triangle. ! ! Output, integer ( kind = 4 ) TRI_NABE(3,TRIANGLE_NUM), the three triangles ! that are direct neighbors of a given triangle. TRI_NABE(1,I) is the index ! of the triangle which touches side 1, defined by nodes 2 and 3, and so on. ! TRI_NABE(1,I) is negative if there is no neighbor on that side. In this ! case, that side of the triangle lies on the boundary of the triangulation. ! implicit none integer ( kind = 4 ) triangle_num integer ( kind = 4 ) i integer ( kind = 4 ) irow integer ( kind = 4 ) j integer ( kind = 4 ) k integer ( kind = 4 ) row(3*triangle_num,4) integer ( kind = 4 ) side1 integer ( kind = 4 ) side2 integer ( kind = 4 ) tri_nabe(3,triangle_num) integer ( kind = 4 ) tri integer ( kind = 4 ) tri_vert(3,triangle_num) integer ( kind = 4 ) tri1 integer ( kind = 4 ) tri2 ! ! Step 1. ! From the list of nodes for triangle T, of the form: (I,J,K) ! construct the three neighbor relations: ! ! (I,J,1,T) or (J,I,1,T), ! (J,K,2,T) or (K,J,2,T), ! (K,I,3,T) or (I,K,3,T) ! ! where we choose (I,J,1,T) if I < J, or else (J,I,1,T) ! do tri = 1, triangle_num i = tri_vert(1,tri) j = tri_vert(2,tri) k = tri_vert(3,tri) if ( i < j ) then row(3*(tri-1)+1,1:4) = (/ i, j, 1, tri /) else row(3*(tri-1)+1,1:4) = (/ j, i, 1, tri /) end if if ( j < k ) then row(3*(tri-1)+2,1:4) = (/ j, k, 2, tri /) else row(3*(tri-1)+2,1:4) = (/ k, j, 2, tri /) end if if ( k < i ) then row(3*(tri-1)+3,1:4) = (/ k, i, 3, tri /) else row(3*(tri-1)+3,1:4) = (/ i, k, 3, tri /) end if end do ! ! Step 2. Perform an ascending dictionary sort on the neighbor relations. ! We only intend to sort on columns 1 and 2; the routine we call here ! sorts on columns 1 through 4 but that won't hurt us. ! ! What we need is to find cases where two triangles share an edge. ! Say they share an edge defined by the nodes I and J. Then there are ! two rows of ROW that start out ( I, J, ?, ? ). By sorting ROW, ! we make sure that these two rows occur consecutively. That will ! make it easy to notice that the triangles are neighbors. ! call i4row_sort_a ( 3*triangle_num, 4, row ) ! ! Step 3. Neighboring triangles show up as consecutive rows with ! identical first two entries. Whenever you spot this happening, ! make the appropriate entries in TRI_NABE. ! tri_nabe(1:3,1:triangle_num) = -1 irow = 1 do if ( 3 * triangle_num <= irow ) then exit end if if ( row(irow,1) /= row(irow+1,1) .or. row(irow,2) /= row(irow+1,2) ) then irow = irow + 1 cycle end if side1 = row(irow,3) tri1 = row(irow,4) side2 = row(irow+1,3) tri2 = row(irow+1,4) tri_nabe(side1,tri1) = tri2 tri_nabe(side2,tri2) = tri1 irow = irow + 2 end do return end subroutine triangulation_order6_neighbor_triangles ( triangle_num, tri_vert, & tri_nabe ) !*****************************************************************************80 ! !! TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES determines triangle neighbors. ! ! Discussion: ! ! A triangulation of a set of nodes can be completely described by ! the coordinates of the nodes, and the list of nodes that make up ! each triangle. However, in some cases, it is necessary to know ! triangle adjacency information, that is, which triangle, if any, ! is adjacent to a given triangle on a particular side. ! ! This routine creates a data structure recording this information. ! ! The primary amount of work occurs in sorting a list of 3 * TRIANGLE_NUM ! data items. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 12 March 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) TRIANGLE_NUM, the number of triangles. ! ! Input, integer ( kind = 4 ) TRI_VERT(6,TRIANGLE_NUM), the nodes that make ! up each triangle. ! ! Output, integer ( kind = 4 ) TRI_NABE(3,TRIANGLE_NUM), the three triangles ! that are direct neighbors of a given triangle. TRI_NABE(1,I) is the index ! of the triangle which touches side 1, defined by nodes 2 and 3, and so on. ! TRI_NABE(1,I) is negative if there is no neighbor on that side. In this ! case, that side of the triangle lies on the boundary of the triangulation. ! implicit none integer ( kind = 4 ) triangle_num integer ( kind = 4 ) i integer ( kind = 4 ) irow integer ( kind = 4 ) j integer ( kind = 4 ) k integer ( kind = 4 ) row(3*triangle_num,4) integer ( kind = 4 ) side1 integer ( kind = 4 ) side2 integer ( kind = 4 ) tri_nabe(3,triangle_num) integer ( kind = 4 ) tri integer ( kind = 4 ) tri_vert(6,triangle_num) integer ( kind = 4 ) tri1 integer ( kind = 4 ) tri2 ! ! Step 1. ! From the list of vertices for triangle T, of the form: (I,J,K) ! construct the three neighbor relations: ! ! (I,J,1,T) or (J,I,1,T), ! (J,K,2,T) or (K,J,2,T), ! (K,I,3,T) or (I,K,3,T) ! ! where we choose (I,J,1,T) if I < J, or else (J,I,1,T) ! do tri = 1, triangle_num i = tri_vert(1,tri) j = tri_vert(2,tri) k = tri_vert(3,tri) if ( i < j ) then row(3*(tri-1)+1,1:4) = (/ i, j, 1, tri /) else row(3*(tri-1)+1,1:4) = (/ j, i, 1, tri /) end if if ( j < k ) then row(3*(tri-1)+2,1:4) = (/ j, k, 2, tri /) else row(3*(tri-1)+2,1:4) = (/ k, j, 2, tri /) end if if ( k < i ) then row(3*(tri-1)+3,1:4) = (/ k, i, 3, tri /) else row(3*(tri-1)+3,1:4) = (/ i, k, 3, tri /) end if end do ! ! Step 2. Perform an ascending dictionary sort on the neighbor relations. ! We only intend to sort on columns 1 and 2; the routine we call here ! sorts on columns 1 through 4 but that won't hurt us. ! ! What we need is to find cases where two triangles share an edge. ! Say they share an edge defined by the nodes I and J. Then there are ! two rows of ROW that start out ( I, J, ?, ? ). By sorting ROW, ! we make sure that these two rows occur consecutively. That will ! make it easy to notice that the triangles are neighbors. ! call i4row_sort_a ( 3*triangle_num, 4, row ) ! ! Step 3. Neighboring triangles show up as consecutive rows with ! identical first two entries. Whenever you spot this happening, ! make the appropriate entries in TRI_NABE. ! tri_nabe(1:3,1:triangle_num) = -1 irow = 1 do if ( 3 * triangle_num <= irow ) then exit end if if ( row(irow,1) /= row(irow+1,1) .or. row(irow,2) /= row(irow+1,2) ) then irow = irow + 1 cycle end if side1 = row(irow,3) tri1 = row(irow,4) side2 = row(irow+1,3) tri2 = row(irow+1,4) tri_nabe(side1,tri1) = tri2 tri_nabe(side2,tri2) = tri1 irow = irow + 2 end do return end