Merge branch 'development' of magit1.mpie.de:damask/DAMASK into development
This commit is contained in:
Zhuowen Zhao
commit
690edaa8dc
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@ -41,7 +41,7 @@ parser.add_option('-f','--formula',
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parser.add_option('-c','--condition',
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parser.add_option('-c','--condition',
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dest = 'condition', metavar='string',
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dest = 'condition', metavar='string',
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help = 'condition to filter rows')
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help = 'condition to alter existing column data')
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parser.set_defaults(condition = None,
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parser.set_defaults(condition = None,
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)
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)
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@ -77,28 +77,27 @@ for name in filenames:
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# --------------------------------------- evaluate condition ---------------------------------------
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# --------------------------------------- evaluate condition ---------------------------------------
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if options.condition is not None:
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if options.condition is not None:
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interpolator = []
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condition = options.condition # copy per file, since might be altered inline
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condition = options.condition # copy per file, since might be altered inline
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breaker = False
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breaker = False
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for position,operand in enumerate(set(re.findall(r'#(([s]#)?(.+?))#',condition))): # find three groups
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for position,(all,marker,column) in enumerate(set(re.findall(r'#(([s]#)?(.+?))#',condition))): # find three groups
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condition = condition.replace('#'+operand[0]+'#',
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idx = table.label_index(column)
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{ '': '{%i}'%position,
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dim = table.label_dimension(column)
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's#':'"{%i}"'%position}[operand[1]])
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if idx < 0 and column not in specials:
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if operand[2] in specials: # special label
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damask.util.croak('column "{}" not found.'.format(column))
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interpolator += ['specials["%s"]'%operand[2]]
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breaker = True
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else:
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else:
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try:
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if column in specials:
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interpolator += ['%s(table.data[%i])'%({ '':'float',
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replacement = 'specials["{}"]'.format(column)
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's#':'str'}[operand[1]],
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elif dim == 1: # scalar input
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table.label_index(operand[2]))] # could be generalized to indexrange as array lookup
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replacement = '{}(table.data[{}])'.format({ '':'float',
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except:
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's#':'str'}[marker],idx) # take float or string value of data column
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damask.util.croak('column "{}" not found.'.format(operand[2]))
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elif dim > 1: # multidimensional input (vector, tensor, etc.)
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breaker = True
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replacement = 'np.array(table.data[{}:{}],dtype=float)'.format(idx,idx+dim) # use (flat) array representation
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if breaker: continue # found mistake in condition evaluation --> next file
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condition = condition.replace('#'+all+'#',replacement)
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evaluator_condition = "'" + condition + "'.format(" + ','.join(interpolator) + ")"
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if breaker: continue # found mistake in condition evaluation --> next file
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# ------------------------------------------ build formulas ----------------------------------------
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# ------------------------------------------ build formulas ----------------------------------------
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@ -162,7 +161,7 @@ for name in filenames:
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# -------------------------------------- evaluate formulas -----------------------------------------
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# -------------------------------------- evaluate formulas -----------------------------------------
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if options.condition is None or eval(eval(evaluator_condition)): # condition for veteran replacement fulfilled
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if options.condition is None or eval(condition): # condition for veteran replacement fulfilled
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for veteran in veterans: # evaluate formulas that overwrite
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for veteran in veterans: # evaluate formulas that overwrite
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table.data[table.label_index(veteran):
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table.data[table.label_index(veteran):
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table.label_index(veteran)+table.label_dimension(veteran)] = \
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table.label_index(veteran)+table.label_dimension(veteran)] = \
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@ -14,7 +14,7 @@ scriptID = ' '.join([scriptName,damask.version])
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# --------------------------------------------------------------------
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# --------------------------------------------------------------------
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parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """
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parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """
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Add data of selected column(s) from (first) row of second ASCIItable that shares the linking column value.
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Add data of selected column(s) from (first) row of linked ASCIItable that shares the linking column value.
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""", version = scriptID)
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""", version = scriptID)
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@ -25,7 +25,7 @@ parser.add_option('--link',
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parser.add_option('-l','--label',
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parser.add_option('-l','--label',
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dest = 'label',
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dest = 'label',
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action = 'extend', metavar = '<string LIST>',
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action = 'extend', metavar = '<string LIST>',
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help = 'column label(s) to be appended')
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help = 'column label(s) to add from linked ASCIItable')
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parser.add_option('-a','--asciitable',
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parser.add_option('-a','--asciitable',
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dest = 'asciitable',
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dest = 'asciitable',
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type = 'string', metavar = 'string',
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type = 'string', metavar = 'string',
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@ -69,7 +69,7 @@ for name in filenames:
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try: table = damask.ASCIItable(name = name,
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try: table = damask.ASCIItable(name = name,
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buffered = False)
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buffered = False)
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except: continue
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except: continue
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damask.util.report(scriptName,name)
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damask.util.report(scriptName,"{} <== {}".format(name,options.asciitable))
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# ------------------------------------------ read header ------------------------------------------
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# ------------------------------------------ read header ------------------------------------------
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@ -51,7 +51,7 @@ parser.add_option('-c','--condition',
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dest = 'condition', metavar='string',
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dest = 'condition', metavar='string',
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help = 'condition to filter rows')
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help = 'condition to filter rows')
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parser.set_defaults(condition = '',
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parser.set_defaults(condition = None,
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)
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)
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(options,filenames) = parser.parse_args()
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(options,filenames) = parser.parse_args()
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@ -98,23 +98,29 @@ for name in filenames:
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else:
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else:
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order = range(len(labels)) # maintain original order of labels
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order = range(len(labels)) # maintain original order of labels
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interpolator = []
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# --------------------------------------- evaluate condition ---------------------------------------
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condition = options.condition # copy per file, might be altered
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if options.condition is not None:
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for position,operand in enumerate(set(re.findall(r'#(([s]#)?(.+?))#',condition))): # find three groups
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condition = options.condition # copy per file, since might be altered inline
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condition = condition.replace('#'+operand[0]+'#',
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breaker = False
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{ '': '{{{}}}' .format(position),
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's#':'"{{{}}}"'.format(position)}[operand[1]])
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if operand[2] in specials: # special label ?
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interpolator += ['specials["{}"]'.format(operand[2])]
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else:
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try:
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interpolator += ['{}(table.data[{}])'.format({ '':'float',
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's#':'str'}[operand[1]],
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table.label_index(operand[2]))]
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except:
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parser.error('column "{}" not found...\n'.format(operand[2]))
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evaluator = "'" + condition + "'.format(" + ','.join(interpolator) + ")"
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for position,(all,marker,column) in enumerate(set(re.findall(r'#(([s]#)?(.+?))#',condition))): # find three groups
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idx = table.label_index(column)
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dim = table.label_dimension(column)
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if idx < 0 and column not in specials:
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damask.util.croak('column "{}" not found.'.format(column))
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breaker = True
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else:
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if column in specials:
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replacement = 'specials["{}"]'.format(column)
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elif dim == 1: # scalar input
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replacement = '{}(table.data[{}])'.format({ '':'float',
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's#':'str'}[marker],idx) # take float or string value of data column
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elif dim > 1: # multidimensional input (vector, tensor, etc.)
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replacement = 'np.array(table.data[{}:{}],dtype=float)'.format(idx,idx+dim) # use (flat) array representation
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condition = condition.replace('#'+all+'#',replacement)
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if breaker: continue # found mistake in condition evaluation --> next file
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# ------------------------------------------ assemble header ---------------------------------------
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# ------------------------------------------ assemble header ---------------------------------------
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@ -129,7 +135,7 @@ for name in filenames:
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outputAlive = True
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outputAlive = True
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while outputAlive and table.data_read(): # read next data line of ASCII table
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while outputAlive and table.data_read(): # read next data line of ASCII table
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specials['_row_'] += 1 # count row
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specials['_row_'] += 1 # count row
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if condition == '' or eval(eval(evaluator)): # valid row ?
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if options.condition is None or eval(condition): # valid row ?
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table.data = [table.data[position] for position in positions] # retain filtered columns
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table.data = [table.data[position] for position in positions] # retain filtered columns
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outputAlive = table.data_write() # output processed line
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outputAlive = table.data_write() # output processed line
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@ -52,7 +52,7 @@ parser.set_defaults(data = [],
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(options, filenames) = parser.parse_args()
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(options, filenames) = parser.parse_args()
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if not options.vtk: parser.error('No VTK file specified.')
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if not options.vtk: parser.error('no VTK file specified.')
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if not os.path.exists(options.vtk): parser.error('VTK file does not exist.')
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if not os.path.exists(options.vtk): parser.error('VTK file does not exist.')
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if os.path.splitext(options.vtk)[1] == '.vtp':
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if os.path.splitext(options.vtk)[1] == '.vtp':
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@ -66,16 +66,16 @@ elif os.path.splitext(options.vtk)[1] == '.vtk':
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reader.Update()
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reader.Update()
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Polydata = reader.GetPolyDataOutput()
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Polydata = reader.GetPolyDataOutput()
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else:
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else:
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parser.error('Unsupported VTK file type extension.')
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parser.error('unsupported VTK file type extension.')
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Npoints = Polydata.GetNumberOfPoints()
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Npoints = Polydata.GetNumberOfPoints()
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Ncells = Polydata.GetNumberOfCells()
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Ncells = Polydata.GetNumberOfCells()
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Nvertices = Polydata.GetNumberOfVerts()
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Nvertices = Polydata.GetNumberOfVerts()
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if Npoints != Ncells or Npoints != Nvertices:
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if Npoints != Ncells or Npoints != Nvertices:
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parser.error('Number of points, cells, and vertices in VTK differ from each other.')
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parser.error('number of points, cells, and vertices in VTK differ from each other.')
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damask.util.croak('{}: {} points, {} vertices, and {} cells...'.format(options.vtk,Npoints,Nvertices,Ncells))
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damask.util.croak('{}: {} points/vertices/cells...'.format(options.vtk,Npoints))
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# --- loop over input files -------------------------------------------------------------------------
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# --- loop over input files -------------------------------------------------------------------------
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@ -97,16 +97,19 @@ for name in filenames:
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VTKarray = {}
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VTKarray = {}
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active = defaultdict(list)
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active = defaultdict(list)
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for datatype,dimension,label in [['data',99,options.data],
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for datatype,dimension,label in [['data',0,options.data],
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['tensor',9,options.tensor],
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['tensor',9,options.tensor],
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['color' ,3,options.color],
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['color' ,3,options.color],
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]:
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]:
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for i,dim in enumerate(table.label_dimension(label)):
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for i,dim in enumerate(table.label_dimension(label)):
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me = label[i]
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me = label[i]
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if dim == -1: remarks.append('{} "{}" not found...'.format(datatype,me))
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if dim == -1: remarks.append('{} "{}" not found...'.format(datatype,me))
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elif dim > dimension: remarks.append('"{}" not of dimension {}...'.format(me,dimension))
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elif dimension > 0 \
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and dim != dimension: remarks.append('"{}" not of dimension {}...'.format(me,dimension))
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else:
|
else:
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remarks.append('adding {} "{}"...'.format(datatype,me))
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remarks.append('adding {}{} "{}"...'.format(datatype if dim > 1 else 'scalar',
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'' if dimension > 0 or dim == 1 else '[{}]'.format(dim),
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me))
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active[datatype].append(me)
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active[datatype].append(me)
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|
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if remarks != []: damask.util.croak(remarks)
|
if remarks != []: damask.util.croak(remarks)
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|
|
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@ -55,7 +55,7 @@ parser.set_defaults(data = [],
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|
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(options, filenames) = parser.parse_args()
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(options, filenames) = parser.parse_args()
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|
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if not options.vtk: parser.error('No VTK file specified.')
|
if not options.vtk: parser.error('no VTK file specified.')
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if not os.path.exists(options.vtk): parser.error('VTK file does not exist.')
|
if not os.path.exists(options.vtk): parser.error('VTK file does not exist.')
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|
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if os.path.splitext(options.vtk)[1] == '.vtr':
|
if os.path.splitext(options.vtk)[1] == '.vtr':
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@ -69,7 +69,7 @@ elif os.path.splitext(options.vtk)[1] == '.vtk':
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reader.Update()
|
reader.Update()
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rGrid = reader.GetRectilinearGridOutput()
|
rGrid = reader.GetRectilinearGridOutput()
|
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else:
|
else:
|
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parser.error('Unsupported VTK file type extension.')
|
parser.error('unsupported VTK file type extension.')
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|
|
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Npoints = rGrid.GetNumberOfPoints()
|
Npoints = rGrid.GetNumberOfPoints()
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Ncells = rGrid.GetNumberOfCells()
|
Ncells = rGrid.GetNumberOfCells()
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|
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@ -96,16 +96,19 @@ for name in filenames:
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VTKarray = {}
|
VTKarray = {}
|
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active = defaultdict(list)
|
active = defaultdict(list)
|
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|
|
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for datatype,dimension,label in [['data',99,options.data],
|
for datatype,dimension,label in [['data',0,options.data],
|
||||||
['tensor',9,options.tensor],
|
['tensor',9,options.tensor],
|
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['color' ,3,options.color],
|
['color' ,3,options.color],
|
||||||
]:
|
]:
|
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for i,dim in enumerate(table.label_dimension(label)):
|
for i,dim in enumerate(table.label_dimension(label)):
|
||||||
me = label[i]
|
me = label[i]
|
||||||
if dim == -1: remarks.append('{} "{}" not found...'.format(datatype,me))
|
if dim == -1: remarks.append('{} "{}" not found...'.format(datatype,me))
|
||||||
elif dim > dimension: remarks.append('"{}" not of dimension {}...'.format(me,dimension))
|
elif dimension > 0 \
|
||||||
|
and dim != dimension: remarks.append('"{}" not of dimension {}...'.format(me,dimension))
|
||||||
else:
|
else:
|
||||||
remarks.append('adding {} "{}"...'.format(datatype,me))
|
remarks.append('adding {}{} "{}"...'.format(datatype if dim > 1 else 'scalar',
|
||||||
|
'' if dimension > 0 or dim == 1 else '[{}]'.format(dim),
|
||||||
|
me))
|
||||||
active[datatype].append(me)
|
active[datatype].append(me)
|
||||||
|
|
||||||
if remarks != []: damask.util.croak(remarks)
|
if remarks != []: damask.util.croak(remarks)
|
||||||
|
|
@ -141,7 +144,7 @@ for name in filenames:
|
||||||
if len(table.data) == Npoints: mode = 'point'
|
if len(table.data) == Npoints: mode = 'point'
|
||||||
elif len(table.data) == Ncells: mode = 'cell'
|
elif len(table.data) == Ncells: mode = 'cell'
|
||||||
else:
|
else:
|
||||||
damask.util.croak('Data count is incompatible with grid...')
|
damask.util.croak('data count is incompatible with grid...')
|
||||||
continue
|
continue
|
||||||
|
|
||||||
damask.util.croak('{} mode...'.format(mode))
|
damask.util.croak('{} mode...'.format(mode))
|
||||||
|
|
|
||||||
|
|
@ -37,12 +37,9 @@ def findClosestSeed(fargs):
|
||||||
return np.argmin(dist) # seed point closest to point
|
return np.argmin(dist) # seed point closest to point
|
||||||
|
|
||||||
|
|
||||||
def laguerreTessellation(undeformed, coords, weights, grains, nonperiodic = False, cpus = 2):
|
def laguerreTessellation(undeformed, coords, weights, grains, periodic = True, cpus = 2):
|
||||||
|
|
||||||
copies = \
|
copies = \
|
||||||
np.array([
|
|
||||||
[ 0, 0, 0 ],
|
|
||||||
]).astype(float) if nonperiodic else \
|
|
||||||
np.array([
|
np.array([
|
||||||
[ -1,-1,-1 ],
|
[ -1,-1,-1 ],
|
||||||
[ 0,-1,-1 ],
|
[ 0,-1,-1 ],
|
||||||
|
|
@ -71,7 +68,10 @@ def laguerreTessellation(undeformed, coords, weights, grains, nonperiodic = Fals
|
||||||
[ -1, 1, 1 ],
|
[ -1, 1, 1 ],
|
||||||
[ 0, 1, 1 ],
|
[ 0, 1, 1 ],
|
||||||
[ 1, 1, 1 ],
|
[ 1, 1, 1 ],
|
||||||
]).astype(float)*info['size']
|
]).astype(float)*info['size'] if periodic else \
|
||||||
|
np.array([
|
||||||
|
[ 0, 0, 0 ],
|
||||||
|
]).astype(float)
|
||||||
|
|
||||||
repeatweights = np.tile(weights,len(copies)).flatten(order='F') # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
|
repeatweights = np.tile(weights,len(copies)).flatten(order='F') # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
|
||||||
for i,vec in enumerate(copies): # periodic copies of seed points ...
|
for i,vec in enumerate(copies): # periodic copies of seed points ...
|
||||||
|
|
@ -121,8 +121,8 @@ group.add_option('--cpus',
|
||||||
type = 'int', metavar = 'int',
|
type = 'int', metavar = 'int',
|
||||||
help = 'number of parallel processes to use for Laguerre tessellation [%default]')
|
help = 'number of parallel processes to use for Laguerre tessellation [%default]')
|
||||||
group.add_option('--nonperiodic',
|
group.add_option('--nonperiodic',
|
||||||
dest = 'nonperiodic',
|
dest = 'periodic',
|
||||||
action = 'store_true',
|
action = 'store_false',
|
||||||
help = 'nonperiodic tessellation')
|
help = 'nonperiodic tessellation')
|
||||||
|
|
||||||
parser.add_option_group(group)
|
parser.add_option_group(group)
|
||||||
|
|
@ -144,6 +144,10 @@ group.add_option('-o',
|
||||||
dest = 'origin',
|
dest = 'origin',
|
||||||
type = 'float', nargs = 3, metavar=' '.join(['float']*3),
|
type = 'float', nargs = 3, metavar=' '.join(['float']*3),
|
||||||
help = 'origin of grid')
|
help = 'origin of grid')
|
||||||
|
group.add_option('--nonnormalized',
|
||||||
|
dest = 'normalized',
|
||||||
|
action = 'store_false',
|
||||||
|
help = 'seed coordinates are not normalized to a unit cube')
|
||||||
|
|
||||||
parser.add_option_group(group)
|
parser.add_option_group(group)
|
||||||
|
|
||||||
|
|
@ -206,7 +210,8 @@ parser.set_defaults(pos = 'pos',
|
||||||
phase = 1,
|
phase = 1,
|
||||||
cpus = 2,
|
cpus = 2,
|
||||||
laguerre = False,
|
laguerre = False,
|
||||||
nonperiodic = False,
|
periodic = True,
|
||||||
|
normalized = True,
|
||||||
config = True,
|
config = True,
|
||||||
)
|
)
|
||||||
(options,filenames) = parser.parse_args()
|
(options,filenames) = parser.parse_args()
|
||||||
|
|
@ -248,7 +253,7 @@ for name in filenames:
|
||||||
for i in range(3):
|
for i in range(3):
|
||||||
if info['size'][i] <= 0.0: # any invalid size?
|
if info['size'][i] <= 0.0: # any invalid size?
|
||||||
info['size'][i] = float(info['grid'][i])/max(info['grid']) # normalize to grid
|
info['size'][i] = float(info['grid'][i])/max(info['grid']) # normalize to grid
|
||||||
remarks.append('rescaling size {} to {}...'.format({0:'x',1:'y',2:'z'}[i],info['size'][i]))
|
remarks.append('rescaling size {} to {}...'.format(['x','y','z'][i],info['size'][i]))
|
||||||
|
|
||||||
if table.label_dimension(options.pos) != 3:
|
if table.label_dimension(options.pos) != 3:
|
||||||
errors.append('seed positions "{}" have dimension {}.'.format(options.pos,
|
errors.append('seed positions "{}" have dimension {}.'.format(options.pos,
|
||||||
|
|
@ -256,6 +261,7 @@ for name in filenames:
|
||||||
else:
|
else:
|
||||||
labels += [options.pos]
|
labels += [options.pos]
|
||||||
|
|
||||||
|
if not options.normalized: remarks.append('using real-space seed coordinates...')
|
||||||
if not hasEulers: remarks.append('missing seed orientations...')
|
if not hasEulers: remarks.append('missing seed orientations...')
|
||||||
else: labels += [options.eulers]
|
else: labels += [options.eulers]
|
||||||
if not hasGrains: remarks.append('missing seed microstructure indices...')
|
if not hasGrains: remarks.append('missing seed microstructure indices...')
|
||||||
|
|
@ -272,7 +278,8 @@ for name in filenames:
|
||||||
# ------------------------------------------ read seeds ---------------------------------------
|
# ------------------------------------------ read seeds ---------------------------------------
|
||||||
|
|
||||||
table.data_readArray(labels)
|
table.data_readArray(labels)
|
||||||
coords = table.data[:,table.label_indexrange(options.pos)] * info['size']
|
coords = table.data[:,table.label_indexrange(options.pos)] * info['size'] if options.normalized \
|
||||||
|
else table.data[:,table.label_indexrange(options.pos)] - info['origin']
|
||||||
eulers = table.data[:,table.label_indexrange(options.eulers)] if hasEulers \
|
eulers = table.data[:,table.label_indexrange(options.eulers)] if hasEulers \
|
||||||
else np.zeros(3*len(coords))
|
else np.zeros(3*len(coords))
|
||||||
grains = table.data[:,table.label_indexrange(options.microstructure)].astype('i') if hasGrains \
|
grains = table.data[:,table.label_indexrange(options.microstructure)].astype('i') if hasGrains \
|
||||||
|
|
@ -291,7 +298,7 @@ for name in filenames:
|
||||||
damask.util.croak('tessellating...')
|
damask.util.croak('tessellating...')
|
||||||
|
|
||||||
grid = np.vstack(meshgrid2(x, y, z)).reshape(3,-1).T
|
grid = np.vstack(meshgrid2(x, y, z)).reshape(3,-1).T
|
||||||
indices = laguerreTessellation(grid, coords, weights, grains, options.nonperiodic, options.cpus)
|
indices = laguerreTessellation(grid, coords, weights, grains, options.periodic, options.cpus)
|
||||||
|
|
||||||
# --- write header ------------------------------------------------------------------------
|
# --- write header ------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -31,7 +31,7 @@ parser.add_option('-b',
|
||||||
help = 'blacklist of grain IDs')
|
help = 'blacklist of grain IDs')
|
||||||
parser.add_option('-p',
|
parser.add_option('-p',
|
||||||
'--pos', '--seedposition',
|
'--pos', '--seedposition',
|
||||||
dest = 'position',
|
dest = 'pos',
|
||||||
type = 'string', metavar = 'string',
|
type = 'string', metavar = 'string',
|
||||||
help = 'label of coordinates [%default]')
|
help = 'label of coordinates [%default]')
|
||||||
|
|
||||||
|
|
|
||||||
640
src/math.f90
640
src/math.f90
|
|
@ -6,7 +6,6 @@
|
||||||
!> @brief Mathematical library, including random number generation and tensor represenations
|
!> @brief Mathematical library, including random number generation and tensor represenations
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
module math
|
module math
|
||||||
use, intrinsic :: iso_c_binding
|
|
||||||
use prec, only: &
|
use prec, only: &
|
||||||
pReal, &
|
pReal, &
|
||||||
pInt
|
pInt
|
||||||
|
|
@ -161,13 +160,10 @@ module math
|
||||||
math_rotate_forward3333, &
|
math_rotate_forward3333, &
|
||||||
math_limit
|
math_limit
|
||||||
private :: &
|
private :: &
|
||||||
math_partition, &
|
|
||||||
halton, &
|
halton, &
|
||||||
halton_memory, &
|
halton_memory, &
|
||||||
halton_ndim_set, &
|
halton_ndim_set, &
|
||||||
halton_seed_set, &
|
halton_seed_set
|
||||||
i_to_halton, &
|
|
||||||
prime
|
|
||||||
|
|
||||||
contains
|
contains
|
||||||
|
|
||||||
|
|
@ -289,60 +285,55 @@ recursive subroutine math_qsort(a, istart, iend)
|
||||||
integer(pInt) :: ipivot
|
integer(pInt) :: ipivot
|
||||||
|
|
||||||
if (istart < iend) then
|
if (istart < iend) then
|
||||||
ipivot = math_partition(a,istart, iend)
|
ipivot = qsort_partition(a,istart, iend)
|
||||||
call math_qsort(a, istart, ipivot-1_pInt)
|
call math_qsort(a, istart, ipivot-1_pInt)
|
||||||
call math_qsort(a, ipivot+1_pInt, iend)
|
call math_qsort(a, ipivot+1_pInt, iend)
|
||||||
endif
|
endif
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
contains
|
||||||
|
|
||||||
|
!-------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief Partitioning required for quicksort
|
||||||
|
!-------------------------------------------------------------------------------------------------
|
||||||
|
integer(pInt) function qsort_partition(a, istart, iend)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
integer(pInt), dimension(:,:), intent(inout) :: a
|
||||||
|
integer(pInt), intent(in) :: istart,iend
|
||||||
|
integer(pInt) :: i,j,k,tmp
|
||||||
|
|
||||||
|
do
|
||||||
|
! find the first element on the right side less than or equal to the pivot point
|
||||||
|
do j = iend, istart, -1_pInt
|
||||||
|
if (a(1,j) <= a(1,istart)) exit
|
||||||
|
enddo
|
||||||
|
! find the first element on the left side greater than the pivot point
|
||||||
|
do i = istart, iend
|
||||||
|
if (a(1,i) > a(1,istart)) exit
|
||||||
|
enddo
|
||||||
|
if (i < j) then ! if the indexes do not cross, exchange values
|
||||||
|
do k = 1_pInt, int(size(a,1_pInt), pInt)
|
||||||
|
tmp = a(k,i)
|
||||||
|
a(k,i) = a(k,j)
|
||||||
|
a(k,j) = tmp
|
||||||
|
enddo
|
||||||
|
else ! if they do cross, exchange left value with pivot and return with the partition index
|
||||||
|
do k = 1_pInt, int(size(a,1_pInt), pInt)
|
||||||
|
tmp = a(k,istart)
|
||||||
|
a(k,istart) = a(k,j)
|
||||||
|
a(k,j) = tmp
|
||||||
|
enddo
|
||||||
|
qsort_partition = j
|
||||||
|
return
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
|
||||||
|
end function qsort_partition
|
||||||
|
|
||||||
end subroutine math_qsort
|
end subroutine math_qsort
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief Partitioning required for quicksort
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
integer(pInt) function math_partition(a, istart, iend)
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
integer(pInt), dimension(:,:), intent(inout) :: a
|
|
||||||
integer(pInt), intent(in) :: istart,iend
|
|
||||||
integer(pInt) :: d,i,j,k,x,tmp
|
|
||||||
|
|
||||||
d = int(size(a,1_pInt), pInt) ! number of linked data
|
|
||||||
! set the starting and ending points, and the pivot point
|
|
||||||
|
|
||||||
i = istart
|
|
||||||
|
|
||||||
j = iend
|
|
||||||
x = a(1,istart)
|
|
||||||
do
|
|
||||||
! find the first element on the right side less than or equal to the pivot point
|
|
||||||
do j = j, istart, -1_pInt
|
|
||||||
if (a(1,j) <= x) exit
|
|
||||||
enddo
|
|
||||||
! find the first element on the left side greater than the pivot point
|
|
||||||
do i = i, iend
|
|
||||||
if (a(1,i) > x) exit
|
|
||||||
enddo
|
|
||||||
if (i < j) then ! if the indexes do not cross, exchange values
|
|
||||||
do k = 1_pInt,d
|
|
||||||
tmp = a(k,i)
|
|
||||||
a(k,i) = a(k,j)
|
|
||||||
a(k,j) = tmp
|
|
||||||
enddo
|
|
||||||
else ! if they do cross, exchange left value with pivot and return with the partition index
|
|
||||||
do k = 1_pInt,d
|
|
||||||
tmp = a(k,istart)
|
|
||||||
a(k,istart) = a(k,j)
|
|
||||||
a(k,j) = tmp
|
|
||||||
enddo
|
|
||||||
math_partition = j
|
|
||||||
return
|
|
||||||
endif
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end function math_partition
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
!> @brief range of integers starting at one
|
!> @brief range of integers starting at one
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
|
@ -2189,6 +2180,52 @@ subroutine halton(ndim, r)
|
||||||
value_halton(1) = 1_pInt
|
value_halton(1) = 1_pInt
|
||||||
call halton_memory ('INC', 'SEED', 1_pInt, value_halton)
|
call halton_memory ('INC', 'SEED', 1_pInt, value_halton)
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
contains
|
||||||
|
|
||||||
|
!-------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief computes an element of a Halton sequence.
|
||||||
|
!> @details Only the absolute value of SEED is considered. SEED = 0 is allowed, and returns R = 0.
|
||||||
|
!> @details Halton Bases should be distinct prime numbers. This routine only checks that each base
|
||||||
|
!> @details is greater than 1.
|
||||||
|
!> @details Reference:
|
||||||
|
!> @details J.H. Halton: On the efficiency of certain quasi-random sequences of points in evaluating
|
||||||
|
!> @details multi-dimensional integrals, Numerische Mathematik, Volume 2, pages 84-90, 1960.
|
||||||
|
!> @author John Burkardt
|
||||||
|
!-------------------------------------------------------------------------------------------------
|
||||||
|
subroutine i_to_halton (seed, base, ndim, r)
|
||||||
|
use IO, only: &
|
||||||
|
IO_error
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
integer(pInt), intent(in) :: &
|
||||||
|
ndim, & !< dimension of the sequence
|
||||||
|
seed !< index of the desired element
|
||||||
|
integer(pInt), intent(in), dimension(ndim) :: base !< Halton bases
|
||||||
|
real(pReal), intent(out), dimension(ndim) :: r !< the SEED-th element of the Halton sequence for the given bases
|
||||||
|
|
||||||
|
real(pReal), dimension(ndim) :: base_inv
|
||||||
|
integer(pInt), dimension(ndim) :: &
|
||||||
|
digit, &
|
||||||
|
seed2
|
||||||
|
|
||||||
|
seed2 = abs(seed)
|
||||||
|
r = 0.0_pReal
|
||||||
|
|
||||||
|
if (any (base(1:ndim) <= 1_pInt)) call IO_error(error_ID=405_pInt)
|
||||||
|
|
||||||
|
base_inv(1:ndim) = 1.0_pReal / real (base(1:ndim), pReal)
|
||||||
|
|
||||||
|
do while ( any ( seed2(1:ndim) /= 0_pInt) )
|
||||||
|
digit(1:ndim) = mod ( seed2(1:ndim), base(1:ndim))
|
||||||
|
r(1:ndim) = r(1:ndim) + real ( digit(1:ndim), pReal) * base_inv(1:ndim)
|
||||||
|
base_inv(1:ndim) = base_inv(1:ndim) / real ( base(1:ndim), pReal)
|
||||||
|
seed2(1:ndim) = seed2(1:ndim) / base(1:ndim)
|
||||||
|
enddo
|
||||||
|
|
||||||
|
end subroutine i_to_halton
|
||||||
|
|
||||||
|
|
||||||
end subroutine halton
|
end subroutine halton
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -2205,6 +2242,8 @@ end subroutine halton
|
||||||
!> @author John Burkardt
|
!> @author John Burkardt
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
subroutine halton_memory (action_halton, name_halton, ndim, value_halton)
|
subroutine halton_memory (action_halton, name_halton, ndim, value_halton)
|
||||||
|
use IO, only: &
|
||||||
|
IO_lc
|
||||||
|
|
||||||
implicit none
|
implicit none
|
||||||
character(len = *), intent(in) :: &
|
character(len = *), intent(in) :: &
|
||||||
|
|
@ -2214,8 +2253,8 @@ subroutine halton_memory (action_halton, name_halton, ndim, value_halton)
|
||||||
integer(pInt), allocatable, save, dimension(:) :: base
|
integer(pInt), allocatable, save, dimension(:) :: base
|
||||||
logical, save :: first_call = .true.
|
logical, save :: first_call = .true.
|
||||||
integer(pInt), intent(in) :: ndim !< dimension of the quantity
|
integer(pInt), intent(in) :: ndim !< dimension of the quantity
|
||||||
integer(pInt):: i
|
|
||||||
integer(pInt), save :: ndim_save = 0_pInt, seed = 1_pInt
|
integer(pInt), save :: ndim_save = 0_pInt, seed = 1_pInt
|
||||||
|
integer(pInt) :: i
|
||||||
|
|
||||||
if (first_call) then
|
if (first_call) then
|
||||||
ndim_save = 1_pInt
|
ndim_save = 1_pInt
|
||||||
|
|
@ -2226,60 +2265,237 @@ subroutine halton_memory (action_halton, name_halton, ndim, value_halton)
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
! Set
|
! Set
|
||||||
if(action_halton(1:1) == 'S' .or. action_halton(1:1) == 's') then
|
actionHalton: if(IO_lc(action_halton(1:1)) == 's') then
|
||||||
|
|
||||||
if(name_halton(1:1) == 'B' .or. name_halton(1:1) == 'b') then
|
|
||||||
|
|
||||||
if(ndim_save /= ndim) then
|
|
||||||
deallocate(base)
|
|
||||||
ndim_save = ndim
|
|
||||||
allocate(base(ndim_save))
|
|
||||||
endif
|
|
||||||
|
|
||||||
base(1:ndim) = value_halton(1:ndim)
|
|
||||||
|
|
||||||
elseif(name_halton(1:1) == 'N' .or. name_halton(1:1) == 'n') then
|
|
||||||
|
|
||||||
|
nameSet: if(IO_lc(name_halton(1:1)) == 'b') then
|
||||||
|
if(ndim_save /= ndim) ndim_save = ndim
|
||||||
|
base = value_halton(1:ndim)
|
||||||
|
elseif(IO_lc(name_halton(1:1)) == 'n') then nameSet
|
||||||
if(ndim_save /= value_halton(1)) then
|
if(ndim_save /= value_halton(1)) then
|
||||||
deallocate(base)
|
|
||||||
ndim_save = value_halton(1)
|
ndim_save = value_halton(1)
|
||||||
allocate(base(ndim_save))
|
base = [(prime(i),i=1_pInt,ndim_save)]
|
||||||
do i = 1_pInt, ndim_save
|
|
||||||
base(i) = prime (i)
|
|
||||||
enddo
|
|
||||||
else
|
else
|
||||||
ndim_save = value_halton(1)
|
ndim_save = value_halton(1)
|
||||||
endif
|
endif
|
||||||
elseif(name_halton(1:1) == 'S' .or. name_halton(1:1) == 's') then
|
elseif(IO_lc(name_halton(1:1)) == 's') then nameSet
|
||||||
seed = value_halton(1)
|
seed = value_halton(1)
|
||||||
endif
|
endif nameSet
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
! Get
|
! Get
|
||||||
elseif(action_halton(1:1) == 'G' .or. action_halton(1:1) == 'g') then
|
elseif(IO_lc(action_halton(1:1)) == 'g') then actionHalton
|
||||||
if(name_halton(1:1) == 'B' .or. name_halton(1:1) == 'b') then
|
nameGet: if(IO_lc(name_halton(1:1)) == 'b') then
|
||||||
if(ndim /= ndim_save) then
|
if(ndim /= ndim_save) then
|
||||||
deallocate(base)
|
ndim_save = ndim
|
||||||
ndim_save = ndim
|
base = [(prime(i),i=1_pInt,ndim_save)]
|
||||||
allocate(base(ndim_save))
|
|
||||||
do i = 1_pInt, ndim_save
|
|
||||||
base(i) = prime(i)
|
|
||||||
enddo
|
|
||||||
endif
|
endif
|
||||||
value_halton(1:ndim_save) = base(1:ndim_save)
|
value_halton(1:ndim_save) = base(1:ndim_save)
|
||||||
elseif(name_halton(1:1) == 'N' .or. name_halton(1:1) == 'n') then
|
elseif(IO_lc(name_halton(1:1)) == 'n') then nameGet
|
||||||
value_halton(1) = ndim_save
|
value_halton(1) = ndim_save
|
||||||
elseif(name_halton(1:1) == 'S' .or. name_halton(1:1) == 's') then
|
elseif(IO_lc(name_halton(1:1)) == 's') then nameGet
|
||||||
value_halton(1) = seed
|
value_halton(1) = seed
|
||||||
endif
|
endif nameGet
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
! Increment
|
! Increment
|
||||||
elseif(action_halton(1:1) == 'I' .or. action_halton(1:1) == 'i') then
|
elseif(IO_lc(action_halton(1:1)) == 'i') then actionHalton
|
||||||
if(name_halton(1:1) == 'S' .or. name_halton(1:1) == 's') then
|
if(IO_lc(name_halton(1:1)) == 's') seed = seed + value_halton(1)
|
||||||
seed = seed + value_halton(1)
|
endif actionHalton
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
contains
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief returns any of the first 1500 prime numbers.
|
||||||
|
!> @details n = 0 is legal, returning PRIME = 1.
|
||||||
|
!> @details Reference:
|
||||||
|
!> @details Milton Abramowitz and Irene Stegun: Handbook of Mathematical Functions,
|
||||||
|
!> @details US Department of Commerce, 1964, pages 870-873.
|
||||||
|
!> @details Daniel Zwillinger: CRC Standard Mathematical Tables and Formulae,
|
||||||
|
!> @details 30th Edition, CRC Press, 1996, pages 95-98.
|
||||||
|
!> @author John Burkardt
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
integer(pInt) function prime(n)
|
||||||
|
use IO, only: &
|
||||||
|
IO_error
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
integer(pInt), intent(in) :: n !< index of the desired prime number
|
||||||
|
integer(pInt), dimension(0:1500), parameter :: &
|
||||||
|
npvec = int([&
|
||||||
|
1, &
|
||||||
|
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, &
|
||||||
|
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, &
|
||||||
|
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, &
|
||||||
|
127, 131, 137, 139, 149, 151, 157, 163, 167, 173, &
|
||||||
|
179, 181, 191, 193, 197, 199, 211, 223, 227, 229, &
|
||||||
|
233, 239, 241, 251, 257, 263, 269, 271, 277, 281, &
|
||||||
|
283, 293, 307, 311, 313, 317, 331, 337, 347, 349, &
|
||||||
|
353, 359, 367, 373, 379, 383, 389, 397, 401, 409, &
|
||||||
|
419, 421, 431, 433, 439, 443, 449, 457, 461, 463, &
|
||||||
|
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, &
|
||||||
|
! 101:200
|
||||||
|
547, 557, 563, 569, 571, 577, 587, 593, 599, 601, &
|
||||||
|
607, 613, 617, 619, 631, 641, 643, 647, 653, 659, &
|
||||||
|
661, 673, 677, 683, 691, 701, 709, 719, 727, 733, &
|
||||||
|
739, 743, 751, 757, 761, 769, 773, 787, 797, 809, &
|
||||||
|
811, 821, 823, 827, 829, 839, 853, 857, 859, 863, &
|
||||||
|
877, 881, 883, 887, 907, 911, 919, 929, 937, 941, &
|
||||||
|
947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, &
|
||||||
|
1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, &
|
||||||
|
1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, &
|
||||||
|
1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, &
|
||||||
|
! 201:300
|
||||||
|
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, &
|
||||||
|
1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, &
|
||||||
|
1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, &
|
||||||
|
1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, &
|
||||||
|
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, &
|
||||||
|
1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, &
|
||||||
|
1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, &
|
||||||
|
1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, &
|
||||||
|
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, &
|
||||||
|
1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, &
|
||||||
|
! 301:400
|
||||||
|
1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, &
|
||||||
|
2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, &
|
||||||
|
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, &
|
||||||
|
2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, &
|
||||||
|
2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, &
|
||||||
|
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, &
|
||||||
|
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, &
|
||||||
|
2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, &
|
||||||
|
2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, &
|
||||||
|
2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, &
|
||||||
|
! 401:500
|
||||||
|
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, &
|
||||||
|
2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, &
|
||||||
|
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, &
|
||||||
|
3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, &
|
||||||
|
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, &
|
||||||
|
3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, &
|
||||||
|
3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, &
|
||||||
|
3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, &
|
||||||
|
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, &
|
||||||
|
3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, &
|
||||||
|
! 501:600
|
||||||
|
3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, &
|
||||||
|
3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, &
|
||||||
|
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, &
|
||||||
|
3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, &
|
||||||
|
3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, &
|
||||||
|
4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, &
|
||||||
|
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, &
|
||||||
|
4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, &
|
||||||
|
4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, &
|
||||||
|
4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, &
|
||||||
|
! 601:700
|
||||||
|
4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, &
|
||||||
|
4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, &
|
||||||
|
4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, &
|
||||||
|
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, &
|
||||||
|
4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, &
|
||||||
|
4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, &
|
||||||
|
4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, &
|
||||||
|
5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, &
|
||||||
|
5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, &
|
||||||
|
5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, &
|
||||||
|
! 701:800
|
||||||
|
5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, &
|
||||||
|
5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, &
|
||||||
|
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, &
|
||||||
|
5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, &
|
||||||
|
5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, &
|
||||||
|
5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, &
|
||||||
|
5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, &
|
||||||
|
5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, &
|
||||||
|
5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, &
|
||||||
|
6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, &
|
||||||
|
! 801:900
|
||||||
|
6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, &
|
||||||
|
6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, &
|
||||||
|
6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, &
|
||||||
|
6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, &
|
||||||
|
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, &
|
||||||
|
6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, &
|
||||||
|
6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, &
|
||||||
|
6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, &
|
||||||
|
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, &
|
||||||
|
6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, &
|
||||||
|
! 901:1000
|
||||||
|
7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, &
|
||||||
|
7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, &
|
||||||
|
7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, &
|
||||||
|
7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, &
|
||||||
|
7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, &
|
||||||
|
7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, &
|
||||||
|
7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, &
|
||||||
|
7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, &
|
||||||
|
7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, &
|
||||||
|
7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, &
|
||||||
|
! 1001:1100
|
||||||
|
7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, &
|
||||||
|
8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, &
|
||||||
|
8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, &
|
||||||
|
8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, &
|
||||||
|
8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, &
|
||||||
|
8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, &
|
||||||
|
8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, &
|
||||||
|
8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, &
|
||||||
|
8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, &
|
||||||
|
8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, &
|
||||||
|
! 1101:1200
|
||||||
|
8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, &
|
||||||
|
8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, &
|
||||||
|
9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, &
|
||||||
|
9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, &
|
||||||
|
9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, &
|
||||||
|
9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, &
|
||||||
|
9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, &
|
||||||
|
9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, &
|
||||||
|
9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, &
|
||||||
|
9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, &
|
||||||
|
! 1201:1300
|
||||||
|
9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, &
|
||||||
|
9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, &
|
||||||
|
9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, &
|
||||||
|
10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, &
|
||||||
|
10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, &
|
||||||
|
10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, &
|
||||||
|
10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, &
|
||||||
|
10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, &
|
||||||
|
10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, &
|
||||||
|
10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, &
|
||||||
|
! 1301:1400
|
||||||
|
10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, &
|
||||||
|
10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, &
|
||||||
|
10861, 10867, 10883, 10889, 10891, 10903, 10909, 19037, 10939, 10949, &
|
||||||
|
10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, &
|
||||||
|
11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, &
|
||||||
|
11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, &
|
||||||
|
11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, &
|
||||||
|
11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, &
|
||||||
|
11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, &
|
||||||
|
11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, &
|
||||||
|
! 1401:1500
|
||||||
|
11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, &
|
||||||
|
11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, &
|
||||||
|
11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, &
|
||||||
|
11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, &
|
||||||
|
12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, &
|
||||||
|
12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, &
|
||||||
|
12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, &
|
||||||
|
12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, &
|
||||||
|
12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, &
|
||||||
|
12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553],pInt)
|
||||||
|
|
||||||
|
if (n < size(npvec)) then
|
||||||
|
prime = npvec(n)
|
||||||
|
else
|
||||||
|
call IO_error(error_ID=406_pInt)
|
||||||
end if
|
end if
|
||||||
endif
|
|
||||||
|
end function prime
|
||||||
|
|
||||||
end subroutine halton_memory
|
end subroutine halton_memory
|
||||||
|
|
||||||
|
|
@ -2288,7 +2504,7 @@ end subroutine halton_memory
|
||||||
!> @brief sets the dimension for a Halton sequence
|
!> @brief sets the dimension for a Halton sequence
|
||||||
!> @author John Burkardt
|
!> @author John Burkardt
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
subroutine halton_ndim_set (ndim)
|
subroutine halton_ndim_set(ndim)
|
||||||
|
|
||||||
implicit none
|
implicit none
|
||||||
integer(pInt), intent(in) :: ndim !< dimension of the Halton vectors
|
integer(pInt), intent(in) :: ndim !< dimension of the Halton vectors
|
||||||
|
|
@ -2325,252 +2541,6 @@ subroutine halton_seed_set(seed)
|
||||||
end subroutine halton_seed_set
|
end subroutine halton_seed_set
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief computes an element of a Halton sequence.
|
|
||||||
!> @details Only the absolute value of SEED is considered. SEED = 0 is allowed, and returns R = 0.
|
|
||||||
!> @details Halton Bases should be distinct prime numbers. This routine only checks that each base
|
|
||||||
!> @details is greater than 1.
|
|
||||||
!> @details Reference:
|
|
||||||
!> @details J.H. Halton: On the efficiency of certain quasi-random sequences of points in evaluating
|
|
||||||
!> @details multi-dimensional integrals, Numerische Mathematik, Volume 2, pages 84-90, 1960.
|
|
||||||
!> @author John Burkardt
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
subroutine i_to_halton (seed, base, ndim, r)
|
|
||||||
use IO, only: &
|
|
||||||
IO_error
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
integer(pInt), intent(in) :: ndim !< dimension of the sequence
|
|
||||||
integer(pInt), intent(in), dimension(ndim) :: base !< Halton bases
|
|
||||||
real(pReal), dimension(ndim) :: base_inv
|
|
||||||
integer(pInt), dimension(ndim) :: digit
|
|
||||||
real(pReal), dimension(ndim), intent(out) ::r !< the SEED-th element of the Halton sequence for the given bases
|
|
||||||
integer(pInt) , intent(in):: seed !< index of the desired element
|
|
||||||
integer(pInt), dimension(ndim) :: seed2
|
|
||||||
|
|
||||||
seed2(1:ndim) = abs(seed)
|
|
||||||
|
|
||||||
r(1:ndim) = 0.0_pReal
|
|
||||||
|
|
||||||
if (any (base(1:ndim) <= 1_pInt)) call IO_error(error_ID=405_pInt)
|
|
||||||
|
|
||||||
base_inv(1:ndim) = 1.0_pReal / real (base(1:ndim), pReal)
|
|
||||||
|
|
||||||
do while ( any ( seed2(1:ndim) /= 0_pInt) )
|
|
||||||
digit(1:ndim) = mod ( seed2(1:ndim), base(1:ndim))
|
|
||||||
r(1:ndim) = r(1:ndim) + real ( digit(1:ndim), pReal) * base_inv(1:ndim)
|
|
||||||
base_inv(1:ndim) = base_inv(1:ndim) / real ( base(1:ndim), pReal)
|
|
||||||
seed2(1:ndim) = seed2(1:ndim) / base(1:ndim)
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end subroutine i_to_halton
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief returns any of the first 1500 prime numbers.
|
|
||||||
!> @details n <= 0 returns 1500, the index of the largest prime (12553) available.
|
|
||||||
!> @details n = 0 is legal, returning PRIME = 1.
|
|
||||||
!> @details Reference:
|
|
||||||
!> @details Milton Abramowitz and Irene Stegun: Handbook of Mathematical Functions,
|
|
||||||
!> @details US Department of Commerce, 1964, pages 870-873.
|
|
||||||
!> @details Daniel Zwillinger: CRC Standard Mathematical Tables and Formulae,
|
|
||||||
!> @details 30th Edition, CRC Press, 1996, pages 95-98.
|
|
||||||
!> @author John Burkardt
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
integer(pInt) function prime(n)
|
|
||||||
use IO, only: &
|
|
||||||
IO_error
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
integer(pInt), intent(in) :: n !< index of the desired prime number
|
|
||||||
integer(pInt), parameter :: PRIME_MAX = 1500_pInt
|
|
||||||
integer(pInt), save :: icall = 0_pInt
|
|
||||||
integer(pInt), save, dimension(PRIME_MAX) :: npvec
|
|
||||||
|
|
||||||
if (icall == 0_pInt) then
|
|
||||||
icall = 1_pInt
|
|
||||||
|
|
||||||
npvec = [&
|
|
||||||
2_pInt, 3_pInt, 5_pInt, 7_pInt, 11_pInt, 13_pInt, 17_pInt, 19_pInt, 23_pInt, 29_pInt, &
|
|
||||||
31_pInt, 37_pInt, 41_pInt, 43_pInt, 47_pInt, 53_pInt, 59_pInt, 61_pInt, 67_pInt, 71_pInt, &
|
|
||||||
73_pInt, 79_pInt, 83_pInt, 89_pInt, 97_pInt, 101_pInt, 103_pInt, 107_pInt, 109_pInt, 113_pInt, &
|
|
||||||
127_pInt, 131_pInt, 137_pInt, 139_pInt, 149_pInt, 151_pInt, 157_pInt, 163_pInt, 167_pInt, 173_pInt, &
|
|
||||||
179_pInt, 181_pInt, 191_pInt, 193_pInt, 197_pInt, 199_pInt, 211_pInt, 223_pInt, 227_pInt, 229_pInt, &
|
|
||||||
233_pInt, 239_pInt, 241_pInt, 251_pInt, 257_pInt, 263_pInt, 269_pInt, 271_pInt, 277_pInt, 281_pInt, &
|
|
||||||
283_pInt, 293_pInt, 307_pInt, 311_pInt, 313_pInt, 317_pInt, 331_pInt, 337_pInt, 347_pInt, 349_pInt, &
|
|
||||||
353_pInt, 359_pInt, 367_pInt, 373_pInt, 379_pInt, 383_pInt, 389_pInt, 397_pInt, 401_pInt, 409_pInt, &
|
|
||||||
419_pInt, 421_pInt, 431_pInt, 433_pInt, 439_pInt, 443_pInt, 449_pInt, 457_pInt, 461_pInt, 463_pInt, &
|
|
||||||
467_pInt, 479_pInt, 487_pInt, 491_pInt, 499_pInt, 503_pInt, 509_pInt, 521_pInt, 523_pInt, 541_pInt, &
|
|
||||||
! 101:200
|
|
||||||
547_pInt, 557_pInt, 563_pInt, 569_pInt, 571_pInt, 577_pInt, 587_pInt, 593_pInt, 599_pInt, 601_pInt, &
|
|
||||||
607_pInt, 613_pInt, 617_pInt, 619_pInt, 631_pInt, 641_pInt, 643_pInt, 647_pInt, 653_pInt, 659_pInt, &
|
|
||||||
661_pInt, 673_pInt, 677_pInt, 683_pInt, 691_pInt, 701_pInt, 709_pInt, 719_pInt, 727_pInt, 733_pInt, &
|
|
||||||
739_pInt, 743_pInt, 751_pInt, 757_pInt, 761_pInt, 769_pInt, 773_pInt, 787_pInt, 797_pInt, 809_pInt, &
|
|
||||||
811_pInt, 821_pInt, 823_pInt, 827_pInt, 829_pInt, 839_pInt, 853_pInt, 857_pInt, 859_pInt, 863_pInt, &
|
|
||||||
877_pInt, 881_pInt, 883_pInt, 887_pInt, 907_pInt, 911_pInt, 919_pInt, 929_pInt, 937_pInt, 941_pInt, &
|
|
||||||
947_pInt, 953_pInt, 967_pInt, 971_pInt, 977_pInt, 983_pInt, 991_pInt, 997_pInt, 1009_pInt, 1013_pInt, &
|
|
||||||
1019_pInt, 1021_pInt, 1031_pInt, 1033_pInt, 1039_pInt, 1049_pInt, 1051_pInt, 1061_pInt, 1063_pInt, 1069_pInt, &
|
|
||||||
1087_pInt, 1091_pInt, 1093_pInt, 1097_pInt, 1103_pInt, 1109_pInt, 1117_pInt, 1123_pInt, 1129_pInt, 1151_pInt, &
|
|
||||||
1153_pInt, 1163_pInt, 1171_pInt, 1181_pInt, 1187_pInt, 1193_pInt, 1201_pInt, 1213_pInt, 1217_pInt, 1223_pInt, &
|
|
||||||
! 201:300
|
|
||||||
1229_pInt, 1231_pInt, 1237_pInt, 1249_pInt, 1259_pInt, 1277_pInt, 1279_pInt, 1283_pInt, 1289_pInt, 1291_pInt, &
|
|
||||||
1297_pInt, 1301_pInt, 1303_pInt, 1307_pInt, 1319_pInt, 1321_pInt, 1327_pInt, 1361_pInt, 1367_pInt, 1373_pInt, &
|
|
||||||
1381_pInt, 1399_pInt, 1409_pInt, 1423_pInt, 1427_pInt, 1429_pInt, 1433_pInt, 1439_pInt, 1447_pInt, 1451_pInt, &
|
|
||||||
1453_pInt, 1459_pInt, 1471_pInt, 1481_pInt, 1483_pInt, 1487_pInt, 1489_pInt, 1493_pInt, 1499_pInt, 1511_pInt, &
|
|
||||||
1523_pInt, 1531_pInt, 1543_pInt, 1549_pInt, 1553_pInt, 1559_pInt, 1567_pInt, 1571_pInt, 1579_pInt, 1583_pInt, &
|
|
||||||
1597_pInt, 1601_pInt, 1607_pInt, 1609_pInt, 1613_pInt, 1619_pInt, 1621_pInt, 1627_pInt, 1637_pInt, 1657_pInt, &
|
|
||||||
1663_pInt, 1667_pInt, 1669_pInt, 1693_pInt, 1697_pInt, 1699_pInt, 1709_pInt, 1721_pInt, 1723_pInt, 1733_pInt, &
|
|
||||||
1741_pInt, 1747_pInt, 1753_pInt, 1759_pInt, 1777_pInt, 1783_pInt, 1787_pInt, 1789_pInt, 1801_pInt, 1811_pInt, &
|
|
||||||
1823_pInt, 1831_pInt, 1847_pInt, 1861_pInt, 1867_pInt, 1871_pInt, 1873_pInt, 1877_pInt, 1879_pInt, 1889_pInt, &
|
|
||||||
1901_pInt, 1907_pInt, 1913_pInt, 1931_pInt, 1933_pInt, 1949_pInt, 1951_pInt, 1973_pInt, 1979_pInt, 1987_pInt, &
|
|
||||||
! 301:400
|
|
||||||
1993_pInt, 1997_pInt, 1999_pInt, 2003_pInt, 2011_pInt, 2017_pInt, 2027_pInt, 2029_pInt, 2039_pInt, 2053_pInt, &
|
|
||||||
2063_pInt, 2069_pInt, 2081_pInt, 2083_pInt, 2087_pInt, 2089_pInt, 2099_pInt, 2111_pInt, 2113_pInt, 2129_pInt, &
|
|
||||||
2131_pInt, 2137_pInt, 2141_pInt, 2143_pInt, 2153_pInt, 2161_pInt, 2179_pInt, 2203_pInt, 2207_pInt, 2213_pInt, &
|
|
||||||
2221_pInt, 2237_pInt, 2239_pInt, 2243_pInt, 2251_pInt, 2267_pInt, 2269_pInt, 2273_pInt, 2281_pInt, 2287_pInt, &
|
|
||||||
2293_pInt, 2297_pInt, 2309_pInt, 2311_pInt, 2333_pInt, 2339_pInt, 2341_pInt, 2347_pInt, 2351_pInt, 2357_pInt, &
|
|
||||||
2371_pInt, 2377_pInt, 2381_pInt, 2383_pInt, 2389_pInt, 2393_pInt, 2399_pInt, 2411_pInt, 2417_pInt, 2423_pInt, &
|
|
||||||
2437_pInt, 2441_pInt, 2447_pInt, 2459_pInt, 2467_pInt, 2473_pInt, 2477_pInt, 2503_pInt, 2521_pInt, 2531_pInt, &
|
|
||||||
2539_pInt, 2543_pInt, 2549_pInt, 2551_pInt, 2557_pInt, 2579_pInt, 2591_pInt, 2593_pInt, 2609_pInt, 2617_pInt, &
|
|
||||||
2621_pInt, 2633_pInt, 2647_pInt, 2657_pInt, 2659_pInt, 2663_pInt, 2671_pInt, 2677_pInt, 2683_pInt, 2687_pInt, &
|
|
||||||
2689_pInt, 2693_pInt, 2699_pInt, 2707_pInt, 2711_pInt, 2713_pInt, 2719_pInt, 2729_pInt, 2731_pInt, 2741_pInt, &
|
|
||||||
! 401:500
|
|
||||||
2749_pInt, 2753_pInt, 2767_pInt, 2777_pInt, 2789_pInt, 2791_pInt, 2797_pInt, 2801_pInt, 2803_pInt, 2819_pInt, &
|
|
||||||
2833_pInt, 2837_pInt, 2843_pInt, 2851_pInt, 2857_pInt, 2861_pInt, 2879_pInt, 2887_pInt, 2897_pInt, 2903_pInt, &
|
|
||||||
2909_pInt, 2917_pInt, 2927_pInt, 2939_pInt, 2953_pInt, 2957_pInt, 2963_pInt, 2969_pInt, 2971_pInt, 2999_pInt, &
|
|
||||||
3001_pInt, 3011_pInt, 3019_pInt, 3023_pInt, 3037_pInt, 3041_pInt, 3049_pInt, 3061_pInt, 3067_pInt, 3079_pInt, &
|
|
||||||
3083_pInt, 3089_pInt, 3109_pInt, 3119_pInt, 3121_pInt, 3137_pInt, 3163_pInt, 3167_pInt, 3169_pInt, 3181_pInt, &
|
|
||||||
3187_pInt, 3191_pInt, 3203_pInt, 3209_pInt, 3217_pInt, 3221_pInt, 3229_pInt, 3251_pInt, 3253_pInt, 3257_pInt, &
|
|
||||||
3259_pInt, 3271_pInt, 3299_pInt, 3301_pInt, 3307_pInt, 3313_pInt, 3319_pInt, 3323_pInt, 3329_pInt, 3331_pInt, &
|
|
||||||
3343_pInt, 3347_pInt, 3359_pInt, 3361_pInt, 3371_pInt, 3373_pInt, 3389_pInt, 3391_pInt, 3407_pInt, 3413_pInt, &
|
|
||||||
3433_pInt, 3449_pInt, 3457_pInt, 3461_pInt, 3463_pInt, 3467_pInt, 3469_pInt, 3491_pInt, 3499_pInt, 3511_pInt, &
|
|
||||||
3517_pInt, 3527_pInt, 3529_pInt, 3533_pInt, 3539_pInt, 3541_pInt, 3547_pInt, 3557_pInt, 3559_pInt, 3571_pInt, &
|
|
||||||
! 501:600
|
|
||||||
3581_pInt, 3583_pInt, 3593_pInt, 3607_pInt, 3613_pInt, 3617_pInt, 3623_pInt, 3631_pInt, 3637_pInt, 3643_pInt, &
|
|
||||||
3659_pInt, 3671_pInt, 3673_pInt, 3677_pInt, 3691_pInt, 3697_pInt, 3701_pInt, 3709_pInt, 3719_pInt, 3727_pInt, &
|
|
||||||
3733_pInt, 3739_pInt, 3761_pInt, 3767_pInt, 3769_pInt, 3779_pInt, 3793_pInt, 3797_pInt, 3803_pInt, 3821_pInt, &
|
|
||||||
3823_pInt, 3833_pInt, 3847_pInt, 3851_pInt, 3853_pInt, 3863_pInt, 3877_pInt, 3881_pInt, 3889_pInt, 3907_pInt, &
|
|
||||||
3911_pInt, 3917_pInt, 3919_pInt, 3923_pInt, 3929_pInt, 3931_pInt, 3943_pInt, 3947_pInt, 3967_pInt, 3989_pInt, &
|
|
||||||
4001_pInt, 4003_pInt, 4007_pInt, 4013_pInt, 4019_pInt, 4021_pInt, 4027_pInt, 4049_pInt, 4051_pInt, 4057_pInt, &
|
|
||||||
4073_pInt, 4079_pInt, 4091_pInt, 4093_pInt, 4099_pInt, 4111_pInt, 4127_pInt, 4129_pInt, 4133_pInt, 4139_pInt, &
|
|
||||||
4153_pInt, 4157_pInt, 4159_pInt, 4177_pInt, 4201_pInt, 4211_pInt, 4217_pInt, 4219_pInt, 4229_pInt, 4231_pInt, &
|
|
||||||
4241_pInt, 4243_pInt, 4253_pInt, 4259_pInt, 4261_pInt, 4271_pInt, 4273_pInt, 4283_pInt, 4289_pInt, 4297_pInt, &
|
|
||||||
4327_pInt, 4337_pInt, 4339_pInt, 4349_pInt, 4357_pInt, 4363_pInt, 4373_pInt, 4391_pInt, 4397_pInt, 4409_pInt, &
|
|
||||||
! 601:700
|
|
||||||
4421_pInt, 4423_pInt, 4441_pInt, 4447_pInt, 4451_pInt, 4457_pInt, 4463_pInt, 4481_pInt, 4483_pInt, 4493_pInt, &
|
|
||||||
4507_pInt, 4513_pInt, 4517_pInt, 4519_pInt, 4523_pInt, 4547_pInt, 4549_pInt, 4561_pInt, 4567_pInt, 4583_pInt, &
|
|
||||||
4591_pInt, 4597_pInt, 4603_pInt, 4621_pInt, 4637_pInt, 4639_pInt, 4643_pInt, 4649_pInt, 4651_pInt, 4657_pInt, &
|
|
||||||
4663_pInt, 4673_pInt, 4679_pInt, 4691_pInt, 4703_pInt, 4721_pInt, 4723_pInt, 4729_pInt, 4733_pInt, 4751_pInt, &
|
|
||||||
4759_pInt, 4783_pInt, 4787_pInt, 4789_pInt, 4793_pInt, 4799_pInt, 4801_pInt, 4813_pInt, 4817_pInt, 4831_pInt, &
|
|
||||||
4861_pInt, 4871_pInt, 4877_pInt, 4889_pInt, 4903_pInt, 4909_pInt, 4919_pInt, 4931_pInt, 4933_pInt, 4937_pInt, &
|
|
||||||
4943_pInt, 4951_pInt, 4957_pInt, 4967_pInt, 4969_pInt, 4973_pInt, 4987_pInt, 4993_pInt, 4999_pInt, 5003_pInt, &
|
|
||||||
5009_pInt, 5011_pInt, 5021_pInt, 5023_pInt, 5039_pInt, 5051_pInt, 5059_pInt, 5077_pInt, 5081_pInt, 5087_pInt, &
|
|
||||||
5099_pInt, 5101_pInt, 5107_pInt, 5113_pInt, 5119_pInt, 5147_pInt, 5153_pInt, 5167_pInt, 5171_pInt, 5179_pInt, &
|
|
||||||
5189_pInt, 5197_pInt, 5209_pInt, 5227_pInt, 5231_pInt, 5233_pInt, 5237_pInt, 5261_pInt, 5273_pInt, 5279_pInt, &
|
|
||||||
! 701:800
|
|
||||||
5281_pInt, 5297_pInt, 5303_pInt, 5309_pInt, 5323_pInt, 5333_pInt, 5347_pInt, 5351_pInt, 5381_pInt, 5387_pInt, &
|
|
||||||
5393_pInt, 5399_pInt, 5407_pInt, 5413_pInt, 5417_pInt, 5419_pInt, 5431_pInt, 5437_pInt, 5441_pInt, 5443_pInt, &
|
|
||||||
5449_pInt, 5471_pInt, 5477_pInt, 5479_pInt, 5483_pInt, 5501_pInt, 5503_pInt, 5507_pInt, 5519_pInt, 5521_pInt, &
|
|
||||||
5527_pInt, 5531_pInt, 5557_pInt, 5563_pInt, 5569_pInt, 5573_pInt, 5581_pInt, 5591_pInt, 5623_pInt, 5639_pInt, &
|
|
||||||
5641_pInt, 5647_pInt, 5651_pInt, 5653_pInt, 5657_pInt, 5659_pInt, 5669_pInt, 5683_pInt, 5689_pInt, 5693_pInt, &
|
|
||||||
5701_pInt, 5711_pInt, 5717_pInt, 5737_pInt, 5741_pInt, 5743_pInt, 5749_pInt, 5779_pInt, 5783_pInt, 5791_pInt, &
|
|
||||||
5801_pInt, 5807_pInt, 5813_pInt, 5821_pInt, 5827_pInt, 5839_pInt, 5843_pInt, 5849_pInt, 5851_pInt, 5857_pInt, &
|
|
||||||
5861_pInt, 5867_pInt, 5869_pInt, 5879_pInt, 5881_pInt, 5897_pInt, 5903_pInt, 5923_pInt, 5927_pInt, 5939_pInt, &
|
|
||||||
5953_pInt, 5981_pInt, 5987_pInt, 6007_pInt, 6011_pInt, 6029_pInt, 6037_pInt, 6043_pInt, 6047_pInt, 6053_pInt, &
|
|
||||||
6067_pInt, 6073_pInt, 6079_pInt, 6089_pInt, 6091_pInt, 6101_pInt, 6113_pInt, 6121_pInt, 6131_pInt, 6133_pInt, &
|
|
||||||
! 801:900
|
|
||||||
6143_pInt, 6151_pInt, 6163_pInt, 6173_pInt, 6197_pInt, 6199_pInt, 6203_pInt, 6211_pInt, 6217_pInt, 6221_pInt, &
|
|
||||||
6229_pInt, 6247_pInt, 6257_pInt, 6263_pInt, 6269_pInt, 6271_pInt, 6277_pInt, 6287_pInt, 6299_pInt, 6301_pInt, &
|
|
||||||
6311_pInt, 6317_pInt, 6323_pInt, 6329_pInt, 6337_pInt, 6343_pInt, 6353_pInt, 6359_pInt, 6361_pInt, 6367_pInt, &
|
|
||||||
6373_pInt, 6379_pInt, 6389_pInt, 6397_pInt, 6421_pInt, 6427_pInt, 6449_pInt, 6451_pInt, 6469_pInt, 6473_pInt, &
|
|
||||||
6481_pInt, 6491_pInt, 6521_pInt, 6529_pInt, 6547_pInt, 6551_pInt, 6553_pInt, 6563_pInt, 6569_pInt, 6571_pInt, &
|
|
||||||
6577_pInt, 6581_pInt, 6599_pInt, 6607_pInt, 6619_pInt, 6637_pInt, 6653_pInt, 6659_pInt, 6661_pInt, 6673_pInt, &
|
|
||||||
6679_pInt, 6689_pInt, 6691_pInt, 6701_pInt, 6703_pInt, 6709_pInt, 6719_pInt, 6733_pInt, 6737_pInt, 6761_pInt, &
|
|
||||||
6763_pInt, 6779_pInt, 6781_pInt, 6791_pInt, 6793_pInt, 6803_pInt, 6823_pInt, 6827_pInt, 6829_pInt, 6833_pInt, &
|
|
||||||
6841_pInt, 6857_pInt, 6863_pInt, 6869_pInt, 6871_pInt, 6883_pInt, 6899_pInt, 6907_pInt, 6911_pInt, 6917_pInt, &
|
|
||||||
6947_pInt, 6949_pInt, 6959_pInt, 6961_pInt, 6967_pInt, 6971_pInt, 6977_pInt, 6983_pInt, 6991_pInt, 6997_pInt, &
|
|
||||||
! 901:1000
|
|
||||||
7001_pInt, 7013_pInt, 7019_pInt, 7027_pInt, 7039_pInt, 7043_pInt, 7057_pInt, 7069_pInt, 7079_pInt, 7103_pInt, &
|
|
||||||
7109_pInt, 7121_pInt, 7127_pInt, 7129_pInt, 7151_pInt, 7159_pInt, 7177_pInt, 7187_pInt, 7193_pInt, 7207_pInt, &
|
|
||||||
7211_pInt, 7213_pInt, 7219_pInt, 7229_pInt, 7237_pInt, 7243_pInt, 7247_pInt, 7253_pInt, 7283_pInt, 7297_pInt, &
|
|
||||||
7307_pInt, 7309_pInt, 7321_pInt, 7331_pInt, 7333_pInt, 7349_pInt, 7351_pInt, 7369_pInt, 7393_pInt, 7411_pInt, &
|
|
||||||
7417_pInt, 7433_pInt, 7451_pInt, 7457_pInt, 7459_pInt, 7477_pInt, 7481_pInt, 7487_pInt, 7489_pInt, 7499_pInt, &
|
|
||||||
7507_pInt, 7517_pInt, 7523_pInt, 7529_pInt, 7537_pInt, 7541_pInt, 7547_pInt, 7549_pInt, 7559_pInt, 7561_pInt, &
|
|
||||||
7573_pInt, 7577_pInt, 7583_pInt, 7589_pInt, 7591_pInt, 7603_pInt, 7607_pInt, 7621_pInt, 7639_pInt, 7643_pInt, &
|
|
||||||
7649_pInt, 7669_pInt, 7673_pInt, 7681_pInt, 7687_pInt, 7691_pInt, 7699_pInt, 7703_pInt, 7717_pInt, 7723_pInt, &
|
|
||||||
7727_pInt, 7741_pInt, 7753_pInt, 7757_pInt, 7759_pInt, 7789_pInt, 7793_pInt, 7817_pInt, 7823_pInt, 7829_pInt, &
|
|
||||||
7841_pInt, 7853_pInt, 7867_pInt, 7873_pInt, 7877_pInt, 7879_pInt, 7883_pInt, 7901_pInt, 7907_pInt, 7919_pInt, &
|
|
||||||
! 1001:1100
|
|
||||||
7927_pInt, 7933_pInt, 7937_pInt, 7949_pInt, 7951_pInt, 7963_pInt, 7993_pInt, 8009_pInt, 8011_pInt, 8017_pInt, &
|
|
||||||
8039_pInt, 8053_pInt, 8059_pInt, 8069_pInt, 8081_pInt, 8087_pInt, 8089_pInt, 8093_pInt, 8101_pInt, 8111_pInt, &
|
|
||||||
8117_pInt, 8123_pInt, 8147_pInt, 8161_pInt, 8167_pInt, 8171_pInt, 8179_pInt, 8191_pInt, 8209_pInt, 8219_pInt, &
|
|
||||||
8221_pInt, 8231_pInt, 8233_pInt, 8237_pInt, 8243_pInt, 8263_pInt, 8269_pInt, 8273_pInt, 8287_pInt, 8291_pInt, &
|
|
||||||
8293_pInt, 8297_pInt, 8311_pInt, 8317_pInt, 8329_pInt, 8353_pInt, 8363_pInt, 8369_pInt, 8377_pInt, 8387_pInt, &
|
|
||||||
8389_pInt, 8419_pInt, 8423_pInt, 8429_pInt, 8431_pInt, 8443_pInt, 8447_pInt, 8461_pInt, 8467_pInt, 8501_pInt, &
|
|
||||||
8513_pInt, 8521_pInt, 8527_pInt, 8537_pInt, 8539_pInt, 8543_pInt, 8563_pInt, 8573_pInt, 8581_pInt, 8597_pInt, &
|
|
||||||
8599_pInt, 8609_pInt, 8623_pInt, 8627_pInt, 8629_pInt, 8641_pInt, 8647_pInt, 8663_pInt, 8669_pInt, 8677_pInt, &
|
|
||||||
8681_pInt, 8689_pInt, 8693_pInt, 8699_pInt, 8707_pInt, 8713_pInt, 8719_pInt, 8731_pInt, 8737_pInt, 8741_pInt, &
|
|
||||||
8747_pInt, 8753_pInt, 8761_pInt, 8779_pInt, 8783_pInt, 8803_pInt, 8807_pInt, 8819_pInt, 8821_pInt, 8831_pInt, &
|
|
||||||
! 1101:1200
|
|
||||||
8837_pInt, 8839_pInt, 8849_pInt, 8861_pInt, 8863_pInt, 8867_pInt, 8887_pInt, 8893_pInt, 8923_pInt, 8929_pInt, &
|
|
||||||
8933_pInt, 8941_pInt, 8951_pInt, 8963_pInt, 8969_pInt, 8971_pInt, 8999_pInt, 9001_pInt, 9007_pInt, 9011_pInt, &
|
|
||||||
9013_pInt, 9029_pInt, 9041_pInt, 9043_pInt, 9049_pInt, 9059_pInt, 9067_pInt, 9091_pInt, 9103_pInt, 9109_pInt, &
|
|
||||||
9127_pInt, 9133_pInt, 9137_pInt, 9151_pInt, 9157_pInt, 9161_pInt, 9173_pInt, 9181_pInt, 9187_pInt, 9199_pInt, &
|
|
||||||
9203_pInt, 9209_pInt, 9221_pInt, 9227_pInt, 9239_pInt, 9241_pInt, 9257_pInt, 9277_pInt, 9281_pInt, 9283_pInt, &
|
|
||||||
9293_pInt, 9311_pInt, 9319_pInt, 9323_pInt, 9337_pInt, 9341_pInt, 9343_pInt, 9349_pInt, 9371_pInt, 9377_pInt, &
|
|
||||||
9391_pInt, 9397_pInt, 9403_pInt, 9413_pInt, 9419_pInt, 9421_pInt, 9431_pInt, 9433_pInt, 9437_pInt, 9439_pInt, &
|
|
||||||
9461_pInt, 9463_pInt, 9467_pInt, 9473_pInt, 9479_pInt, 9491_pInt, 9497_pInt, 9511_pInt, 9521_pInt, 9533_pInt, &
|
|
||||||
9539_pInt, 9547_pInt, 9551_pInt, 9587_pInt, 9601_pInt, 9613_pInt, 9619_pInt, 9623_pInt, 9629_pInt, 9631_pInt, &
|
|
||||||
9643_pInt, 9649_pInt, 9661_pInt, 9677_pInt, 9679_pInt, 9689_pInt, 9697_pInt, 9719_pInt, 9721_pInt, 9733_pInt, &
|
|
||||||
! 1201:1300
|
|
||||||
9739_pInt, 9743_pInt, 9749_pInt, 9767_pInt, 9769_pInt, 9781_pInt, 9787_pInt, 9791_pInt, 9803_pInt, 9811_pInt, &
|
|
||||||
9817_pInt, 9829_pInt, 9833_pInt, 9839_pInt, 9851_pInt, 9857_pInt, 9859_pInt, 9871_pInt, 9883_pInt, 9887_pInt, &
|
|
||||||
9901_pInt, 9907_pInt, 9923_pInt, 9929_pInt, 9931_pInt, 9941_pInt, 9949_pInt, 9967_pInt, 9973_pInt,10007_pInt, &
|
|
||||||
10009_pInt,10037_pInt,10039_pInt,10061_pInt,10067_pInt,10069_pInt,10079_pInt,10091_pInt,10093_pInt,10099_pInt, &
|
|
||||||
10103_pInt,10111_pInt,10133_pInt,10139_pInt,10141_pInt,10151_pInt,10159_pInt,10163_pInt,10169_pInt,10177_pInt, &
|
|
||||||
10181_pInt,10193_pInt,10211_pInt,10223_pInt,10243_pInt,10247_pInt,10253_pInt,10259_pInt,10267_pInt,10271_pInt, &
|
|
||||||
10273_pInt,10289_pInt,10301_pInt,10303_pInt,10313_pInt,10321_pInt,10331_pInt,10333_pInt,10337_pInt,10343_pInt, &
|
|
||||||
10357_pInt,10369_pInt,10391_pInt,10399_pInt,10427_pInt,10429_pInt,10433_pInt,10453_pInt,10457_pInt,10459_pInt, &
|
|
||||||
10463_pInt,10477_pInt,10487_pInt,10499_pInt,10501_pInt,10513_pInt,10529_pInt,10531_pInt,10559_pInt,10567_pInt, &
|
|
||||||
10589_pInt,10597_pInt,10601_pInt,10607_pInt,10613_pInt,10627_pInt,10631_pInt,10639_pInt,10651_pInt,10657_pInt, &
|
|
||||||
! 1301:1400
|
|
||||||
10663_pInt,10667_pInt,10687_pInt,10691_pInt,10709_pInt,10711_pInt,10723_pInt,10729_pInt,10733_pInt,10739_pInt, &
|
|
||||||
10753_pInt,10771_pInt,10781_pInt,10789_pInt,10799_pInt,10831_pInt,10837_pInt,10847_pInt,10853_pInt,10859_pInt, &
|
|
||||||
10861_pInt,10867_pInt,10883_pInt,10889_pInt,10891_pInt,10903_pInt,10909_pInt,19037_pInt,10939_pInt,10949_pInt, &
|
|
||||||
10957_pInt,10973_pInt,10979_pInt,10987_pInt,10993_pInt,11003_pInt,11027_pInt,11047_pInt,11057_pInt,11059_pInt, &
|
|
||||||
11069_pInt,11071_pInt,11083_pInt,11087_pInt,11093_pInt,11113_pInt,11117_pInt,11119_pInt,11131_pInt,11149_pInt, &
|
|
||||||
11159_pInt,11161_pInt,11171_pInt,11173_pInt,11177_pInt,11197_pInt,11213_pInt,11239_pInt,11243_pInt,11251_pInt, &
|
|
||||||
11257_pInt,11261_pInt,11273_pInt,11279_pInt,11287_pInt,11299_pInt,11311_pInt,11317_pInt,11321_pInt,11329_pInt, &
|
|
||||||
11351_pInt,11353_pInt,11369_pInt,11383_pInt,11393_pInt,11399_pInt,11411_pInt,11423_pInt,11437_pInt,11443_pInt, &
|
|
||||||
11447_pInt,11467_pInt,11471_pInt,11483_pInt,11489_pInt,11491_pInt,11497_pInt,11503_pInt,11519_pInt,11527_pInt, &
|
|
||||||
11549_pInt,11551_pInt,11579_pInt,11587_pInt,11593_pInt,11597_pInt,11617_pInt,11621_pInt,11633_pInt,11657_pInt, &
|
|
||||||
! 1401:1500
|
|
||||||
11677_pInt,11681_pInt,11689_pInt,11699_pInt,11701_pInt,11717_pInt,11719_pInt,11731_pInt,11743_pInt,11777_pInt, &
|
|
||||||
11779_pInt,11783_pInt,11789_pInt,11801_pInt,11807_pInt,11813_pInt,11821_pInt,11827_pInt,11831_pInt,11833_pInt, &
|
|
||||||
11839_pInt,11863_pInt,11867_pInt,11887_pInt,11897_pInt,11903_pInt,11909_pInt,11923_pInt,11927_pInt,11933_pInt, &
|
|
||||||
11939_pInt,11941_pInt,11953_pInt,11959_pInt,11969_pInt,11971_pInt,11981_pInt,11987_pInt,12007_pInt,12011_pInt, &
|
|
||||||
12037_pInt,12041_pInt,12043_pInt,12049_pInt,12071_pInt,12073_pInt,12097_pInt,12101_pInt,12107_pInt,12109_pInt, &
|
|
||||||
12113_pInt,12119_pInt,12143_pInt,12149_pInt,12157_pInt,12161_pInt,12163_pInt,12197_pInt,12203_pInt,12211_pInt, &
|
|
||||||
12227_pInt,12239_pInt,12241_pInt,12251_pInt,12253_pInt,12263_pInt,12269_pInt,12277_pInt,12281_pInt,12289_pInt, &
|
|
||||||
12301_pInt,12323_pInt,12329_pInt,12343_pInt,12347_pInt,12373_pInt,12377_pInt,12379_pInt,12391_pInt,12401_pInt, &
|
|
||||||
12409_pInt,12413_pInt,12421_pInt,12433_pInt,12437_pInt,12451_pInt,12457_pInt,12473_pInt,12479_pInt,12487_pInt, &
|
|
||||||
12491_pInt,12497_pInt,12503_pInt,12511_pInt,12517_pInt,12527_pInt,12539_pInt,12541_pInt,12547_pInt,12553_pInt]
|
|
||||||
endif
|
|
||||||
|
|
||||||
if(n < 0_pInt) then
|
|
||||||
prime = PRIME_MAX
|
|
||||||
else if (n == 0_pInt) then
|
|
||||||
prime = 1_pInt
|
|
||||||
else if (n <= PRIME_MAX) then
|
|
||||||
prime = npvec(n)
|
|
||||||
else
|
|
||||||
prime = -1_pInt
|
|
||||||
call IO_error(error_ID=406_pInt)
|
|
||||||
end if
|
|
||||||
|
|
||||||
end function prime
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
!> @brief factorial
|
!> @brief factorial
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue