sortTies is a bottleneck when adding ties to a multi-domain function

[RichardWaiteSTFC]

Describe the bug

In PR #38515 a MultiDomainFunction is used to share peak parameters across adjacent pixels.

However the execution time for the algorithm IntegratePeaks1DProfile has increased by an order of magnitude (or more!) - the bottleneck is due to sortTies being run for each tie added. The actual fit is very quick.

mantid/Framework/API/src/IFunction.cpp

Line 1600 in 13795d0

void IFunction::sortTies(const bool checkOnly) {

To Reproduce
(1) Run this script in debug with a breakpoint at the line above

from mantid.simpleapi import *
from mantid.api import MultiDomainFunction, FunctionFactory
from mantid.fitfunctions import FunctionWrapper
                          

comp_func = CompositeFunction(Gaussian(Height=1, Sigma=0.3, PeakCentre=3), FunctionWrapper("FlatBackground"), NumDeriv=True)
ws = CreateSampleWorkspace(OutputWorkspace='ws', Function='User Defined', UserDefinedFunction=str(comp_func), XUnit='DeltaE', 
                           XMax=7, BinWidth=0.1, NumBanks=1, BankPixelWidth=2)

func = MultiDomainFunction()        
md_fit_kwargs = {}
for ispec in range(ws.getNumberHistograms()):
    func.add(comp_func.function)
    func.setDomainIndex(ispec,ispec)
    key_suffix = f"_{ispec}" if ispec > 0 else ""
    md_fit_kwargs["InputWorkspace" + key_suffix] = ws.name()
    md_fit_kwargs["StartX" + key_suffix] = 0.1
    md_fit_kwargs["EndX" + key_suffix] = 6.8
    md_fit_kwargs["WorkspaceIndex" + key_suffix] = ispec

add_ties = True
if add_ties:
    ties = []
    for idom in range(1, ws.getNumberHistograms()):
        for ifunc in range(func[0].nFunctions()):
            for ipar in range(func[0][ifunc].nParams()):
                par = func[0][ifunc].getParamName(ipar)
                ties.append(f"f{idom}.f{ifunc}.{par}=f0.f{ifunc}.{par}")
    func_str = f"{str(func)};ties=({','.join(ties)})"
else:
    func_str = str(func)
    
out = Fit(Function=func_str, Output='ws', StoreInADS=True, CreateOutput=True, OutputCompositeMembers=True,
          **md_fit_kwargs)

You will see sortTies gets called for every tie

(2) Increase the number of spectra

ws = CreateSampleWorkspace(OutputWorkspace='ws', Function='User Defined', UserDefinedFunction=str(comp_func), XUnit='DeltaE', 
                           XMax=7, BinWidth=0.1, NumBanks=25, BankPixelWidth=2)

Observe that it takes a lot longer - if you set this too high (e.g. NumBanks=100 Mantid will hang)

Expected behavior
Would call sortTies once after all ties added?

Screenshots

Platform/Version (please complete the following information):

• OS: [e.g. Windows, RHEL 7, Ubuntu, macOS]
• OS Version:
• Mantid Version [e.g. 6.0.0]

Additional context