Comp-phys-alps-users

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1244 discussions

XYZ interaction in alps-looper algorithm
by Saeed S. Jahromi 17 Oct '15

17 Oct '15

Dear All, I am trying to run the QMC "loop" code for the Kitaev honeycomb model which is actually an XYZ two-spin interaction on a honeycomb lattice with three different link types i.e. x,y and z. *The parameter file that I use is defined as:* parms = [] for t in [0.05, 0.1, 0.2, 0.3]: parms.append( { 'LATTICE' : "honeycomb kitaev lattice", 'T' : t, 'Jx' : .1 , 'Jz' : .1 , 'Jy' : .1 , 'ALGORITHM' : "loop", 'THERMALIZATION' : 65536/8, 'SWEEPS' : 65536, 'MODEL' : "K-H", 'L' : 4 } ) *The model that I use is defined as: * <HAMILTONIAN name="K-H"> <PARAMETER name="Jz" default="0"/> <PARAMETER name="Jx" default="0"/> <PARAMETER name="Jy" default="0"/> <PARAMETER name="hx" default="0"/> <PARAMETER name="hz" default="0"/> <BASIS ref="spin"/> <SITETERM site="i"> -hz*Sz(i)-hx*Sx(i) </SITETERM> <BONDTERM type="0" source="i" target="j"> Jz*Sz(i)*Sz(j) </BONDTERM> <BONDTERM type="1" source="i" target="j"> Jx*Sx(i)*Sx(j) </BONDTERM> <BONDTERM type="2" source="i" target="j"> Jy*Sy(i)*Sy(j) </BONDTERM> </HAMILTONIAN> *and the lattice is defined as**:* <UNITCELL name="honeycomb inhomogeneous" dimension="2"> <VERTEX><COORDINATE>0 0</COORDINATE></VERTEX> <VERTEX><COORDINATE>-0.288665771484375 0.5773468017578125</COORDINATE></VERTEX> <EDGE type="0"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="1" offset="0 1"/></EDGE> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2" offset="1 -1"/></EDGE> </UNITCELL> <LATTICEGRAPH name = "honeycomb kitaev lattice"> <FINITELATTICE> <LATTICE ref="triangular lattice"/> <PARAMETER name="W" default="L"/> <EXTENT dimension="1" size="L"/> <EXTENT dimension="2" size="W"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL ref="honeycomb inhomogeneous"/> </LATTICEGRAPH> *when I run the simulation with the "loop" code, the following message is produced and the simulation stops:* multi-cluster quantum Monte Carlo algorithms for spin systems available from http://wistaria.comp-phys.org/alps-looper/ copyright (c) 1997-2010 by Synge Todo <wistaria(a)comp-phys.org> using ALPS/parapack scheduler a Monte Carlo scheduler for multiple-level parallelization copyright (c) 1997-2013 by Synge Todo <wistaria(a)comp-phys.org> based on the ALPS libraries version 2.2.b3 available from http://alps.comp-phys.org/ copyright (c) 1994-2013 by the ALPS collaboration. Consult the web page for license details. For details see the publication: B. Bauer et al., J. Stat. Mech. (2011) P05001. [2015-Oct-17 14:46:49]: starting scheduler on jahromi-Sharif master input file = /home/jahromi/Desktop/MyComputations/ALPS/Looper/parmlooper.in.xml master output file = /home/jahromi/Desktop/MyComputations/ALPS/Looper/parmlooper.out.xml termination file = [disabled] total number of thread(s) = 1 thread(s) per clone = 1 number of thread group(s) = 1 auto evaluation = yes time limit = unlimited interval between checkpointing = 3600 seconds interval between progress report = 600 seconds interval between vmusage report = infinity task range = all worker dump format = hdf5 worker dump policy = running workers only [2015-Oct-17 14:46:49]: task status: total number of tasks = 4 new = 4, running = 0, continuing = 0, suspended = 0, finished = 0, completed = 0, skipped = 0 [2015-Oct-17 14:46:49]: starting 1 threadgroup(s) [2015-Oct-17 14:46:49]: dispatching a new clone[1,1] on threadgroup[1] (Jx+Jy) and (Jx-Jy) may not have opposite signs FYI, I have enable the xyz bond support as instructed in this link and recompiled alps. https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/2013/002282.html I also tested the algorithm for the "XYZ spin" model available on the alps-looper source on wistaria GitHub and the results is the same and the problem exist there, either. I would be so thankful if you could help me on this matter Best -- Saeed S. Jahromi ========================================================== Postdoctoral Researcher Physics Department, Sharif University of Technology P.O. Box 11155-9161, Tehran , Iran. Mailing Adrress: Azadi Ave., 14588-89694, Tehran, Iran Homepage: http://www.saeedjahromi.com ==========================================================

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inhomogeneous Bose-Hubbard model with MPS
by Dominique Delande 09 Oct '15

09 Oct '15

Dear all, Since at least r7593 (end of July 2015), it is possible to study with MPS inhomogeneous systems, for example an 1D inhomogeneous Bose-Hubbard model with an harmonic trap by using 'inhomogeneous chain lattice' for the lattice and the following definition for the Hamiltonian <HAMILTONIAN name="harm boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="V" default="0"/> <PARAMETER name="t'" default="0"/> <PARAMETER name="V'" default="0"/> <PARAMETER name="U" default="0"/> <PARAMETER name="t0" default="t"/> <PARAMETER name="t1" default="t'"/> <PARAMETER name="V0" default="V"/> <PARAMETER name="V1" default="V'"/> <PARAMETER name="K" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> <PARAMETER name="U#" default="U"/> <PARAMETER name="K#" default="K"/> -mu#*n(i)+U#*n(i)*(n(i)-1)/2+K#*n(i)*(x-0.5*(L-1))^2 </SITETERM> <BONDTERM source="i" target="j"> <PARAMETER name="t#" default="0"/> <PARAMETER name="V#" default="0"/> -t#*(bdag(i)*b(j)+bdag(j)*b(i)) + V#*n(i)*n(j) </BONDTERM> </HAMILTONIAN> I would like to use an inhomogeneous BONDTERM. I tried things like -(t#+tharm#*(i+j-L)^2)*(bdag(i)*b(j)+bdag(j)*b(i)) or -(t#+tharm#*(x-0.5*(L-1))^2)*(bdag(i)*b(j)+bdag(j)*b(i)) in the definition of the Hamiltonian, but they all produce error messages indicating that mps_optim cannot evaluate such a Hamiltonian. I thus have two questions: * Is inhomogeneous BONDTERM possible with MPS, and how to proceed? * MORE IMPORTANTLY: How can I figure out whether it is possible or not? I find nothing in the documentation, nothing in the Wiki. Is the only solution to look in the guts of the code, or to ask on the mailing list? Thanks a lot in advance for your help. Dominique -- Dominique Delande (Dominique.Delande(a)lkb.upmc.fr) Laboratoire Kastler-Brossel - Case 74 - Universite P. et M. Curie 4, place Jussieu, F-75252 Paris Cedex 05, FRANCE Phone : +33 1 44 27 27 97 - Fax : +33 1 44 27 38 45 Acces : Tour 13, Couloir 12-13, 3eme etage - Bureau 316

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A question about the DMRG of alps
by 郭怀明 06 Oct '15

06 Oct '15

Dear all, Recently I use dmrg of alps. I run three dmrg programs simultaneously and sometimes I get the following information, which stop the program. I raise a question: since the dmrg write files while it is running, is there a problem when several programs run? These program may wirte the same files to the same folder, which will cause a problem. (I use the alps in windows 7). Thank you very much. Sincerely, Huaiming Guo The group '/spectrum' does not exist. Traceback (most recent call last): File "C:\Program Files\VisTrails\Python27_64\lib\site-packages\pyalps\load.py" , line 269, in ReadDiagDataFromFile if 'results' in self.h5f.list_children(respath): PathNotFound: The group '/spectrum' does not exist.

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Defining lattice using graph
by Huaiming Guo 02 Oct '15

02 Oct '15

Dear All, I want to ask how to use graph to define the lattice. I write a graph file named as "a.xml". In the parameter file, I use: GRAPH="C:\alpsproject\lattice\a.xml"; . The a.xml file is as the following. However the output is "could not find". I want to ask how to use it. Thank you very much. Sincerely, Huaiming Guo <GRAPH dimension="2" vertices="8" edges="12"> <VERTEX id="1" type="0"><COORDINATE>0 0</COORDINATE></VERTEX> <VERTEX id="2" type="0"><COORDINATE>0 1</COORDINATE></VERTEX> <VERTEX id="3" type="0"><COORDINATE>1 0</COORDINATE></VERTEX> <VERTEX id="4" type="0"><COORDINATE>1 1</COORDINATE></VERTEX> <VERTEX id="5" type="0"><COORDINATE>2 0</COORDINATE></VERTEX> <VERTEX id="6" type="0"><COORDINATE>2 1</COORDINATE></VERTEX> <VERTEX id="7" type="0"><COORDINATE>3 0</COORDINATE></VERTEX> <VERTEX id="8" type="0"><COORDINATE>3 1</COORDINATE></VERTEX> <EDGE source="1" target="3" id="1" type="0" vector="1 0"/> <EDGE source="1" target="2" id="2" type="1" vector="0 1"/> <EDGE source="2" target="4" id="3" type="0" vector="1 0"/> <EDGE source="3" target="5" id="4" type="0" vector="1 0"/> <EDGE source="3" target="4" id="5" type="1" vector="0 1"/> <EDGE source="4" target="6" id="6" type="0" vector="1 0"/> <EDGE source="5" target="7" id="7" type="0" vector="1 0"/> <EDGE source="5" target="6" id="8" type="1" vector="0 1"/> <EDGE source="6" target="8" id="9" type="0" vector="1 0"/> <EDGE source="7" target="1" id="10" type="0" vector="1 0"/> <EDGE source="7" target="8" id="11" type="1" vector="0 1"/> <EDGE source="8" target="2" id="12" type="0" vector="1 0"/> </GRAPH>

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Re: [ALPS-users] Complex terms in DMRG
by Michele Dolfi 02 Oct '15

02 Oct '15

Hi, The error that you see is not an ALPS problem, but an error from the Python interpreter saying that the variable “I” is not defined. You just have to define the parameter as a string: ‘t0' :-1.0*I, becomes: ‘t0’ : '-1.0*I', Michele -- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland dolfim(a)phys.ethz.ch www.itp.phys.ethz.ch +41 44 633 78 56 phone +41 44 633 11 15 fax > On Oct 2, 2015, at 10:42 AM, Huaiming Guo <hmguo(a)buaa.edu.cn> wrote: > > Dear Michele Dolfi, > I use DMRG of alps with complex value. I use Complex=1 in the command line and that works. However when I use the expression in the python way, it return that “I is not defined”. I wonder how to write it in the python way. Thank you very much. > > Sincerely, > Huaiming Guo > <parm.py>

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Problem running ALPS executables in parallel over Mac OS X and Ubuntu
by Andre Vieira 30 Sep '15

30 Sep '15

Hello, I would be glad if ALPS users could help me with a problem I've been experiencing. I have ALPS 2.2.b3 installed in an iMac (i5 mid 2011) and an i7 desktop running Ubuntu 15.04 64 bits, with openmpi (1.6.5) also present. I have no problem running ALPS executables in either computer, nor running basic programs using openmpi (for instance `mpirun -host <host> hostname`) from either machine to the other. I can also successfully run ALPS executables in either machine using openmpi locally. However, when I try to run an ALPS executable (e.g. loop) via openmpi using both machines simultaneously, the jobs are initiated, keep running indefinitely, but no output is produced, not even to the screen. Using mpirun with the -v flag gives no additional information. All I get is the following: dirac-2:qmc apvieira$ mpirun -v -np 7 loop --mpi heisloop20.in.xml --Tmin 5 ALPS/looper version 3.2b12-20100128 (2010/01/28) multi-cluster quantum Monte Carlo algorithms for spin systems available from http://wistaria.comp-phys.org/alps-looper/ copyright (c) 1997-2010 by Synge Todo <wistaria(a)comp-phys.org> using ALPS/parapack scheduler a Monte Carlo scheduler for multiple-level parallelization copyright (c) 1997-2013 by Synge Todo <wistaria(a)comp-phys.org> based on the ALPS libraries version 2.2.b3 available from http://alps.comp-phys.org/ copyright (c) 1994-2013 by the ALPS collaboration. Consult the web page for license details. For details see the publication: B. Bauer et al., J. Stat. Mech. (2011) P05001. Did anyone have this kind of problem before? Thanks, Andre Vieira

2 5

dirloop_sse
by Huaiming Guo 27 Sep '15

27 Sep '15

Dear all, I use dirloop_sse to calculate the hardcore-boson Hubbard model, but with next nearest neighbor hoppings. I revised the model and lattice as below or in the attached file. However the result is not correct. I want to know where the problem is. Thank you very much. Sincerely, Huaiming Guo <HAMILTONIAN name="hardcore boson"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="V" default="0"/> <PARAMETER name="t'" default="0"/> <PARAMETER name="V'" default="0"/> <PARAMETER name="t''" default="0"/> <PARAMETER name="V''" default="0"/> <PARAMETER name="t0" default="t"/> <PARAMETER name="t1" default="t'"/> <PARAMETER name="V0" default="V"/> <PARAMETER name="V1" default="V'"/> <BASIS ref="hardcore boson"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> -mu#*n(i) </SITETERM> <BONDTERM source="i" target="j"> <PARAMETER name="t#" default="0"/> <PARAMETER name="V#" default="0"/> -t#*(bdag(i)*b(j)+bdag(j)*b(i)) + V#*n(i)*n(j) </BONDTERM> </HAMILTONIAN> <UNITCELL name="nnn2d" dimension="2"> <VERTEX/> <EDGE type="0"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE> <EDGE type="1"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE> <EDGE type="2"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 1"/></EDGE> <EDGE type="2"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 -1"/></EDGE> </UNITCELL> <LATTICEGRAPH name = "ladder" vt_name="LadderLattice"> <FINITELATTICE> <LATTICE ref="square lattice"/> <PARAMETER name="W" default="2"/> <EXTENT dimension="1" size="L"/> <EXTENT dimension="2" size="W"/> <BOUNDARY dimension="1" type="periodic"/> <BOUNDARY dimension="2" type="open"/> </FINITELATTICE> <UNITCELL ref="nnn2d"/> </LATTICEGRAPH>

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Report an inconsistency in QMC measurement of stiffness
by 郭怀明 27 Sep '15

27 Sep '15

Dear all, Recently I calculate hardcore on a two-leg ladder with nearest and next nearest neighbor hopping using QMC with direct loop update (dirloop_sse). I can define the lattice in two different ways (see the followings). The problem is the stiffness since the two ways give differnet resutls. I find the result from way 2 is about double of the one from way 1. This addresses a question that some measurement is related to the way how to define the lattice. It seems to me that the users should know more about the details of the codes. Sincerely, Huaiming Guo way1 (see the following): the unitcell contain one site, but is viewed as two dimension. It is the standard file provided by alps software. <UNITCELL name="nnn2d" dimension="2"> <VERTEX/> <EDGE type="0"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE> <EDGE type="1"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE> <EDGE type="2"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 1"/></EDGE> <EDGE type="2"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 -1"/></EDGE> </UNITCELL> <LATTICEGRAPH name = "ladder" vt_name="LadderLattice"> <FINITELATTICE> <LATTICE ref="square lattice"/> <PARAMETER name="W" default="2"/> <EXTENT dimension="1" size="L"/> <EXTENT dimension="2" size="W"/> <BOUNDARY dimension="1" type="periodic"/> <BOUNDARY dimension="2" type="open"/> </FINITELATTICE> <UNITCELL ref="nnn2d"/> </LATTICEGRAPH> way2: the unitcell contains two sites (the two sites on the rung which is vertical to the legs). <UNITCELL name="nnn1d" dimension="1" vertices="2"> <VERTEX type="0" /> <VERTEX type="1" /> <EDGE type="0"><SOURCE vertex="1" offset="0"/><TARGET vertex="1" offset="1"/></EDGE> <EDGE type="1"><SOURCE vertex="2" offset="0"/><TARGET vertex="2" offset="1"/></EDGE> <EDGE type="2"><SOURCE vertex="1" offset="0"/><TARGET vertex="2" offset="0"/></EDGE> <EDGE type="3"><SOURCE vertex="1" offset="0"/><TARGET vertex="2" offset="1"/></EDGE> <EDGE type="3"><SOURCE vertex="2" offset="0"/><TARGET vertex="1" offset="1"/></EDGE> </UNITCELL> <LATTICEGRAPH name = "chain lattice"> <FINITELATTICE> <LATTICE ref="chain lattice"/> <EXTENT dimension="1" size ="L"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL ref="nnn1d"/> </LATTICEGRAPH>

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About the class DataSet
by Huaiming Guo 27 Sep '15

27 Sep '15

Dear All, I have a question about the dataset class. Suppose I have a variable "magnetization" in class dataset (see below). I prefer the data form as the following, X(1), y(1) X(2), y(2).. I want to know how I use the x of magnetization. I tried magnetization.x or magnetization.y, but it does not give me results. Many thanks for the reply. Sincerely, Huaiming class DataSet(ResultProperties): magnetization [x=[ 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 1.2 1.4 1.6 1.8 2. 2.2 2.4 2.5] y=[0.000125981483652 +/- 0.000122322506977 0.00860528601563 +/- 0.000365690783567 0.0222620599739 +/- 0.00089047889358 0.0370211267606 +/- 0.000570927849528 0.048406793936 +/- 0.000429342486559 0.0584663763909 +/- 0.0004796634673 0.0728869134363 +/- 0.000659369158556 0.0893286949981 +/- 0.000587776900735 0.101889483066 +/- 0.000593519471563 0.1160502693 +/- 0.000825142408233 0.133805849632 +/- 0.00057575130612 0.165816585036 +/- 0.000469748080503 0.208087821355 +/- 0.000521162407847 0.258726150393 +/- 0.000553055778572 0.331226556639 +/- 0.000601625820527 0.434736729908 +/- 0.000675053120055 0.491099090239 +/- 0.0003387686197 0.499313131313 +/- 8.51581569713e-05 0.499728317659 +/- 5.31002968192e-05] props={'observable': 'Magnetization Density', 'local_S': 0.5, 'THERMALIZATION': 100.0, 'J': 1.0, 'SWEEPS': 100.0, 'L': 20.0, 'LATTICE': 'chain lattice', 'hdf5_p ath': '/simulation/results/Magnetization Density', 'xlabel': 'h', 'T': 0.08, 'yl abel': 'Magnetization Density', 'MODEL': 'spin', 'label': ''}]

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Re: [ALPS-users] dwa - bug?
by Mateusz Łącki 17 Sep '15

17 Sep '15

Dear Tama, I paste the files below. If I run dwa like that dwa conf.in.xml —Tmin=2 —Tmax=2 then the python script prints a 3x3 matrix for local density and local density^2 and if like this: mpirun -np 10 dwa —mpi conf.in.xml —Tmin=2 —Tmax=2 then it prints a 9x1 vector ******* conf.in.xml ******* <?xml version="1.0" encoding="UTF-8"?> <?xml-stylesheet type="text/xsl" href="ALPS.xsl"?> <JOB xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://xml.comp-phys.org/2003/8/job.xsd"> <OUTPUT file="conf.out.xml"/> <TASK status="new"> <INPUT file="conf.task1.in.xml"/> <OUTPUT file="conf.task1.out.xml"/> </TASK> </JOB> ******* conf.task1.in.xml ******* <?xml version="1.0" encoding="UTF-8"?> <?xml-stylesheet type="text/xsl" href="ALPS.xsl"?> <SIMULATION xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://xml.comp-phys.org/2003/8/QMCXML.xsd"> <PARAMETERS> <PARAMETER name="SKIP">32</PARAMETER> <PARAMETER name="L">3</PARAMETER> <PARAMETER name="MEASURE[Local Density]">True</PARAMETER> <PARAMETER name="LATTICE">square lattice</PARAMETER> <PARAMETER name="SEED">1504313687</PARAMETER> <PARAMETER name="U">1.0</PARAMETER> <PARAMETER name="T">0.04</PARAMETER> <PARAMETER name="MODEL">boson Hubbard</PARAMETER> <PARAMETER name="Nmax">5</PARAMETER> <PARAMETER name="THERMALIZATION">5000</PARAMETER> <PARAMETER name="SWEEPS">50000</PARAMETER> <PARAMETER name="NONLOCAL">0</PARAMETER> <PARAMETER name="mu">0.3828125</PARAMETER> <PARAMETER name="MEASURE[Local Density^2]">True</PARAMETER> <PARAMETER name="t">0.0595</PARAMETER> </PARAMETERS> </SIMULATION> ********** python script ******* import pyalps data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='conf’)) print data > On 16 Sep 2015, at 04:29, P. N. MA - Yotcopi Technologies <tamama(a)yotcopi.com> wrote: > > Hi Matthias, > > By default, I have disabled error bars for local densities. This is because for a more general case like 3D, the binned analysis use too much resource. > > @Mateusz: can you send me your python script, for me to reproduce this error? > > Thank you very much. > > Best regards, > Tama Ma > > Sent from my iPhone > >> On 16 Sep, 2015, at 3:20 am, Matthias Troyer <troyer(a)phys.ethz.ch> wrote: >> >> Tama, can you please check why there are no error bars and it is a 2D array when running with one process and a 1D array with error bars when using more? >> >> Matthias >> >>> On 15 Sep 2015, at 19:57, Mateusz Łącki <mateusz.lacki(a)gmail.com> wrote: >>> >>> I would like to report something I thing is a bug. >>> >>> If i measure “MEASURE[Local Density]” for the “square lattice”, the result is (output of the “.y” field of the : >>> >>> [[ 0.99406836 1.00126848 0.99186967 ] >>> [ 0.99634558 0.98947165 0.99828454 ] >>> [ 0.98602864 0.99223814 0.98709175 ]] >>> >>> and >>> 1.10723308538 +/- 0.000732833211551 >>> 1.09709344128 +/- 0.000725375608498 >>> 1.10916580731 +/- 0.000737136950109 >>> 1.09653825096 +/- 0.000711748290787 >>> 1.09386893991 +/- 0.000713199643571 >>> 1.09495623341 +/- 0.000711331680729 >>> 1.09890852882 +/- 0.000721818241453 >>> 1.09269699362 +/- 0.000716545982708 >>> 1.08871501476 +/- 0.000706327757539 >>> >>> if I compute it using MPI. >>> >>> I load the data using: >>> data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix=pfix)) >>> >>> and I am speaking about proper element of the list data[0] that of one for which s.props['observable']=='Local Density' >>> >>> Please neglect different results as they come from different parameters. >>> >>> Best, >>> Mateusz Łącki >> >

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