CN107644143A - A kind of high-performance city CA model construction method based on vectorization and parallel computation - Google Patents
A kind of high-performance city CA model construction method based on vectorization and parallel computation Download PDFInfo
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Abstract
The invention discloses a kind of high-performance city CA model construction method based on vectorization and parallel computation, urban land use matrix is initially set up, matrix key element corresponds to each cellular, and space of matrices corresponds to cellular space;Cellular space is divided into more sub-spaces, and every sub-spaces are distributed to different processors;Gather neighbours' cellular of same position in each center cellular neighborhood, form the neighborhood collection of each subspace different azimuth;Then realize that the information between two neighboring processor exchanges, and transmits the cellular information on adjacent subarea domain border by the way of memory vector;Realize that the neighborhood density of different subspace calculates, transition probability calculates and cellular state changes by matrix operation;Finally the analog result of all subspaces is merged, obtains final Urban Expansion analog result.The present invention constructs vectorization and paralleling elementary cell automatic machine model, and above-mentioned model is applied in Urban Expansion simulation, contributes to more efficient, rapidly simulating city expansion.
Description
Technical field
The invention belongs to high-performance geocomputation technical field, is related to a kind of high-performance city CA model construction method, especially
It is related to a kind of high-performance city CA model construction method based on vectorization and parallel computation.
Background technology
Cellular automata is that a kind of time, space and state are all discrete, has powerful spatial modeling ability and computing energy
The dynamical system of power, it has been widely used in the system simulation research with complicated space-time characteristic such as Urban Expansion.With city
The big geographical scale of city's extended simulation Research tendency and the unit that becomes more meticulous, city CA data volume and calculating time will exponentially increase
It is long, it is difficult to the requirement for meeting efficient rapid computations in actual applications, there is an urgent need to carry out Urban Expansion CA high-performance calculations.Through
Allusion quotation CA mathematical algorithm is usually to be carried out by the way of " traversal " cellular.Because CA simulations need to enter substantial amounts of spatial data
Row pretreatment, and the interative computation in time domain is constantly carried out, its operational efficiency is lower.Therefore striograph resolution ratio is worked as
Higher, cellular quantity is larger, and when being especially considering that geographical phenomenon by many influences, cellular is caused by the way of traversal
The iteration of state and renewal time length, efficiency of algorithm is low, is unfavorable for the application and popularization of CA models.
Scholars with Li Xia, Guan, Blecic I. etc. for representative have done on paralleling elementary cell automatic machine model much to be had
The practice of meaning is attempted, but the research of current high performance cellular automata is still primarily upon carrying in the performance of computer hardware and software equipment
Rise and the application of parallel computing on, the research on algorithm improvement in itself and lifting is less.Parallel computation or distribution
Calculating must take into consideration in the case of increasingly being expanded with amount of calculation by data volume, be that current main flow can effectively lift calculating
The method of efficiency, but its logical construction and maintenance cost are very high, and study and enforcement difficulty are big.It is fast-developing in Geography
And under the historical background of geographical space-time big data, requirement of the current geographic CA analog studies to rapidly and efficiently computing capability is increasingly
Height, need a kind of efficient suitable processing multi-layer image of proposition, computation-intensive data badly and there is the cellular of notable space characteristics certainly
Motivation algorithm, for improving city CA simulation precisions.
The content of the invention
In order to solve the above-mentioned technical problem, the invention provides a kind of vectorization and parallelization cellular automata algorithm to carry
High city CA simulation precisions, this method can greatly promote the simulation precision of urban cellular automata, particularly suitable for based on fine
Change the simulation of the complicated geosystem such as unit or the Urban Expansion of Large-scale areas.
The technical solution adopted in the present invention is:A kind of high-performance city CA model structure based on vectorization and parallel computation
Construction method, it is characterised in that comprise the following steps:
Step 1:Urban land use matrix is established, matrix key element corresponds to each cellular, and space of matrices corresponds to cellular sky
Between;
Step 2:Cellular space is divided into some sub-spaces, and every sub-spaces are distributed to different processors;
Step 3:Gather neighbours' cellular of same position in each center cellular neighborhood, form the neighbour of each subspace different azimuth
Domain collection;
Its specific implementation includes following sub-step:
Step 3.1:The land use state matrix of each subspace is established, two kinds of values, city are only existed in state matrix
City's land used value is 1, and non-urban land value is 0;
Step 3.2:According to neighborhood shapes and sizes, by the way that state matrix space is translated into corresponding units shape to each orientation
Into the neighborhood collection of each subspace different azimuth;
Step 3.3:The neighborhood collection of different azimuth and each subspace are realized by reducing excess edge and increase null boundary
It is consistent with size in position;
Step 4:Realize that the information between two neighboring processor exchanges by the way of memory vector, transmit adjacent subarea domain
The cellular information on border;
Its specific implementation includes following sub-step:
Step 4.1:According to the symmetry of cellular neighborhood, the memory for establishing all subregion right boundary is vectorial;
Step 4.2:Using message model, the memory vector of all subregion is sent to the border cellular of adjacent area, it is real
Information transmission between existing adjacent subarea domain;
Step 5:Realize that the neighborhood density of different subspace calculates, transition probability calculates and cellular state by matrix operation
Transformation;
Its specific implementation includes following sub-step:
Step 5.1:The different azimuth neighborhood collection sum in cellular space and the ratio of neighborhood collection number are calculated, it is empty to obtain each son
Between neighborhood density, realize neighborhood density calculate vectorization;
Step 5.2:The Hadamard products in matrix operation are used to enter instead of loop body in transition probability calculating process
Row multiplying, realize the vectorization that transition probability calculates;
Step 5.3:By the matrix of transition probabilities compared with switching threshold, the cellular for the condition that meets is switched into city and used
Ground, realize the vectorization of cellular state transformation;
Step 6:After meeting stopping criterion for iteration, the analog result of all subspaces is merged, final city is obtained and expands
Open up analog result.
Compared with prior art, the present invention has advantages below and beneficial effect:
The inventive method constructs vectorization and parallel optimization cellular Automation Model, and above-mentioned model is applied into city
In extended simulation, contribute to more efficient, rapidly simulating city expansion.
Brief description of the drawings
Fig. 1 is mole type neighborhood (left side) and neighborhood collection (right side) schematic diagram of the extension of the embodiment of the present invention;
Fig. 2 is that the memory vector techniques of the embodiment of the present invention realize schematic diagram;
Fig. 3 is the decomposition in the cellular space of the embodiment of the present invention with merging schematic diagram (being decomposed by row);
Fig. 4 is research zone position schematic diagram of the embodiment of the present invention;
Fig. 5 is the research area urban land use historical data of the embodiment of the present invention;
Fig. 6 is the vectorization based on the different radius of neighbourhood (left side) and based on different cellular sizes (right side) of the embodiment of the present invention
Duration is simulated with parallel urban cellular automata;
Fig. 7 is the speed-up ratio and efficiency schematic diagram of the embodiment of the present invention;From left to right from top to bottom, it is respectively:Based on not
With the speed-up ratio of the radius of neighbourhood, based on the efficiency of the different radius of neighbourhood, based on the speed-up ratio of different cellular sizes, based on different members
The efficiency of born of the same parents' size.
Embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with the accompanying drawings and embodiment is to this hair
It is bright to be described in further detail, it will be appreciated that implementation example described herein is merely to illustrate and explain the present invention, not
For limiting the present invention.
A kind of high-performance city CA model construction method based on vectorization and parallel computation provided by the invention, including with
Lower step:
Step 1:Urban land use matrix S is established, matrix key element corresponds to each cellular, and space of matrices corresponds to cellular sky
Between;
Step 2:Cellular is spatially uniformly divided into using column split by n sub-spaces, and will be sent out respectively per sub-spaces
To n processor;Wherein, cellular space size is row × col, and i-th of subspace size is row (i) × col (i), i=1,
2,3...n;
Step 3:Gather the neighbours cellular N of same position in each center cellular neighborhood, form each subspace different azimuth
Neighborhood collection CN;
Its specific implementation includes following sub-step:
Step 3.1:The land use state matrix M of each subspace is established, two kinds of values are only existed in state matrix M,
Urban land value is 1, and non-urban land value is 0;
Step 3.2:According to neighborhood shapes and sizes, by the way that state matrix space is translated into corresponding units shape to each orientation
Into the neighborhood collection of each subspace different azimuth;If the radius of neighbourhood of cellular is set to r, neighbour structure is using mole type neighbour extended
Domain, for each cellular, have (2r+1) in its neighborhood2- 1 cellular, it is represented by { N (1,1) ..., N (k, l) ..., N (2r
+ 1,2r+1) }, if t cellular subspace i neighborhood is CNt:
Wherein, k=1,2,3 ..., 2r+1, l=1,2,3 ..., 2r+1, mole type neighborhood of the signal extension of accompanying drawing 1 and
Neighborhood collection in center cellular upper left positionTo cellular subspace i neighborhood collectionHave:
Left neighborhood collection LN and right neighborhood collection RN is divided according to cellular space partitioning scheme:
Step 3.3:The neighborhood collection of different azimuth and each subspace are realized by reducing excess edge and increase null boundary
It is consistent with size in position;
Step 4:Realize that the information between two neighboring processor exchanges by the way of memory vector, transmit adjacent subarea domain
The cellular information (accompanying drawing 2) on border;Wherein, the right neighborhood collection of i-th of subspace right margin cellular, equal to i+1 sub-spaces
The memory vector of left margin cellular;The left neighborhood collection of i-th of subspace left margin cellular, equal to the i-th -1 sub-spaces right margin
The memory vector of cellular;
Its specific implementation includes following sub-step:
Step 4.1:According to the symmetry of cellular neighborhood, i.e. the right neighborhood collection of jth row cellular is equal to (j+r+1) row cellular
Left neighborhood collection, similarly, the left neighborhood collection of jth row cellular is equal to the right neighborhood collection of (j-r-1) row cellular;I-th of subspace
The memory vector of right margin cellular, it is that (col (i)-r-1) is arranged to the right side of (col (i) -1) row cellular in i-th of subspace
Neighborhood collection;Similarly, the memory vector of i-th of subspace left margin cellular, it is that the 2nd row arrange member to (r+2) in i-th of subspace
The left neighborhood collection of born of the same parents:
Wherein, j=1,2,3 ..., col (i), k=1,2,3 ..., 2r+1, r be the radius of neighbourhood;
Step 4.2:Using message model, the memory vector of all subregion is sent to the border cellular of adjacent area, it is real
Information transmission between existing adjacent subarea domain;Utilized specially under Matlab environment in Parallel Computing Toolbox
SPMD functions carry out parallel computation, when set call CPU core number be CoreNum when, CoreNum platforms will be gone out in local virtual
Matlab work station can be run, now co-exists in CoreNum+1 Matlab (including 1 Client and CoreNum from the background
Individual Workers), wherein Client is mainly responsible for calling and assigns tasks to other Workers in parallel pond, does not join directly
With computing.SPMD supports similar MPI message sending function, including:
LabSend (data, srclabindex), data are sent to another computing unit;
LabReceive (data, rcvlabindex), receive data from another computing unit;
DataReceived=labSendReceive (rcvlabindex, srclabindex, dataSent), it is and another
Individual computing unit exchanges data;
Step 5:Loop body is replaced using matrix operation, realizes that the neighborhood density of different subspace calculates, transition probability meter
Calculate and cellular state changes;
Step 5.1:The different azimuth neighborhood collection sum in cellular space and the ratio of neighborhood collection number are calculated, it is empty to obtain each son
Between neighborhood density Pl, realize the vectorization that neighborhood density calculates:
Step 5.2:The Hadamard products in matrix operation are used to enter instead of loop body in transition probability calculating process
Row multiplying, realize the vectorization that transition probability calculates;In CA transition probability calculating process, it is related to itself category of cellular
Property (such as earth development probability PoWith global limiting factor Pc), and these attributes will not become with the progress of iteration
Change, usually as input data, and data are stored in the form of matrix or vector;And enchancement factor rule PrIt can be considered in cellular
The random matrix of a random distribution between [0,1] is produced in space.Matrix of transition probabilities P is represented by:
P=P0.×Pl.×Pc.×Pr
× and Hadamard products are represented, input element is vector or matrix with output result.
Step 5.3:By the matrix of transition probabilities and switching threshold PthredIt is compared, by the cellular S for the condition that meets next
Moment switchs to urban land, realizes the vectorization of cellular state transformation:
St+1(P > Pthred)=1
Wherein, 1 urban land is represented, 0 represents non-urban land, by comparing matrix of transition probabilities P and threshold value Pthred's
Size, the subscript of the element for the condition that meets is returned to, then by St+1Middle relevant position cellular is changed into urban land.
Step 6:After meeting stopping criterion for iteration, the analog result of all subspaces is merged, final city is obtained and expands
Open up analog result;Wherein, stopping criterion for iteration is to reach maximum iteration 100 times, or conversion cellular number exceedes actual city
City's land used cellular change sum;It is P to concurrently set switching thresholdthred=0.6, for judging whether some cellular develops into city
Land used;Accompanying drawing 3 is the schematic diagram that cellular space divides and merged.
As one embodiment, present invention selection Wuhan City Jiangxia District is test block (accompanying drawing 4), and experimental data mainly includes
Jiangxia District 2007 and two phase present status of land utilization vector datas, urban development center, traffic network in 2011 etc..It is based on
The platforms of ArcGIS 10.0 are pre-processed to land use vector data, and land use pattern is classified as into urban land, non-city
Land used and water body, and by Grid of vector data (accompanying drawing 5).By taking 5m resolution ratio as an example, each figure layer includes 10792 × 12580
Individual cellular, with TIFF or BMP forms storage (>500M).To obtain training data needed for experiment, using ArcGIS instruments to history
Data carry out Spatial Overlap Analysis and Euclidean distance calculates, and extract urban land use change and space variable data, and carry out data
Standardization and then the spatial data after standardization is sampled using random top and bottom process, during sampling in 20% ratio from
Be converted to urban land cellular and cellular that is convertible and being not yet converted to urban land in randomly select sampling point respectively, pass through
Check and reject error dot, obtain final space training sample, finally train obtaining space change using Logistic regression models
The weight parameter of amount, so as to carry out earth development probability PoCalculating.
It is a variety of in Matlab, Python, C++ etc. respectively for the performance of verification vectors and paralleling elementary cell automatic machine algorithm
Vectorization is realized under language environment, and the SPMD work(in Parallel Computing Toolbox is utilized under Matlab environment
Parallel computation, the scalability of verification algorithm can be carried out to vectorization algorithm.Wherein, matrix function storehouse powerful built in Matlab
MKL, Python carry out matrix manipulation by linking Numpy+MKL, and C++ equally has stronger matrix by importing Eigen storehouses
Operational capability, the later Eigen storehouses of 3.1 versions can obtain the optimization of built-in MKL function libraries.Experiment is enterprising in a computer
OK, operating system is 64 professional versions of Windows7, and CPU processor is four cores, model Intel CoreTM i5-4460
3.20GHz, inside save as 8G.It is fixed all the time by file read-write and parallel environment configure the consumed time, therefore is begging for
Do not considered during by efficiency of algorithm lifting and speed-up ratio.
The file read-write of table 1 and parallel environment setup time
The city CA simulated times contrast (radius of neighbourhood R=1) based on different resolution under 2 different development environments of table
(cellular size is 5 for the city CA simulated times contrast based on the different radius of neighbourhood under 3 different development environments of table
×5)
From table 1-3 results, the cellular that vectorization algorithm is superior to judge point by point under different programmed environments is automatic
Machine algorithm, it significantly improves CA operational efficiency.This shows to use different programming languages, and vectorization programming can bring huge
Acceleration income, using neighborhood as 3 × 3, exemplified by Research scale is 5 × 5, obtained using vectorization algorithm compared with ergodic algorithm efficiency bright
Aobvious lifting, meanwhile, there is some difference for the run time of each algorithm under different programmed environments, in Matlab simulated time by
38220.43s being changed into 803.36s, speed-up ratio reaches 48X;Simulated time is changed into 2131.61s from 169823.39s in Python,
Speed-up ratio reaches 80X, and simulated time is changed into 674.87 from 997.52 in C++, and speed-up ratio reaches 1.5X.Vectorization efficiency of algorithm with
There is association in programmed environment, this has special compilation process mainly due to compiled language (such as C++) before code execution,
Need not be again machine language by code translation when program is run, and interpretation type language (such as Matlab/Python) exists
It is required for being translated when code is run each time, efficiency is low, therefore uses vectorization algorithm can be with simplified code, and brings
Greatly accelerate income.In general, it is obviously improved using vectorization algorithm compared with ergodic algorithm efficiency, vectorization algorithm can
Significantly to improve the efficiency of city CA simulations.In addition, by the way that research zoning is divided into 4 parts, 4 CPU cores are sent respectively to
The heart carries out parallel computation, and simulated time is reduced to 476.53s by 803.36s in Matlab.From accompanying drawing 6-7 it can be found that
When research granularity is larger or the radius of neighbourhood is smaller, speed-up ratio is undesirable, or even when survey region is smaller, parallel computation causes
Time not anti-reflection is calculated to increase, and as the radius of neighbourhood increases, speed-up ratio is then increasingly closer to preferable speed-up ratio, and this shows when research
Granularity is larger or algorithm amount of calculation is smaller when neighborhood is smaller, and the time income for causing to bring using parallel computation can not make up communication
Increase with the time caused by data exchange, and as research granularity reduces the increase with neighborhood amount of calculation, the benefit of parallel computation
Start to display.Therefore, when data volume is larger, vectorization algorithm can also be relatively easy to be combined with parallel computation,
Further boosting algorithm efficiency.
More than analysis demonstrate that the present invention builds a kind of efficient be adapted to processing multi-layer image, computation-intensive data and tool
There is the cellular automata algorithm of notable space characteristics, it greatly promotes city cellular certainly by combining vectorization and parallel computation
The simulation precision of motivation, particularly suitable for complicated geosystems such as the urban sprawls based on become more meticulous unit or Large-scale areas
Simulation.
It should be appreciated that the part that this specification does not elaborate belongs to prior art.
It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, therefore can not be considered to this
The limitation of invention patent protection scope, one of ordinary skill in the art are not departing from power of the present invention under the enlightenment of the present invention
Profit is required under protected ambit, can also be made replacement or deformation, be each fallen within protection scope of the present invention, this hair
It is bright scope is claimed to be determined by the appended claims.
Claims (8)
1. a kind of high-performance city CA model construction method based on vectorization and parallel computation, it is characterised in that including following
Step:
Step 1:Urban land use matrix is established, matrix key element corresponds to each cellular, and space of matrices corresponds to cellular space;
Step 2:Cellular space is divided into some sub-spaces, and every sub-spaces are distributed to different processors;
Step 3:Gather neighbours' cellular of same position in each center cellular neighborhood, form the neighborhood of each subspace different azimuth
Collection;
Its specific implementation includes following sub-step:
Step 3.1:The land use state matrix of each subspace is established, two kinds of values are only existed in state matrix, city is used
Ground value is 1, and non-urban land value is 0;
Step 3.2:According to neighborhood shapes and sizes, formed respectively by the way that state matrix space is translated into corresponding units to each orientation
The neighborhood collection of subspace different azimuth;
Step 3.3:Realize that the neighborhood collection of different azimuth and each subspace are in place by reducing excess edge and increase null boundary
Put consistent with size;
Step 4:Realize that the information between two neighboring processor exchanges by the way of memory vector, transmit adjacent subarea domain border
Cellular information;
Its specific implementation includes following sub-step:
Step 4.1:According to the symmetry of cellular neighborhood, the memory for establishing all subregion right boundary is vectorial;
Step 4.2:Using message model, the memory vector of all subregion is sent to the border cellular of adjacent area, realizes phase
Information transmission between adjacent subregion;
Step 5:Realize that the neighborhood density of different subspace calculates, transition probability calculates and cellular state turns by matrix operation
Become;
Its specific implementation includes following sub-step:
Step 5.1:The different azimuth neighborhood collection sum in cellular space and the ratio of neighborhood collection number are calculated, obtains each subspace
Neighborhood density, realize the vectorization that neighborhood density calculates;
Step 5.2:The Hadamard products in matrix operation are used to be multiplied instead of loop body in transition probability calculating process
Method computing, realize the vectorization that transition probability calculates;
Step 5.3:By the matrix of transition probabilities compared with switching threshold, the cellular for the condition that meets is switched into urban land, it is real
The vectorization of existing cellular state transformation;
Step 6:After meeting stopping criterion for iteration, the analog result of all subspaces is merged, obtains final Urban Expansion mould
Intend result.
2. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:Cellular is spatially uniformly divided into using column split or row segmentation by n sub-spaces in step 2, wherein, cellular space
Size is row × col, and i-th of subspace size is row (i) × col (i), i=1,2,3...n.
3. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:The neighborhood collection of different azimuth is divided into two classes according to cellular space partitioning scheme in step 3.2, and column split divides left neighbour
Domain collection and right neighborhood collection, the row upper neighborhood collection of segmentation division and lower neighborhood collection.
4. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:The right side/lower neighborhood collection of i-th of subspace right side/lower boundary cellular in step 4, equal to an i+1 sub-spaces left side/top
The memory vector of boundary's cellular;A left side for i-th of subspace left side/coboundary cellular/upper neighborhood collection, right equal to the i-th -1 sub-spaces/under
The memory vector of border cellular.
5. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:In step 4.1 symmetry of cellular neighborhood refer to jth column/row cellular the right side/lower neighborhood collection be equal to (j+r+1) row/
A left side for row cellular/upper neighborhood collection, similarly, a left side/upper neighborhood collection of jth column/row cellular be equal to the right side of (j-r-1) column/row cellular/
Lower neighborhood collection;The memory vector of i-th of subspace right side/lower boundary cellular, be (col (i)-r-1) row in i-th subspace/
(row (i)-r-1) row arranges the right side/lower neighborhood collection of/the (row (i) -1) row cellular to (col (i) -1);Similarly, i-th of son
The memory vector of a space left side/coboundary cellular, be in i-th subspace the 2nd column/row to the left side of (r+2) column/row cellular/on
Neighborhood collection;J=1,2,3 ..., col (i) or j=1,2,3 ..., row (i);R is the radius of neighbourhood.
6. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:In step 5.2 in CA transition probability calculating process, it is related to the self attributes of cellular, and these attributes will not be with
The progress of iteration and change, as input data, and data store with a matrix type.
7. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:In step 5.2 in CA transition probability calculating process, it is related to enchancement factor rule, can be considered in cellular space
Produce the random matrix of a random distribution between [0,1].
8. the high-performance city CA model construction method according to claim 1 based on vectorization and parallel computation, it is special
Sign is:Stopping criterion for iteration in step 6 is to reach maximum iteration, or conversion cellular number exceedes actual cities land used
Cellular change sum.
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