nagrealcholeskyskylinesolvenagrealcholeskyskylinesolve(f04mcc)computestheapproximatesolutionofasystemofrealvariable-bandwidthmatrix,whichhaspreviouslybeenfactorizedbynagrealcholeskyskyline(f01mcc).Relatedsystemsmayalsobesolved.#lude#ludevoig_real_cholesky_skyline_solve(Nag_SolveSystemselct,Integern,Integernrhs,doubleal[],Integerlal,doubled[],Integerrow[],doubleb[],Integertdb,doublex[],Integertdx,NagErrorThenormaluseofthisfunctionisthesolutionofthesystemsAX=B,followingacallofnagrealcholeskyskyline(f01mcc)todetermheCholeskyfactorizationA=LDLTofthesymmetricpositive-de?nitevariable-bandwidthmatrixA.LDLTX=B(usual DLTLLT=LTordern,andBasetofright-handsides.ThematrixLisrepresentedbytheelementslyingwithinivelope,i.e.,betweenthe?rstnon-zeroofeachrowandthediagonal(seeSection8foranexample).Thewidthrow[i]oftheithn

selct=NagLDLTX:solveLDLTX=selct=NagLDX:solveLDX=Bselct=NagDLTX:solveDLTX=Bselct=NagLLTX:solveLLTX=Bselct=NagLX:solveLX=Bselct=NagLTX:solveLTX=Constraint:selctmustbeoneofNagLDLTX,NagLDX,NagDLTX,NagLLTX,NagLX,NagLTX.Input:n,theorderofthematrixL.Constraint:n≥1.Constraint:nrhs≥1.

Input:theelementswithintheenvelopeofthelowertriangularmatrixL,takeninrowbyLmustbestoredexplicitly.Input:thedimensionofthearrayalasdeclaredinthefunctionfromwhichnagrealcholeskyskylinesolveiscalled.Constraint:lal≥row[0]+row[1]+...+row[n?Input:thediagonalelementsofthediagonalmatrixD.disnotreferencedifselctNagLLTX,NagLXorNag?rst(left-most)non-zeroelementandtheelementonthediagonal, Constraint:1≤row[i]≤i+1fori=0,1,...,n?1.

Input:theseconddimensionofthearraybasdeclaredinthefunctionfromwhichnagrealcholeskyskylinesolveiscalled.Constraint:tdb≥Output:thenbyrsolutionmatrixX.SeealsoSection

Input:theseconddimensionofthearrayxasdeclaredinthefunctionfromwhichnagrealcholeskyskylinesolveiscalled.Constraint:tdx≥ErrorIndicationsandNEINTARGOnentry,nmustnotbelessthan1:n=Onentry,nrhsmustnotbelessthan1:nrhs=hvaluei.NE2INTARGNE2INTARGOnentry,lal=hvalueiwhilerow[0]+...+row[n?1]=hvaluei.Theseparametersmustsatisfylal≥row[0]+...+row[n?1].Onentry,tdb=hvalueiwhilenrhs=hvaluei.Theseparametersmustsatisfytdb≥nrhs.Onentry,tdx=hvalueiwhilenrhs=hvaluei.Theseparametersmustsatisfytdx≥nrhs.NEBADNEZEROhasbeenlocatedinthearrayd[hvaluei]NENOTUNITThe?rstnon-uni ementhasbeenlocatedinthearrayal[hvaluei]Further...+row[n?Thefunctionmaybecalledwiththesameactualarraydfortheparametersbandx,inwhichcasethesolutionmatrixwilloverwritetheright-handsidematrix.Theusualbackwarderrorysisofthesolutionoftriangularsystemapplies:eachcomputedReinsch(1971)pp25-27and54-55).WilkinsonJHandReinschC(1971)HandbookforAutomaticComputation(Vol,Linear-SeenagrealcholeskyskylineTosolvethesystemofequationsAX=B, A

3

855 02417660Program/*nag_real_cholesky_skyline_solve(f04mcc)Example*Copyright1996NumericalAlgorithms*Mark4, lude<nag.h> lude<math.h> lude lude<nag_stdlib.h> lude<nagf01.h> lude#defineNMAX DB DX{Integeri,nrhs,k,k1,k2,lal,Integerrow[NMAX];Nag_SolveSystemselect;staticNagErrorfail;/*Skipheadingindatafile*/{Vprintf("\nnisoutofrange:n=%ld\n",n);}for(i=0;i<n;++i)k2=for(i=0;i<n;{k1=k2=k2+for(k=k1;k<k2;++k)}lal=if(lal>{Vprintf("\nlalisoutofrange:lal=%ld\n",lal);}if(nrhs<1||{Vprintf("\nnrhsisoutofrange:nrhs=%ld\n",nrhs);}for(i=0;i<n;for(k=0;k<nrhs;++k)fail.print=f01mcc(n,a,lal,row,al,d,&fail);if(fail.code!=NE_NOERROR)select=f04mcc(select,n,nrhs,al,lal,d,row,(double*)b,(Integer)TDB,(double*)x,(Integer)TDX,&fail);if(fail.code!=NE_NOERROR)Vprintf("\nSolution\n");for(i=0;i<n;++i){for(k=0;k<nrhs;++k)}}Programf04mccExampleProgramData12215 ---2Programnagcholeskynagrealcholeskyskylinesolv(f04mcc)AXB的近似解，其中A是對稱正定有限變帶寬矩陣，其具有之前已被nagrealcholeskyskyline(f01mcc)分解。相關(guān)系統(tǒng)也可能得到解決。規(guī)范包含<nag.h># lude<nagf04.h>voig_real_cholesky_skyline_solve(Nag_SolveSystemselct,整數(shù)n,整數(shù)nrhs,雙al[],整數(shù)lal,雙d[],整數(shù)row[],雙b[],整數(shù)tdb,雙x[],整數(shù)tdx,NagError*失敗)AXBnagrealcholeskyskylineCholeskyALDLTA。LDLTXB（通常系統(tǒng)）(1)LDXB（下三角系統(tǒng)）2DLTXB（上三角系統(tǒng)）(3)LLTB4LXB（單位下三角系統(tǒng)）(5)LTXB（單位上三角系）LnDn，B的示例）irow[i]（含）NagLDLTX：LDLTXBNagLDXLDXBNagDLTX：求解DLTXBNagLLTX：LLTXBNagLXLXBNagLTX：LTXB。約束：selctNagLDLTX、NagLDX、NagDLTX、NagLLTX、NagLX、NagLTX之一。nnL約束：nrhs≥1。]LnagrealcholeskyskylineLlalnagrealcholeskyskylinesolveallal≥row[0]+row[1]+...+row[n。1]。d[n]DselctNagLLTX、NagLXNagLTX，dorow[n]輸入：row[i]必須包含L的第i行的寬度，即第一個（最左邊）非零元素和對角線上的元素（包括）之間的元素數(shù)量。約束：1≤row[i]≤i+1（i=0,1,...,n）。1.輸入：nrB6tdbnagrealcholeskyskylinesolveb束：tdb≥nrhs。輸出：nrX6tdxnagrealcholeskyskylinesolvex束：tdx≥nrhs。failNAG錯誤參數(shù)，請參見NAGC錯誤指示和警告NEINTARGLT輸入時，n不得小于1：n=value。輸入時，row[]不得小于1：rowvaluevalue。輸入時，nrhs不得小于1：nrhsvalue2INTARGGTrow[i]=valueivaluerow[i]i+1。2INTARGLT輸入時，lal=valuewhilerow[0]+...+row[n。1]=值。這些參數(shù)必須滿足lalrow[0]row[n1tdbvaluenrhsvaluetdbnrhstdxvaluenrhsvaluetdxnrhs。NEBADPARAM輸入時，參數(shù)selct具有非法值。d[valueNENOTUNITDIAGL1。第一個非單位元素已位于數(shù)組al[value]中prprow[0]row[1]row[n。1]。D來說是精確的（視情況而定）（參見Wilkinson和Reinsch(1971)第25-27頁和54-55）。6.2.WilkinsonJHReinschC1971)（第二nagrealcholeskyskylineAXB，120050253014003130180000168245141800024和.1015.211130245146Anagrealcholeskyskyline(f01mcc)nag_real_cholesky_skyline_solve(f04mcc)*1996數(shù)值算法組。**1996年4號。*/lude<nag.h>#lude<math.h>#lude<stdio.h>#lude<nag_stdlib.h>#<nagf01.h>#ludeNMAX6NRHSMAX2TDBNRHSMAXTDXNRHSMAXLALMAXx[NMAX][TDX]；整數(shù)行[NMAX]；Nag_SolveSystem選擇；靜態(tài)NagError失敗；Vprintf("f04mcc示例程序結(jié)果\n");/*跳過數(shù)據(jù)文件中的標(biāo)題*/Vscanf("%*[^\n]");Vscanf("%ld",&n);如果(n<1||n>NMAX)Vprintf("\nnn%ld\n",n);退出（EXIT_FAILURE）；對于(i=0;i<n;++i)Vscanf("%ld",&row[i]);k