X-Git-Url: https://git.donarmstrong.com/?p=mothur.git;a=blobdiff_plain;f=pcacommand.cpp;h=7103adb8a150a3e6f9871989ba94bd45d2b6a542;hp=ef89ae50cd43ad16101b4288931881027d03dcd6;hb=1a20e24ee786195ab0e1cccd4f5aede7a88f3f4e;hpb=f27b66ce6415eb14c434f9850019c7cf140e023e diff --git a/pcacommand.cpp b/pcacommand.cpp index ef89ae5..7103adb 100644 --- a/pcacommand.cpp +++ b/pcacommand.cpp @@ -1,597 +1,468 @@ - /* * pcacommand.cpp - * Mothur + * mothur * - * Created by westcott on 1/4/10. - * Copyright 2010 Schloss Lab. All rights reserved. + * Created by westcott on 1/7/11. + * Copyright 2011 Schloss Lab. All rights reserved. * */ #include "pcacommand.h" +#include "inputdata.h" + +//********************************************************************************************************************** +vector PCACommand::setParameters(){ + try { + CommandParameter pshared("shared", "InputTypes", "", "", "LRSS", "LRSS", "none","pca-loadings",false,false,true); parameters.push_back(pshared); + CommandParameter prelabund("relabund", "InputTypes", "", "", "LRSS", "LRSS", "none","pca-loadings",false,false,true); parameters.push_back(prelabund); + CommandParameter pgroups("groups", "String", "", "", "", "", "","",false,false); parameters.push_back(pgroups); + CommandParameter pmetric("metric", "Boolean", "", "T", "", "", "","",false,false); parameters.push_back(pmetric); + CommandParameter plabel("label", "String", "", "", "", "", "","",false,false); parameters.push_back(plabel); + CommandParameter pinputdir("inputdir", "String", "", "", "", "", "","",false,false); parameters.push_back(pinputdir); + CommandParameter poutputdir("outputdir", "String", "", "", "", "", "","",false,false); parameters.push_back(poutputdir); + + vector myArray; + for (int i = 0; i < parameters.size(); i++) { myArray.push_back(parameters[i].name); } + return myArray; + } + catch(exception& e) { + m->errorOut(e, "PCACommand", "setParameters"); + exit(1); + } +} +//********************************************************************************************************************** +string PCACommand::getHelpString(){ + try { + string helpString = ""; + helpString += "The pca command parameters are shared, relabund, label, groups and metric. shared or relabund is required unless you have a valid current file."; + helpString += "The label parameter is used to analyze specific labels in your input. Default is the first label in your shared or relabund file. Multiple labels may be separated by dashes.\n"; + helpString += "The groups parameter allows you to specify which groups you would like analyzed. Groupnames are separated by dashes.\n"; + helpString += "The metric parameter allows you to indicate if would like the pearson correlation coefficient calculated. Default=True"; + helpString += "Example pca(groups=yourGroups).\n"; + helpString += "Example pca(groups=A-B-C).\n"; + helpString += "Note: No spaces between parameter labels (i.e. groups), '=' and parameters (i.e.yourGroups).\n"; + return helpString; + } + catch(exception& e) { + m->errorOut(e, "PCACommand", "getHelpString"); + exit(1); + } +} +//********************************************************************************************************************** +string PCACommand::getOutputPattern(string type) { + try { + string pattern = ""; + + if (type == "pca") { pattern = "[filename],[distance],pca.axes"; } + else if (type == "loadings") { pattern = "[filename],[distance],pca.loadings"; } + else { m->mothurOut("[ERROR]: No definition for type " + type + " output pattern.\n"); m->control_pressed = true; } + + return pattern; + } + catch(exception& e) { + m->errorOut(e, "PCACommand", "getOutputPattern"); + exit(1); + } +} +//********************************************************************************************************************** +PCACommand::PCACommand(){ + try { + abort = true; calledHelp = true; + setParameters(); + vector tempOutNames; + outputTypes["pca"] = tempOutNames; + outputTypes["loadings"] = tempOutNames; + } + catch(exception& e) { + m->errorOut(e, "PCACommand", "PCACommand"); + exit(1); + } +} //********************************************************************************************************************** -PCACommand::PCACommand(string option){ +PCACommand::PCACommand(string option) { try { - abort = false; + abort = false; calledHelp = false; //allow user to run help - if(option == "help") { help(); abort = true; } + if(option == "help") { help(); abort = true; calledHelp = true; } + else if(option == "citation") { citation(); abort = true; calledHelp = true;} else { - //valid paramters for this command - string Array[] = {"phylip","lt"}; - vector myArray (Array, Array+(sizeof(Array)/sizeof(string))); + vector myArray = setParameters(); OptionParser parser(option); map parameters = parser. getParameters(); ValidParameters validParameter; - + map::iterator it; + //check to make sure all parameters are valid for command - for (map::iterator it = parameters.begin(); it != parameters.end(); it++) { + for (it = parameters.begin(); it != parameters.end(); it++) { if (validParameter.isValidParameter(it->first, myArray, it->second) != true) { abort = true; } } + + //initialize outputTypes + vector tempOutNames; + outputTypes["pca"] = tempOutNames; + outputTypes["loadings"] = tempOutNames; - //required parameters - phylipfile = validParameter.validFile(parameters, "phylip", true); - if (phylipfile == "not open") { abort = true; } - else if (phylipfile == "not found") { phylipfile = ""; abort = true; } - else { filename = phylipfile; } + //if the user changes the input directory command factory will send this info to us in the output parameter + string inputDir = validParameter.validFile(parameters, "inputdir", false); + if (inputDir == "not found"){ inputDir = ""; } + else { + string path; + it = parameters.find("shared"); + //user has given a template file + if(it != parameters.end()){ + path = m->hasPath(it->second); + //if the user has not given a path then, add inputdir. else leave path alone. + if (path == "") { parameters["shared"] = inputDir + it->second; } + } + + it = parameters.find("relabund"); + //user has given a template file + if(it != parameters.end()){ + path = m->hasPath(it->second); + //if the user has not given a path then, add inputdir. else leave path alone. + if (path == "") { parameters["relabund"] = inputDir + it->second; } + } + } - //columnfile = validParameter.validFile(parameters, "column", true); - //if (columnfile == "not open") { abort = true; } - //else if (columnfile == "not found") { columnfile = ""; } - //else { format = "column"; } + //check for required parameters + sharedfile = validParameter.validFile(parameters, "shared", true); + if (sharedfile == "not open") { sharedfile = ""; abort = true; } + else if (sharedfile == "not found") { sharedfile = ""; } + else { mode = "sharedfile"; inputFile = sharedfile; m->setSharedFile(sharedfile); } - //namefile = validParameter.validFile(parameters, "name", true); - //if (namefile == "not open") { abort = true; } - //else if (namefile == "not found") { namefile = ""; } + relabundfile = validParameter.validFile(parameters, "relabund", true); + if (relabundfile == "not open") { relabundfile = ""; abort = true; } + else if (relabundfile == "not found") { relabundfile = ""; } + else { mode = "relabund"; inputFile = relabundfile; m->setRelAbundFile(relabundfile); } - //error checking on files - if (phylipfile == "") { mothurOut("You must provide a distance file before running the pca command."); mothurOutEndLine(); abort = true; } - //if ((phylipfile == "") && (columnfile == "")) { mothurOut("You must provide a distance file before running the pca command."); mothurOutEndLine(); abort = true; } - //else if ((phylipfile != "") && (columnfile != "")) { mothurOut("You may not use both the column and the phylip parameters."); mothurOutEndLine(); abort = true; } + if ((sharedfile == "") && (relabundfile == "")) { + //is there are current file available for any of these? + //give priority to shared, then list, then rabund, then sabund + //if there is a current shared file, use it + sharedfile = m->getSharedFile(); + if (sharedfile != "") { inputFile = sharedfile; mode = "sharedfile"; m->mothurOut("Using " + sharedfile + " as input file for the shared parameter."); m->mothurOutEndLine(); } + else { + relabundfile = m->getRelAbundFile(); + if (relabundfile != "") { inputFile = relabundfile; mode = "relabund"; m->mothurOut("Using " + relabundfile + " as input file for the relabund parameter."); m->mothurOutEndLine(); } + else { + m->mothurOut("No valid current files. You must provide a relabund or shared file."); m->mothurOutEndLine(); + abort = true; + } + } + } + + //if the user changes the output directory command factory will send this info to us in the output parameter + outputDir = validParameter.validFile(parameters, "outputdir", false); if (outputDir == "not found"){ + outputDir = ""; + outputDir += m->hasPath(inputFile); //if user entered a file with a path then preserve it + } + + string temp = validParameter.validFile(parameters, "metric", false); if (temp == "not found"){ temp = "T"; } + metric = m->isTrue(temp); - //if (columnfile != "") { - // if (namefile == "") { mothurOut("You need to provide a namefile if you are going to use the column format."); mothurOutEndLine(); abort = true; } - //} + label = validParameter.validFile(parameters, "label", false); + if (label == "not found") { label = ""; if(labels.size() == 0) { m->mothurOut("You did not provide a label, I will use the first label in your inputfile."); m->mothurOutEndLine(); } } + else { m->splitAtDash(label, labels); } - string temp = validParameter.validFile(parameters, "lt", false); if (temp == "not found") { temp = "false"; } - bool lt = isTrue(temp); + groups = validParameter.validFile(parameters, "groups", false); + if (groups == "not found") { groups = ""; } + else { m->splitAtDash(groups, Groups); } + m->setGroups(Groups); - if (lt) { matrix = 2; } - else { matrix = 1; } - - } - - } - catch(exception& e) { - errorOut(e, "PCACommand", "PCACommand"); - exit(1); - } -} -//********************************************************************************************************************** -void PCACommand::help(){ - try { - - mothurOut("The pca command..."); mothurOutEndLine(); + } catch(exception& e) { - errorOut(e, "PCACommand", "help"); + m->errorOut(e, "PCACommand", "PCACommand"); exit(1); } } //********************************************************************************************************************** -PCACommand::~PCACommand(){} -//********************************************************************************************************************** int PCACommand::execute(){ try { - - if (abort == true) { return 0; } + + if (abort == true) { if (calledHelp) { return 0; } return 2; } cout.setf(ios::fixed, ios::floatfield); cout.setf(ios::showpoint); cerr.setf(ios::fixed, ios::floatfield); cerr.setf(ios::showpoint); - vector names; - vector > D; - - fbase = filename; - if(fbase.find_last_of(".")!=string::npos){ - fbase.erase(fbase.find_last_of(".")+1); + //get first line of shared file + vector< vector > matrix; + InputData* input; + if (mode == "sharedfile") { + input = new InputData(inputFile, "sharedfile"); + }else if (mode == "relabund") { + input = new InputData(inputFile, "relabund"); + }else { m->mothurOut("[ERROR]: filetype not recognized."); m->mothurOutEndLine(); return 0; } + + vector lookupFloat = input->getSharedRAbundFloatVectors(); + string lastLabel = lookupFloat[0]->getLabel(); + + set processedLabels; + set userLabels = labels; + + //if the user gave no labels, then use the first one read + if (labels.size() == 0) { + label = lastLabel; + + process(lookupFloat); } - else{ - fbase += "."; + + //as long as you are not at the end of the file or done wih the lines you want + while((lookupFloat[0] != NULL) && (userLabels.size() != 0)) { + + if (m->control_pressed) { for (int i = 0; i < outputNames.size(); i++) { m->mothurRemove(outputNames[i]); } delete input; for (int i = 0; i < lookupFloat.size(); i++) { delete lookupFloat[i]; } lookupFloat.clear(); return 0; } + + if(labels.count(lookupFloat[0]->getLabel()) == 1){ + processedLabels.insert(lookupFloat[0]->getLabel()); + userLabels.erase(lookupFloat[0]->getLabel()); + + process(lookupFloat); + } + + if ((m->anyLabelsToProcess(lookupFloat[0]->getLabel(), userLabels, "") == true) && (processedLabels.count(lastLabel) != 1)) { + string saveLabel = lookupFloat[0]->getLabel(); + + for (int i = 0; i < lookupFloat.size(); i++) { delete lookupFloat[i]; } lookupFloat.clear(); + lookupFloat = input->getSharedRAbundFloatVectors(lastLabel); + + process(lookupFloat); + + processedLabels.insert(lookupFloat[0]->getLabel()); + userLabels.erase(lookupFloat[0]->getLabel()); + + //restore real lastlabel to save below + lookupFloat[0]->setLabel(saveLabel); + } + + lastLabel = lookupFloat[0]->getLabel(); + + //get next line to process + //prevent memory leak + for (int i = 0; i < lookupFloat.size(); i++) { delete lookupFloat[i]; } lookupFloat.clear(); + lookupFloat = input->getSharedRAbundFloatVectors(); } - read(filename, matrix, names, D); - - double offset = 0.0000; - vector d; - vector e; - vector > G = D; - vector > copy_G; - int rank = D.size(); - cout << "\nProcessing...\n"; - for(int count=0;count<2;count++){ - recenter(offset, D, G); - tred2(G, d, e); - qtli(d, e, G); - offset = d[d.size()-1]; - if(offset > 0.0) break; - } + if (m->control_pressed) { for (int i = 0; i < outputNames.size(); i++) { m->mothurRemove(outputNames[i]); } delete input; for (int i = 0; i < lookupFloat.size(); i++) { delete lookupFloat[i]; } lookupFloat.clear(); return 0; } + //output error messages about any remaining user labels + set::iterator it; + bool needToRun = false; + for (it = userLabels.begin(); it != userLabels.end(); it++) { + m->mothurOut("Your file does not include the label " + *it); + if (processedLabels.count(lastLabel) != 1) { + m->mothurOut(". I will use " + lastLabel + "."); m->mothurOutEndLine(); + needToRun = true; + }else { + m->mothurOut(". Please refer to " + lastLabel + "."); m->mothurOutEndLine(); + } + } - output(fbase, names, G, d); + //run last label if you need to + if (needToRun == true) { + for (int i = 0; i < lookupFloat.size(); i++) { if (lookupFloat[i] != NULL) { delete lookupFloat[i]; } } lookupFloat.clear(); + lookupFloat = input->getSharedRAbundFloatVectors(lastLabel); + + process(lookupFloat); + + for (int i = 0; i < lookupFloat.size(); i++) { if (lookupFloat[i] != NULL) { delete lookupFloat[i]; } } lookupFloat.clear(); + } - return 0; - } - catch(exception& e) { - errorOut(e, "PCACommand", "execute"); - exit(1); - } -} -/*********************************************************************************************************************************/ - -inline double SIGN(const double a, const double b) -{ - return b>=0 ? (a>=0 ? a:-a) : (a>=0 ? -a:a); -} - -/*********************************************************************************************************************************/ - -void PCACommand::get_comment(istream& f, char begin, char end){ - try { - char d=f.get(); - while(d != end){ d = f.get(); } - d = f.peek(); - } - catch(exception& e) { - errorOut(e, "PCACommand", "get_comment"); - exit(1); - } -} - -/*********************************************************************************************************************************/ - -void PCACommand::read_mega(istream& f, int square_m, vector& name_list, vector >& d){ - try { - get_comment(f, '#', '\n'); + for (int i = 0; i < lookupFloat.size(); i++) { if (lookupFloat[i] != NULL) { delete lookupFloat[i]; } } lookupFloat.clear(); + delete input; - char test = f.peek(); + if (m->control_pressed) { for (int i = 0; i < outputNames.size(); i++) { m->mothurRemove(outputNames[i]); } return 0; } - while(test == '!'){ //get header comments - get_comment(f, '!', ';'); - while(isspace(test=f.get())) {;} - f.putback(test); - test = f.peek(); - } - while(test != '\n'){ //get sequence names - get_comment(f, '[', ']'); - char d = f.get(); - d = f.get(); - if(d == '#'){ - string name; - f >> name; - name_list.push_back(name); - while(isspace(test=f.get())) {;} - f.putback(test); - } - else{ - break; - } - } - int rank = name_list.size(); - d.resize(rank); - for(int i=0;i> d[i][j]; - if (d[i][j] == -0.0000) - d[i][j] = 0.0000; - d[j][i]=d[i][j]; - } - } + m->mothurOutEndLine(); + m->mothurOut("Output File Names: "); m->mothurOutEndLine(); + for (int i = 0; i < outputNames.size(); i++) { m->mothurOut(outputNames[i]); m->mothurOutEndLine(); } + m->mothurOutEndLine(); + + return 0; } catch(exception& e) { - errorOut(e, "PCACommand", "read_mega"); + m->errorOut(e, "PCACommand", "execute"); exit(1); } } -/*********************************************************************************************************************************/ - -void PCACommand::read_phylip(istream& f, int square_m, vector& name_list, vector >& d){ +/********************************************************************************************************************** +vector< vector > PCACommand::createMatrix(vector lookupFloat){ try { - // int count1=0; - // int count2=0; - - int rank; - f >> rank; - - name_list.resize(rank); - d.resize(rank); - if(square_m == 1){ - for(int i=0;i> name_list[i]; - // cout << i << "\t" << name_list[i] << endl; - for(int j=0;j> d[i][j]; - if (d[i][j] == -0.0000) - d[i][j] = 0.0000; - } + vector< vector > matrix; matrix.resize(lookupFloat.size()); + + //fill matrix with shared files relative abundances + for (int i = 0; i < lookupFloat.size(); i++) { + for (int j = 0; j < lookupFloat[i]->getNumBins(); j++) { + matrix[i].push_back(lookupFloat[i]->getAbundance(j)); } } - else if(square_m == 2){ - for(int i=0;i> name_list[0]; - for(int i=1;i> name_list[i]; - d[i][i]=0.0000; - for(int j=0;j> d[i][j]; - if (d[i][j] == -0.0000) - d[i][j] = 0.0000; - d[j][i]=d[i][j]; - } + + vector< vector > transposeMatrix; transposeMatrix.resize(matrix[0].size()); + for (int i = 0; i < transposeMatrix.size(); i++) { + for (int j = 0; j < matrix.size(); j++) { + transposeMatrix[i].push_back(matrix[j][i]); } } - } - catch(exception& e) { - errorOut(e, "PCACommand", "read_phylip"); - exit(1); - } - -} - -/*********************************************************************************************************************************/ - -void PCACommand::read(string fname, int m, vector& names, vector >& D){ - try { - ifstream f(fname.c_str()); - if(!f) { - cerr << "Error: Could not open " << fname << endl; - exit(1); - } - char test = f.peek(); - if(test == '#'){ - read_mega(f, m, names, D); - } - else{ - read_phylip(f, m, names, D); - } + matrix = linearCalc.matrix_mult(matrix, transposeMatrix); - int rank = D.size(); + return matrix; } catch(exception& e) { - errorOut(e, "PCACommand", "read"); + m->errorOut(e, "PCACommand", "createMatrix"); exit(1); } -} - -/*********************************************************************************************************************************/ -double PCACommand::pythag(double a, double b){ - return(pow(a*a+b*b,0.5)); -} -/*********************************************************************************************************************************/ +}*/ +//********************************************************************************************************************** -void PCACommand::matrix_mult(vector > first, vector > second, vector >& product){ +int PCACommand::process(vector& lookupFloat){ try { - int first_rows = first.size(); - int first_cols = first[0].size(); - int second_cols = second[0].size(); + m->mothurOut("\nProcessing " + lookupFloat[0]->getLabel()); m->mothurOutEndLine(); + + int numOTUs = lookupFloat[0]->getNumBins(); + int numSamples = lookupFloat.size(); - product.resize(first_rows); - for(int i=0;i > matrix(numSamples); + vector colMeans(numOTUs); - for(int i=0;igetAbundance(j); + colMeans[j] += matrix[i][j]; } } - } - catch(exception& e) { - errorOut(e, "PCACommand", "matrix_mult"); - exit(1); - } - -} - -/*********************************************************************************************************************************/ - -void PCACommand::recenter(double offset, vector > D, vector >& G){ - try { - int rank = D.size(); - vector > A(rank); - vector > C(rank); - for(int i=0;i > centered = matrix; + for(int i=0;i >& a, vector& d, vector& e){ - try { - double scale, hh, h, g, f; - - int n = a.size(); - - d.resize(n); - e.resize(n); - for(int i=n-1;i>0;i--){ - int l=i-1; - h = scale = 0.0000; - if(l>0){ - for(int k=0;k= 0.0 ? -sqrt(h) : sqrt(h)); - e[i] = scale * g; - h -= f * g; - a[i][l] = f - g; - f = 0.0; - for(int j=0;j > transpose(numOTUs); + for (int i = 0; i < numOTUs; i++) { + transpose[i].resize(numSamples, 0); - d[i] = h; - } - - d[0] = 0.0000; - e[0] = 0.0000; - - for(int i=0;i > crossProduct = linearCalc.matrix_mult(transpose, centered); + + vector d; + vector e; -void PCACommand::qtli(vector& d, vector& e, vector >& z) { - try { - int m, i, iter; - double s, r, p, g, f, dd, c, b; + linearCalc.tred2(crossProduct, d, e); if (m->control_pressed) { return 0; } + linearCalc.qtli(d, e, crossProduct); if (m->control_pressed) { return 0; } - int n = d.size(); - for(int i=1;i<=n;i++){ - e[i-1] = e[i]; - } - e[n-1] = 0.0000; - - for(int l=0;l=l;i--){ - f = s * e[i]; - b = c * e[i]; - e[i+1] = (r=pythag(f,g)); - if(r==0.0){ - d[i+1] -= p; - e[m] = 0.0000; - break; - } - s = f / r; - c = g / r; - g = d[i+1] - p; - r = (d[i] - g) * s + 2.0 * c * b; - d[i+1] = g + ( p = s * r); - g = c * r - b; - for(int k=0;k= l) continue; - d[l] -= p; - e[l] = g; - e[m] = 0.0; - } - } while (m != l); - } + vector > X = linearCalc.matrix_mult(centered, crossProduct); - int k; - for(int i=0;i= p){ - p=d[k=j]; - } - } - if(k!=i){ - d[k]=d[i]; - d[i]=p; - for(int j=0;jcontrol_pressed) { return 0; } + + string fbase = outputDir + m->getRootName(m->getSimpleName(inputFile)); + //string outputFileName = fbase + lookupFloat[0]->getLabel(); + output(fbase, lookupFloat[0]->getLabel(), m->getGroups(), X, d); + + if (metric) { + + vector > observedEuclideanDistance = linearCalc.getObservedEuclideanDistance(centered); + + for (int i = 1; i < 4; i++) { + + vector< vector > PCAEuclidDists = linearCalc.calculateEuclidianDistance(X, i); //G is the pca file + + if (m->control_pressed) { for (int i = 0; i < outputNames.size(); i++) { m->mothurRemove(outputNames[i]); } return 0; } + + double corr = linearCalc.calcPearson(PCAEuclidDists, observedEuclideanDistance); + + m->mothurOut("Rsq " + toString(i) + " axis: " + toString(corr * corr)); m->mothurOutEndLine(); + + if (m->control_pressed) { for (int i = 0; i < outputNames.size(); i++) { m->mothurRemove(outputNames[i]); } return 0; } } } + + return 0; } catch(exception& e) { - errorOut(e, "PCACommand", "qtli"); + m->errorOut(e, "PCACommand", "process"); exit(1); } } - /*********************************************************************************************************************************/ -void PCACommand::output(string fnameRoot, vector name_list, vector > G, vector d) { +void PCACommand::output(string fbase, string label, vector name_list, vector >& G, vector d) { try { - int rank = name_list.size(); + + int numEigenValues = d.size(); double dsum = 0.0000; - for(int i=0;i= 0) { G[i][j] *= pow(d[j],0.5); } - else { G[i][j] = 0.00000; } - } } - ofstream pcaData((fnameRoot+"pca").c_str(), ios::trunc); + ofstream pcaData; + map variables; + variables["[filename]"] = fbase; + variables["[distance]"] = label; + string pcaFileName = getOutputFileName("pca",variables); + m->openOutputFile(pcaFileName, pcaData); pcaData.setf(ios::fixed, ios::floatfield); pcaData.setf(ios::showpoint); + outputNames.push_back(pcaFileName); + outputTypes["pca"].push_back(pcaFileName); - ofstream pcaLoadings((fnameRoot+"pca.loadings").c_str(), ios::trunc); + ofstream pcaLoadings; + string loadingsFilename = getOutputFileName("loadings",variables); + m->openOutputFile(loadingsFilename, pcaLoadings); pcaLoadings.setf(ios::fixed, ios::floatfield); - pcaLoadings.setf(ios::showpoint); + pcaLoadings.setf(ios::showpoint); + outputNames.push_back(loadingsFilename); + outputTypes["loadings"].push_back(loadingsFilename); pcaLoadings << "axis\tloading\n"; - for(int i=0;ierrorOut(e, "PCACommand", "output"); exit(1); } } - /*********************************************************************************************************************************/ -void PCACommand::print_matrix(vector > A) { - try { - int rank = A.size(); - for(int i=0;i