Sample ROC points at fixed FAR values for easy vertical averaging. Display conf…

…idence intervals in tables and plots.

Sample ROC points at fixed FAR values for easy vertical averaging. Display conf…
…idence intervals in tables and plots.
bhklein
1 parent cb9c5416
Showing 2 changed files with 71 additions and 50 deletions
openbr/core/eval.cpp
openbr/core/plot.cpp
@@ -48,22 +48,26 @@ struct OperatingPoint
         : score(_score), FAR(_FAR), TAR(_TAR) {}
 };
-static float getTAR(const QList<OperatingPoint> &operatingPoints, float FAR)
+static OperatingPoint getOperatingPoint(const QList<OperatingPoint> &operatingPoints, float FAR)
 {
     int index = 0;
     while (operatingPoints[index].FAR < FAR) {
         index++;
         if (index == operatingPoints.size())
-            return 1;
+            return OperatingPoint(operatingPoints.last().score, FAR, operatingPoints.last().TAR);
     }
-    const float x1 = (index == 0 ? 0 : operatingPoints[index-1].FAR);
-    const float y1 = (index == 0 ? 0 : operatingPoints[index-1].TAR);
-    const float x2 = operatingPoints[index].FAR;
-    const float y2 = operatingPoints[index].TAR;
-    const float m = (y2 - y1) / (x2 - x1);
-    const float b = y1 - m*x1;
-    return m * FAR + b;
+    const float FAR1 = (index == 0 ? 0 : operatingPoints[index-1].FAR);
+    const float TAR1 = (index == 0 ? 0 : operatingPoints[index-1].TAR);
+    const float score1 = (index == 0 ? operatingPoints[index].score : operatingPoints[index-1].score);
+    const float FAR2 = operatingPoints[index].FAR;
+    const float TAR2 = operatingPoints[index].TAR;
+    const float score2 = operatingPoints[index].score;
+    const float mTAR = (TAR2 - TAR1) / (FAR2 - FAR1);
+    const float bTAR = TAR1 - mTAR*FAR1;
+    const float mScore = (score2 - score1) / (FAR2 - FAR1);
+    const float bScore = score1 - mScore*FAR1;
+    return OperatingPoint(mScore * FAR + bScore,FAR, mTAR * FAR + bTAR);
 }
 static float getCMC(const QVector<int> &firstGenuineReturns, int rank)
@@ -266,23 +270,26 @@ float Evaluate(const Mat &amp;simmat, const Mat &amp;mask, const QString &amp;csv, const QSt
     }
     // Write Detection Error Tradeoff (DET), PRE, REC
-    int points = qMin(operatingPoints.size(), Max_Points);
-    for (int i=0; i<points; i++) {
-        const OperatingPoint &operatingPoint = operatingPoints[double(i) / double(points-1) * double(operatingPoints.size()-1)];
-        lines.append(QString("DET,%1,%2").arg(QString::number(operatingPoint.FAR),
+    float FAR=0.000001;
+    for (int i=0; i<Max_Points; i++) {
+        OperatingPoint operatingPoint = getOperatingPoint(operatingPoints, FAR);
+        lines.append(QString("DET,%1,%2").arg(QString::number(FAR),
                                               QString::number(1-operatingPoint.TAR)));
         lines.append(QString("FAR,%1,%2").arg(QString::number(operatingPoint.score),
-                                              QString::number(operatingPoint.FAR)));
+                                              QString::number(FAR)));
         lines.append(QString("FRR,%1,%2").arg(QString::number(operatingPoint.score),
                                               QString::number(1-operatingPoint.TAR)));
+        //multiplier roughly spans 10E-6 to 1
+        FAR *=1.02807;
     }
+
     // Write FAR/TAR Table (FT)
-    lines.append(qPrintable(QString("FT,0.000001,%1").arg(QString::number(getTAR(operatingPoints, 0.000001), 'f', 3))));
-    lines.append(qPrintable(QString("FT,0.00001,%1").arg(QString::number(getTAR(operatingPoints, 0.00001), 'f', 3))));
-    lines.append(qPrintable(QString("FT,0.0001,%1").arg(QString::number(getTAR(operatingPoints, 0.0001), 'f', 3))));
-    lines.append(qPrintable(QString("FT,0.001,%1").arg(QString::number(getTAR(operatingPoints, 0.001), 'f', 3))));
-    lines.append(qPrintable(QString("FT,0.01,%1").arg(QString::number(getTAR(operatingPoints, 0.01), 'f', 3))));    
-    lines.append(qPrintable(QString("FT,0.1,%1").arg(QString::number(getTAR(operatingPoints, 0.1), 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.000001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.000001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.00001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.00001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.0001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.0001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.01,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.01).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("FT,0.1,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.1).TAR, 'f', 3))));
     //Write CMC Table (CT)
     lines.append(qPrintable(QString("CT,1,%1").arg(QString::number(getCMC(firstGenuineReturns, 1), 'f', 3))));
@@ -293,19 +300,18 @@ float Evaluate(const Mat &amp;simmat, const Mat &amp;mask, const QString &amp;csv, const QSt
     lines.append(qPrintable(QString("CT,100,%1").arg(QString::number(getCMC(firstGenuineReturns, 100), 'f', 3))));
     // Write FAR/TAR Bar Chart (BC)
-    lines.append(qPrintable(QString("BC,0.001,%1").arg(QString::number(getTAR(operatingPoints, 0.001), 'f', 3))));
-    lines.append(qPrintable(QString("BC,0.01,%1").arg(QString::number(result = getTAR(operatingPoints, 0.01), 'f', 3))));
+    lines.append(qPrintable(QString("BC,0.001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("BC,0.01,%1").arg(QString::number(result = getOperatingPoint(operatingPoints, 0.01).TAR, 'f', 3))));
     // Attempt to read template size from enrolled gallery and write to output CSV
     size_t maxSize(0);
     if (target.endsWith(".gal")) {
         foreach (const Template &t, TemplateList::fromGallery(target)) maxSize = max(maxSize, t.bytes());
+        lines.append(QString("TS,,%1").arg(QString::number(maxSize)));
     }
-    lines.append(QString("TS,,%1").arg(QString::number(maxSize)));
-
     // Write SD & KDE
-    points = qMin(qMin(Max_Points, genuines.size()), impostors.size());
+    int points = qMin(qMin(Max_Points, genuines.size()), impostors.size());
     QList<double> sampledGenuineScores; sampledGenuineScores.reserve(points);
     QList<double> sampledImpostorScores; sampledImpostorScores.reserve(points);
@@ -332,10 +338,10 @@ float Evaluate(const Mat &amp;simmat, const Mat &amp;mask, const QString &amp;csv, const QSt
     QtUtils::writeFile(csv, lines);
     if (maxSize > 0) qDebug("Template Size: %i bytes", (int)maxSize);
-    qDebug("TAR @ FAR = 0.01:    %.3f",getTAR(operatingPoints, 0.01));
-    qDebug("TAR @ FAR = 0.001:   %.3f",getTAR(operatingPoints, 0.001));
-    qDebug("TAR @ FAR = 0.0001:  %.3f",getTAR(operatingPoints, 0.0001));
-    qDebug("TAR @ FAR = 0.00001: %.3f",getTAR(operatingPoints, 0.00001));
+    qDebug("TAR @ FAR = 0.01:    %.3f",getOperatingPoint(operatingPoints, 0.01).TAR);
+    qDebug("TAR @ FAR = 0.001:   %.3f",getOperatingPoint(operatingPoints, 0.001).TAR);
+    qDebug("TAR @ FAR = 0.0001:  %.3f",getOperatingPoint(operatingPoints, 0.0001).TAR);
+    qDebug("TAR @ FAR = 0.00001: %.3f",getOperatingPoint(operatingPoints, 0.00001).TAR);
     qDebug("\nRetrieval Rate @ Rank = %d: %.3f", Report_Retrieval, getCMC(firstGenuineReturns, Report_Retrieval));
@@ -560,8 +566,8 @@ float InplaceEval(const QString &amp;simmat, const QString &amp;target, const QString &amp;q
     float result;
     // Write FAR/TAR Bar Chart (BC)
-    lines.append(qPrintable(QString("BC,0.001,%1").arg(QString::number(getTAR(operatingPoints, 0.001), 'f', 3))));
-    lines.append(qPrintable(QString("BC,0.01,%1").arg(QString::number(result = getTAR(operatingPoints, 0.01), 'f', 3))));
+    lines.append(qPrintable(QString("BC,0.001,%1").arg(QString::number(getOperatingPoint(operatingPoints, 0.001).TAR, 'f', 3))));
+    lines.append(qPrintable(QString("BC,0.01,%1").arg(QString::number(result = getOperatingPoint(operatingPoints, 0.01).TAR, 'f', 3))));
     qDebug("TAR @ FAR = 0.01: %.3f", result);
     QtUtils::writeFile(csv, lines);
@@ -108,7 +108,6 @@ struct RPlot
         pivotItems = QVector< QSet<QString> >(pivotHeaders.size());
         foreach (const QString &fileName, files) {
             QStringList pivots = getPivots(fileName, false);
-            
             // If the number of pivots don't match, abandon the directory/filename labeling scheme
             if (pivots.size() != pivotHeaders.size()) {
                 pivots.clear();
@@ -132,7 +131,6 @@ struct RPlot
                 minor = Pivot(i, size, pivotHeaders[i]);
             }
         }
-
         const QString &smooth = destination.get<QString>("smooth", "");
         major.smooth = !smooth.isEmpty() && (major.header == smooth) && (major.size > 1);
         minor.smooth = !smooth.isEmpty() && (minor.header == smooth) && (minor.size > 1);
@@ -177,29 +175,42 @@ struct RPlot
                        "TS$Y <- as.character(TS$Y)\n"
                        "CMC$Y <- as.numeric(as.character(CMC$Y))\n"
                        "\n"
+                       "if (%1) {\n\tsummarySE <- function(data=NULL, measurevar, groupvars=NULL, na.rm=FALSE, conf.interval=.95, .drop=TRUE) {\n\t\t"
+                       "require(plyr)\n\n\t\tlength2 <- function (x, na.rm=FALSE) {\n\t\t\tif (na.rm) sum(!is.na(x))\n\t\t\telse       length(x)"
+                       "\n\t\t}\n\n\t\tdatac <- ddply(data, groupvars, .drop=.drop, .fun = function(xx, col) {\n\t\t\t"
+                       "c(N=length2(xx[[col]], na.rm=na.rm), mean=mean(xx[[col]], na.rm=na.rm), sd=sd(xx[[col]], na.rm=na.rm))\n\t\t\t},"
+                       "\n\t\t\tmeasurevar\n\t\t)\n\n\t\tdatac <- rename(datac, c(\"mean\" = measurevar))\n\t\tdatac$se <- datac$sd / sqrt(datac$N)"
+                       "\n\t\tciMult <- qt(conf.interval/2 + .5, datac$N-1)\n\t\tdatac$ci <- datac$se * ciMult\n\n\t\treturn(datac)\n\t}\n\t"
+                       "DET <- summarySE(DET, measurevar=\"Y\", groupvars=c(\"%2\", \"X\"))\n\t"
+                       "ERR <- summarySE(ERR, measurevar=\"X\", groupvars=c(\"Error\", \"%2\", \"Y\"))\n\t"
+                       "FT <- summarySE(FT, measurevar=\"Y\", groupvars=c(\"%2\", \"X\"))\n\t"
+                       "CT <- summarySE(CT, measurevar=\"Y\", groupvars=c(\"%2\", \"X\"))\n}\n\n"
                        "# Code to format FAR values\n"
                        "far_names <- list('0.001'=\"FAR = 0.1%\", '0.01'=\"FAR = 1%\")\n"
                        "far_labeller <- function(variable,value) { return(far_names[as.character(value)]) }\n"
                        "\n"
                        "# Code to format TAR@FAR table\n"
-                       "algs <- unique(FT$%1)\n"
+                       "algs <- unique(FT$%2)\n"
                        "algs <- algs[!duplicated(algs)]\n"
-                       "mat <- matrix(FT$Y,nrow=6,ncol=length(algs),byrow=FALSE)\n"
+                       "mat <- matrix(%3,nrow=6,ncol=length(algs),byrow=FALSE)\n"
                        "colnames(mat) <- algs \n"
                        "rownames(mat) <- c(\"FAR = 1e-06\", \"FAR = 1e-05\", \"FAR = 1e-04\", \"FAR = 1e-03\", \"FAR = 1e-02\", \"FAR = 1e-01\")\n"
                        "FTtable <- as.table(mat)\n"
                        "\n"
                        "# Code to format CMC Table\n"
-                       "mat <- matrix(CT$Y,nrow=6,ncol=length(algs),byrow=FALSE)\n"
+                       "mat <- matrix(%4,nrow=6,ncol=length(algs),byrow=FALSE)\n"
                        "colnames(mat) <- algs \n"
                        "rownames(mat) <- c(\" Rank 1\", \"Rank 5\", \"Rank 10\", \"Rank 20\", \"Rank 50\", \"Rank 100\")\n"
                        "CMCtable <- as.table(mat)\n"
                        "\n"
                        "# Code to format Template Size Table\n"
-                       "mat <- matrix(TS$Y,nrow=1,ncol=length(algs),byrow=FALSE)\n"
-                       "colnames(mat) <- algs\n"
-                       "rownames(mat) <- c(\"Template Size (bytes):\")\n"
-                       "TStable <- as.table(mat)\n").arg(major.header)));
+                       "if (nrow(TS) != 0) {\n\t"
+                       "mat <- matrix(TS$Y,nrow=1,ncol=length(algs),byrow=FALSE)\n\t"
+                       "colnames(mat) <- algs\n\t"
+                       "rownames(mat) <- c(\"Template Size (bytes):\")\n\t"
+                       "TStable <- as.table(mat)\n}\n").arg(((major.smooth || minor.smooth) ? "TRUE" : "FALSE"), major.size > 1 ? major.header : (minor.header.isEmpty() ? major.header : minor.header),
+                                                            (major.smooth || minor.smooth) ? "paste(as.character(round(FT$Y, 3)), round(FT$ci, 3), sep=\"\\u00b1\")" : "FT$Y",
+                                                            (major.smooth || minor.smooth) ? "paste(as.character(round(CT$Y, 3)), round(CT$ci, 3), sep=\"\\u00b1\")" : "CT$Y")));
         // Open output device
         file.write(qPrintable(QString("\n"
@@ -231,8 +242,9 @@ struct RPlot
                                "print(title(\"Table of True Accept Rates at various False Accept Rates\"))\n"
                                "print(textplot(CMCtable))\n"
                                "print(title(\"Table of retrieval rate at various ranks\"))\n"
-                               "print(textplot(TStable, cex=1.15))\n"
-                               "print(title(\"Template Size by Algorithm\"))\n";
+                               "if (nrow(TS) != 0) {\n\t"
+                               "print(textplot(TStable, cex=1.15))\n\t"
+                               "print(title(\"Template Size by Algorithm\"))\n}\n";
             file.write(qPrintable(textplot.arg(PRODUCT_NAME, PRODUCT_VERSION)));
         }
@@ -281,11 +293,12 @@ bool Plot(const QStringList &amp;files, const File &amp;destination, bool show)
     RPlot p(files, destination);
-    p.file.write(qPrintable(QString("qplot(X, 1-Y, data=DET%1, main=\"%2\"").arg((p.major.smooth || p.minor.smooth) ? ", geom=\"smooth\", method=loess, level=0.99" : ", geom=\"line\"", rocOpts.get<QString>("title",QString())) +
+    p.file.write(qPrintable(QString("qplot(X, 1-Y, data=DET, geom=\"line\", main=\"%1\"").arg(rocOpts.get<QString>("title",QString())) +
                             (p.major.size > 1 ? QString(", colour=factor(%1)").arg(p.major.header) : QString()) +
                             (p.minor.size > 1 ? QString(", linetype=factor(%1)").arg(p.minor.header) : QString()) +
                             QString(", xlab=\"False Accept Rate\", ylab=\"True Accept Rate\") + theme_minimal()") +
-                            (p.major.size > 1 ? getScale("colour", "Algorithm", p.major.size) : QString()) +
+                            ((p.major.smooth || p.minor.smooth) ? " + geom_errorbar(data=DET[seq(1, NROW(DET), by = 29),], aes(x=X, ymin=(1-Y)-ci, ymax=(1-Y)+ci), width=0.1, alpha=I(1/2))" : QString()) +
+                            (p.major.size > 1 ? getScale("colour", p.major.header, p.major.size) : QString()) +
                             (p.minor.size > 1 ? QString(" + scale_linetype_discrete(\"%1\")").arg(p.minor.header) : QString()) +
                             QString(" + scale_x_log10(labels=trans_format(\"log10\", math_format()))") +
                             (rocOpts.contains("yLimits") ? QString(" + scale_y_continuous(labels=percent) + coord_cartesian(ylim=%1)").arg("c"+QtUtils::toString(rocOpts.get<QPointF>("yLimits",QPointF()))) : QString(" + scale_y_continuous(labels=percent)")) +
@@ -293,12 +306,14 @@ bool Plot(const QStringList &amp;files, const File &amp;destination, bool show)
                             QString(" + theme(legend.title = element_text(size = %1), plot.title = element_text(size = %1), axis.text = element_text(size = %1), axis.title.x = element_text(size = %1), axis.title.y = element_text(size = %1),"
                             " legend.position=%2, legend.background = element_rect(fill = 'white'), panel.grid.major = element_line(colour = \"gray\"), panel.grid.minor = element_line(colour = \"gray\", linetype = \"dashed\"), legend.text = element_text(size = %1))\n\n").arg(QString::number(rocOpts.get<float>("textSize",12)), rocOpts.contains("legendPosition") ? "c"+QtUtils::toString(rocOpts.get<QPointF>("legendPosition")) : "'bottom'")));
-    p.file.write(qPrintable(QString("qplot(X, Y, data=DET%1").arg((p.major.smooth || p.minor.smooth) ? ", geom=\"smooth\", method=loess, level=0.99" : ", geom=\"line\"") +
+    p.file.write(qPrintable(QString("qplot(X, Y, data=DET, geom=\"line\"") +
                             (p.major.size > 1 ? QString(", colour=factor(%1)").arg(p.major.header) : QString()) +
                             (p.minor.size > 1 ? QString(", linetype=factor(%1)").arg(p.minor.header) : QString()) +
                             QString(", xlab=\"False Accept Rate\", ylab=\"False Reject Rate\") + geom_abline(alpha=0.5, colour=\"grey\", linetype=\"dashed\") + theme_minimal()") +
-                            (p.major.size > 1 ? getScale("colour", "Algorithm", p.major.size) : QString()) +
+                            ((p.major.smooth || p.minor.smooth) ? " + geom_errorbar(data=DET[seq(1, NROW(DET), by = 29),], aes(x=X, ymin=Y-ci, ymax=Y+ci), width=0.1, alpha=I(1/2))" : QString()) +
+                            (p.major.size > 1 ? getScale("colour", p.major.header, p.major.size) : QString()) +
                             (p.minor.size > 1 ? QString(" + scale_linetype_discrete(\"%1\")").arg(p.minor.header) : QString()) +
+                            QString(" + theme(legend.position=%1)").arg(rocOpts.contains("legendPosition") ? "c"+QtUtils::toString(rocOpts.get<QPointF>("legendPosition")) : "'bottom'") +
                             QString(" + scale_x_log10(labels=trans_format(\"log10\", math_format())) + scale_y_log10(labels=trans_format(\"log10\", math_format())) + annotation_logticks()\n\n")));
     p.file.write(qPrintable(QString("qplot(X, data=SD, geom=\"histogram\", fill=Y, position=\"identity\", alpha=I(1/2)") +
@@ -311,7 +326,7 @@ bool Plot(const QStringList &amp;files, const File &amp;destination, bool show)
                             QString(((p.major.smooth || p.minor.smooth) ? (!uncertainty ? " + stat_summary(geom=\"line\", fun.y=mean, size=%1)" : " + stat_summary(geom=\"line\", fun.y=min, aes(linetype=\"Min/Max\"), size=%1) + stat_summary(geom=\"line\", "
                             "fun.y=max, aes(linetype=\"Min/Max\"), size=%1) + stat_summary(geom=\"line\", fun.y=mean, aes(linetype=\"Mean\"), size=%1) + scale_linetype_manual(\"Legend\", values=c(\"Mean\"=1, \"Min/Max\"=2))") : " + geom_line(size=%1)")).arg(QString::number(cmcOpts.get<float>("thickness",1))) +
                             (minimalist ? "" : " + scale_x_log10(labels=c(1,5,10,50,100), breaks=c(1,5,10,50,100)) + annotation_logticks(sides=\"b\")") +
-                            (p.major.size > 1 ? getScale("colour", "Algorithm", p.major.size) : QString()) +
+                            (p.major.size > 1 ? getScale("colour", p.major.header, p.major.size) : QString()) +
                             (p.minor.size > 1 ? QString(" + scale_linetype_discrete(\"%1\")").arg(p.minor.header) : QString()) +
                             (cmcOpts.contains("yLimits") ? QString(" + scale_y_continuous(labels=percent) + coord_cartesian(ylim=%1)").arg("c"+QtUtils::toString(cmcOpts.get<QPointF>("yLimits",QPointF()))) : QString(" + scale_y_continuous(labels=percent)")) +
                             QString(" + theme_minimal() + theme(legend.title = element_text(size = %1), plot.title = element_text(size = %1), axis.text = element_text(size = %1), axis.title.x = element_text(size = %1), axis.title.y = element_text(size = %1),"
@@ -320,14 +335,14 @@ bool Plot(const QStringList &amp;files, const File &amp;destination, bool show)
     p.file.write(qPrintable(QString("qplot(factor(%1)%2, data=BC, %3").arg(p.major.smooth ? (p.minor.header.isEmpty() ? "Algorithm" : p.minor.header) : p.major.header, (p.major.smooth || p.minor.smooth) ? ", Y" : "", (p.major.smooth || p.minor.smooth) ? "geom=\"boxplot\"" : "geom=\"bar\", position=\"dodge\", weight=Y") +
                             (p.major.size > 1 ? QString(", fill=factor(%1)").arg(p.major.header) : QString()) +
                             QString(", xlab=\"False Accept Rate\", ylab=\"True Accept Rate\") + theme_minimal()") +
-                            (p.major.size > 1 ? getScale("fill", "Algorithm", p.major.size) : QString()) +
+                            (p.major.size > 1 ? getScale("fill", p.major.header, p.major.size) : QString()) +
                             (p.minor.size > 1 ? QString(" + facet_grid(%2 ~ X)").arg(p.minor.header) : QString(" + facet_grid(. ~ X, labeller=far_labeller)")) +
                             QString(" + scale_y_continuous(labels=percent) + theme(legend.position=\"none\", axis.text.x=element_text(angle=-90, hjust=0))%1").arg((p.major.smooth || p.minor.smooth) ? "" : " + geom_text(data=BC, aes(label=Y, y=0.05))") + "\n\n"));
-    p.file.write(qPrintable(QString("qplot(X, Y, data=ERR%1, linetype=Error").arg((p.major.smooth || p.minor.smooth) ? ", geom=\"smooth\", method=loess, level=0.99" : ", geom=\"line\"") +
+    p.file.write(qPrintable(QString("qplot(X, Y, data=ERR, geom=\"line\", linetype=Error") +
                             ((p.flip ? p.major.size : p.minor.size) > 1 ? QString(", colour=factor(%1)").arg(p.flip ? p.major.header : p.minor.header) : QString()) +
                             QString(", xlab=\"Score\", ylab=\"Error Rate\") + theme_minimal()") +
-                            ((p.flip ? p.major.size : p.minor.size) > 1 ? getScale("colour", p.flip ? "Algorithm" : "Algorithm", p.flip ? p.major.size : p.minor.size) : QString()) +
+                            ((p.flip ? p.major.size : p.minor.size) > 1 ? getScale("colour", p.flip ? p.major.header : p.minor.header, p.flip ? p.major.size : p.minor.size) : QString()) +
                             QString(" + scale_y_log10(labels=percent) + annotation_logticks(sides=\"l\")") +
                             ((p.flip ? p.minor.size : p.major.size) > 1 ? QString(" + facet_wrap(~ %1, scales=\"free_x\")").arg(p.flip ? p.minor.header : p.major.header) : QString()) +
                             QString(" + theme(aspect.ratio=1)\n\n")));