blas-benchmarks/results.Rmd

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---
title: "BLAS libraries benchmarks"
author: "Andrzej Wójtowicz"
output:
html_document:
keep_md: yes
---
Document generation date: `r Sys.time()`
This document presents timing results for BLAS ([Basic Linear Algebra Subprograms](https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms)) libraries in [R](https://en.wikipedia.org/wiki/R_(programming_language)) on diverse CPUs and GPUs.
### Changelog
* 2016-12-01: **results:** updated timing for Intel Xeon E3-1275 v5; **code:** added possible compilation fix for invalid operands error in GotoBLAS2.
* 2016-11-30: **results:** added Intel Xeon E5-1620 v4.
* 2016-11-29: **results:** added Intel Xeon E3-1275 v5.
* 2016-11-25: **results:** added Intel Atom C2758.
* 2016-07-14: **results:** added Intel Core i5-6500; changed results view of gcbd benchmark to relative performance gain; changed reference CPU (Intel Pentium Dual-Core E5300) and GPU (NVIDIA GeForce GT 630M); **code:** fixed target architecture detection for Intel Core i5-6500-like CPUs in multi-threaded Atlas library; added info how to force target architecture in GotoBLAS2 and BLIS libraries.
```{r checkpoint, echo=FALSE, warning=FALSE, message=FALSE}
library(checkpoint)
checkpoint("2016-04-01", scanForPackages=FALSE, verbose=FALSE)
library(reshape2)
library(dplyr)
library(ggplot2)
library(RColorBrewer)
```
## Table of Contents
1. [Configuration](#configuration)
2. [Results per host](#results-per-host)
* [Intel Xeon E3-1275 v5](#intel-xeon-e3-1275-v5)
* [Intel Xeon E5-1620 v4](#intel-xeon-e5-1620-v4)
* [Intel Core i7-4790K + MSI GeForce GTX 980 Ti Lightning](#intel-core-i7-4790k--msi-geforce-gtx-980-ti-lightning)
* [Intel Core i5-4590 + NVIDIA GeForce GT 430](#intel-core-i5-4590--nvidia-geforce-gt-430)
* [Intel Core i5-4590 + NVIDIA GeForce GTX 750 Ti](#intel-core-i5-4590--nvidia-geforce-gtx-750-ti)
* [Intel Core i5-6500](#intel-core-i5-6500)
* [Intel Core i5-3570](#intel-core-i5-3570)
* [Intel Core i3-2120](#intel-core-i3-2120)
* [Intel Core i3-3120M](#intel-core-i3-3120m)
* [Intel Core i5-3317U + NVIDIA GeForce GT 630M](#intel-core-i5-3317u--nvidia-geforce-gt-630m)
* [Intel Atom C2758](#intel-atom-c2758)
* [Intel Pentium Dual-Core E5300](#intel-pentium-dual-core-e5300)
3. [Results per library](#results-per-library)
* [Netlib](#netlib)
* [Atlas (st)](#atlas-st)
* [OpenBLAS](#openblas)
* [Atlas (mt)](#atlas-mt)
* [GotoBLAS2](#gotoblas2)
* [MKL](#mkl)
* [BLIS](#blis)
* [cuBLAS](#cublas)
***
## Configuration
**OS**: [Debian](https://www.debian.org/) Jessie, kernel 4.4
**R software**: [Microsoft R Open](https://mran.microsoft.com/open/) (3.2.4)
**Libraries**:
|CPU (single-threaded)|CPU (multi-threaded)|GPU|
|---|---|---|
|[Netlib](http://www.netlib.org/) (debian package, blas 1.2.20110419, lapack 3.5.0)|[OpenBLAS](http://www.openblas.net/) (debian package, 0.2.12)|[NVIDIA cuBLAS](https://developer.nvidia.com/cublas) (NVBLAS 6.5 + Intel MKL)|
|[ATLAS](http://math-atlas.sourceforge.net/) (debian package, 3.10.2)|[ATLAS](http://math-atlas.sourceforge.net/) (dev branch, 3.11.38)| |
| |[GotoBLAS2](https://prs.ism.ac.jp/~nakama/SurviveGotoBLAS2/) (Survive fork, 3.141)| |
| |[Intel MKL](https://mran.microsoft.com/download/) (part of RevoMath package, 3.2.4)| |
| |[BLIS](https://github.com/flame/blis) (dev branch, 0.2.0+/17.05.2016)| |
**Hosts**:
|No.|CPU|GPU|
|---|---|---|
|1.|[Intel Xeon E3-1275 v5](http://ark.intel.com/products/88177/Intel-Xeon-Processor-E3-1275-v5-8M-Cache-3_60-GHz)| - |
|2.|[Intel Xeon E5-1620 v4](http://ark.intel.com/products/64621/Intel-Xeon-Processor-E5-1620-10M-Cache-3_60-GHz-0_0-GTs-Intel-QPI)| - |
|3.|[Intel Core i7-4790K](http://ark.intel.com/products/80807/Intel-Core-i7-4790K-Processor-8M-Cache-up-to-4_40-GHz) (OC 4.5 GHz)|[MSI GeForce GTX 980 Ti Lightning](https://us.msi.com/Graphics-card/GTX-980-Ti-LIGHTNING.html#hero-specification)|
|4.|[Intel Core i5-4590](http://ark.intel.com/products/80815/Intel-Core-i5-4590-Processor-6M-Cache-up-to-3_70-GHz)|[NVIDIA GeForce GT 430](http://www.geforce.com/hardware/desktop-gpus/geforce-gt-430/specifications)|
|5.|[Intel Core i5-4590](http://ark.intel.com/products/80815/Intel-Core-i5-4590-Processor-6M-Cache-up-to-3_70-GHz)|[NVIDIA GeForce GTX 750 Ti](http://www.geforce.com/hardware/desktop-gpus/geforce-gtx-750-ti/specifications)|
|6.|[Intel Core i5-6500](http://ark.intel.com/products/88184/Intel-Core-i5-6500-Processor-6M-Cache-up-to-3_60-GHz)| - |
|7.|[Intel Core i5-3570](http://ark.intel.com/products/65702/Intel-Core-i5-3570-Processor-6M-Cache-up-to-3_80-GHz)| - |
|8.|[Intel Core i3-2120](http://ark.intel.com/products/53426/Intel-Core-i3-2120-Processor-3M-Cache-3_30-GHz)| - |
|9.|[Intel Core i3-3120M](http://ark.intel.com/products/71465/Intel-Core-i3-3120M-Processor-3M-Cache-2_50-GHz)| - |
|10.|[Intel Core i5-3317U](http://ark.intel.com/products/65707/Intel-Core-i5-3317U-Processor-3M-Cache-up-to-2_60-GHz)|[NVIDIA GeForce GT 630M](http://www.geforce.com/hardware/notebook-gpus/geforce-gt-630m/specifications)|
|11.|[Intel Atom C2758](http://ark.intel.com/products/77988/Intel-Atom-Processor-C2758-4M-Cache-2_40-GHz)| - |
|12.|[Intel Pentium Dual-Core E5300](http://ark.intel.com/products/35300/Intel-Pentium-Processor-E5300-2M-Cache-2_60-GHz-800-MHz-FSB)| - |
**Benchmarks**: [R-benchmark-25](http://r.research.att.com/benchmarks/R-benchmark-25.R), [Revolution](https://gist.github.com/andrie/24c9672f1ea39af89c66#file-rro-mkl-benchmark-r), [Gcbd](https://cran.r-project.org/web/packages/gcbd/vignettes/gcbd.pdf).
```{r config, echo=FALSE}
HOSTNAMES = suppressWarnings(readLines("hosts-list.txt"))
BENCHMARKS = c("urbanek",
"revolution",
"gcbd")
LIBRARIES = c("netlib",
"atlas_st",
"openblas",
"atlas_mt",
"gotoblas2",
"mkl",
"blis",
"cublas")
LIBRARY.REF = "netlib"
HOST.REF = "Intel Pentium Dual-Core E5300"
HOST.REF.SEC = "Intel Core i5-3317U"
HOST.REF.GPU = "NVIDIA GeForce GT 630M"
HOST.INFO.PATTERN = "host-info-<HOST>.log"
BENCHMARK.PATTERN = "test-<BENCHMARK>-<HOST>-<LIBRARY>.rds"
RESULTS.DIR = "results"
GEN.DIR = "gen"
DATA.DIR = file.path(GEN.DIR, "data")
IMAGES.DIR = file.path(GEN.DIR, "img")
```
```{r read-write-data, echo=FALSE}
for (d in c(GEN.DIR, DATA.DIR, IMAGES.DIR))
if (!dir.exists(d))
dir.create(d)
hosts.info = data.frame(Host=character(), CPU=character(), GPU=character())
for (hostname in HOSTNAMES)
{
fp = file.path(RESULTS.DIR, gsub("<HOST>", hostname, HOST.INFO.PATTERN))
if (file.exists(fp))
{
dr = readLines(fp)
dr = unname(sapply(dr, trimws))
hosts.info = rbind(hosts.info,
data.frame(Host= hostname,
CPU = gsub("\\(.*?\\)", "", dr[1]),
GPU = ifelse(length(dr)==3,
gsub("(NVIDIA|MSI).*\\[(.*)\\]", "\\1 \\2", dr[3]), NA)))
} else {
warning(paste("File", fp, "does not exist"))
}
}
saveRDS(hosts.info, file.path(DATA.DIR, "hosts.info.rds"))
benchmark.results = data.frame(Host=character(), Benchmark=character(),
Library=character(), Test=character(),
Runs=integer(), Size=integer(),
Time=numeric())
for (host in hosts.info$Host)
{
for (benchmark in BENCHMARKS)
{
for (lib in LIBRARIES)
{
if (lib=="cublas" && is.na(hosts.info[which(hosts.info$Host==host),
"GPU"]))
next
fp = file.path(RESULTS.DIR, gsub("<HOST>", host, (
gsub("<LIBRARY>", lib, (
gsub("<BENCHMARK>", benchmark, BENCHMARK.PATTERN)))))
)
if (file.exists(fp))
{
db = readRDS(fp)
runs = NA
if (length(attr(db, "runs"))==1) {
runs = attr(db, "runs")
} else {
# gcbd
db = melt(cbind(db, runs=attr(db, "runs"),
size=attr(db, "size")),
id.vars=c("runs", "size"),
variable.name="name",
value.name="time")
runs = db$runs
}
size = NA
if ("size" %in% colnames(db)) # gcbd
size = db$size
benchmark.results = rbind(benchmark.results,
data.frame(Host=host, Benchmark=benchmark,
Library=lib, Test=db$name,
Runs=runs, Size=size,
Time=db$time))
} else {
warning(paste("File", fp, "does not exist"))
}
}
}
}
saveRDS(benchmark.results, file.path(DATA.DIR, "benchmark.results.rds"))
```
```{r per-host, echo=FALSE, results='asis'}
cat("# Results per host\n\n")
for (host in hosts.info$Host)
{
host.cpu = hosts.info[which(hosts.info$Host==host), "CPU"]
host.gpu = hosts.info[which(hosts.info$Host==host), "GPU"]
cat(paste("##", host.cpu))
if (!is.na(host.gpu))
cat(paste(" +", host.gpu))
cat("\n\n\n\n")
for (benchmark in BENCHMARKS)
{
cat(paste0("### ",
ifelse(benchmark=="urbanek", "R-benchmark-25", # fix to common name
paste(toupper(substring(benchmark, 1,1)),
substring(benchmark, 2), " benchmark", sep="", collapse=" ")),
"\n\n"))
testnames = benchmark.results %>%
filter(Benchmark == benchmark) %>%
select(Test) %>%
unique
if (benchmark == "urbanek")
# remove tests with almost the same results
testnames = testnames %>% filter(row_number() %in% c(4, 5, 7, 8, 9, 10, 15))
for (i in 1:nrow(testnames))
{
test = as.character(testnames[i, "Test"])
data.to.plot = benchmark.results %>%
filter(Host == host & Benchmark == benchmark &
Test == test)
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05),
PerfGain=data.to.plot[which(data.to.plot$Library==LIBRARY.REF), "Time"]/Time)
renamedLibs = list(
"cuBLAS"="cublas",
"BLIS"="blis",
"MKL"="mkl",
"ATLAS (mt)"="atlas_mt",
"OpenBLAS"="openblas",
"GotoBLAS2"="gotoblas2",
"ATLAS (st)"="atlas_st",
"Netlib"="netlib")
if (benchmark != "gcbd")
levels(data.to.plot$Library) = renamedLibs
else
levels(data.to.plot$Library) = rev(renamedLibs)
data.to.plot = data.to.plot %>%
mutate(Color=sapply(Library, function(x){
if(x=="Netlib") "A"
else if(x=="ATLAS (st)") "B"
else if(x=="cuBLAS") "D"
else "C"}))
cat(paste0("#### ", # fix urbanek errors in names
gsub(" \\(.*\\)", "",
gsub("Linear regr. over a 3000x3000 matrix",
"Linear regr. over a 2000x2000 matrix",
gsub("Eigenvalues of a 640x640",
"Eigenvalues of a 600x600", test))
)
),
"\n\n")
if (any(data.to.plot$Time == Inf, na.rm = TRUE))
{
cat(paste(as.character(data.to.plot[which(data.to.plot$Time == Inf), "Library"])), "hangs in this test\n\n")
}
if (any(is.na(data.to.plot$Time)))
{
cat(paste(unique(as.character(data.to.plot[which(is.na(data.to.plot$Time)), "Library"]))), "crashes in this test\n\n")
}
data.to.plot = data.to.plot[data.to.plot$Time != Inf & !is.na(data.to.plot$Time), ]
image.path = file.path(IMAGES.DIR,
paste0("img_ph",
"_h", which(host == hosts.info$Host),
"_b", which(benchmark == BENCHMARKS),
"_t", i,
".png"))
if (benchmark != "gcbd")
cat(paste0("Time in seconds - ", data.to.plot$Runs[1], " runs - lower is better\n\n"))
else
cat(paste0("Performance gain regarding matrix size - reference: ", names(which(renamedLibs==LIBRARY.REF)), " - from ", max(data.to.plot$Runs), " to ", min(data.to.plot$Runs), " runs - higher is better\n\n"))
myColors = c("#E6191A", "#F25F1E", "#636363", "#5AAC45")
names(myColors) = levels(data.to.plot$Color)
colScale = scale_fill_manual(name = "Color", values = myColors)
if (benchmark != "gcbd")
{
png(image.path, width=600, height=35*nrow(data.to.plot))
print(ggplot(data.to.plot, aes(x=reorder(Library, -Time), y=Time, fill=Color)) +
theme_classic() +
theme(
panel.border = element_blank(),
axis.title.x=element_blank(),
axis.title.y=element_blank(),
axis.text.x = element_text(colour="grey60"),
axis.ticks.x=element_line(color="grey60"),
axis.ticks.y=element_line(color="grey60"),
legend.position="none"
) +
scale_y_continuous(expand = c(0, 0),
limits = c(0, 1.20*max(data.to.plot$Time))) +
geom_bar(stat="identity", width=.7) +
coord_flip() +
geom_text(aes(y=Time, x=Library, label=format(Time, digits=2, nsmall=2)), hjust=-0.25, size=3, colour="grey45") +
geom_text(aes(y=1.2*max(data.to.plot$Time), x=Library, label=paste0("x", trimws(format(PerfGain, digits=1, nsmall=1)))), hjust=1, size=4) +
geom_hline(yintercept = 0, color="grey") +
geom_vline(xintercept = 0.4, color="grey") +
annotate("text", x=nrow(data.to.plot)+0.55, y=1.2*max(data.to.plot$Time), label="Performance gain", hjust=1) +
colScale
)
dev.off()
cat(paste0("![](", image.path, ")\n\n\n\n"))
} else {
rbColors = c("#F40000","#FF8000","#0094FF","#E900FF","#B35807","#7F00FF","#FFBC70","#00DD0E")
png(image.path, width=600, height=400, type="cairo")
print(ggplot(data.to.plot,
aes(x=Size, y=PerfGain, group=Library, color=Library,
shape=Library, fill=Library)) +
theme_classic() +
theme(
panel.border = element_blank(),
axis.title.x=element_blank(),
axis.title.y=element_blank(),
axis.text.x = element_text(colour="grey60"),
axis.text.y = element_text(colour="grey60"),
axis.ticks.x=element_line(color="grey60"),
axis.ticks.y=element_line(color="grey60"),
legend.margin=unit(c(-13,8), "mm"),
legend.title=element_blank()
) +
geom_line(size=1) +
geom_point(size=2, color="grey30") +
scale_x_log10(expand=c(0,0),
breaks=c(100, 200, 400, 800, 1600, 3200, 5000),
limits=c(90, 5500)) +
scale_y_continuous(expand = c(0, 0)) +
geom_hline(yintercept = 0, color="grey") +
geom_vline(xintercept = 90, color="grey") +
scale_shape_manual(values=c(21,24,22,25,23,21,22,23)) +
scale_color_manual(values=rbColors) +
scale_fill_manual(values=rbColors)
)
dev.off()
cat(paste0("![](", image.path, ")\n\n\n\n"))
}
}
}
}
```
```{r per-library, echo=FALSE, results='asis'}
cat("# Results per library\n\n")
renamedLibs = list(
"cublas"="cuBLAS",
"blis"="BLIS",
"mkl"="MKL",
"atlas_mt"="ATLAS (mt)",
"openblas"="OpenBLAS",
"gotoblas2"="GotoBLAS2",
"atlas_st"="ATLAS (st)",
"netlib"="Netlib")
for (lib in LIBRARIES)
{
cat(paste("##", renamedLibs[[lib]]))
cat("\n\n\n\n")
for (benchmark in BENCHMARKS)
{
cat(paste0("### ",
ifelse(benchmark=="urbanek", "R-benchmark-25", # fix to common name
paste(toupper(substring(benchmark, 1,1)),
substring(benchmark, 2), " benchmark", sep="", collapse=" ")),
"\n\n"))
testnames = benchmark.results %>%
filter(Benchmark == benchmark) %>%
select(Test) %>%
unique
if (benchmark == "urbanek")
# remove tests with almost the same results
testnames = testnames %>% filter(row_number() %in% c(4, 5, 7, 8, 9, 10, 15))
for (i in 1:nrow(testnames))
{
test = as.character(testnames[i, "Test"])
data.to.plot = benchmark.results %>%
filter(Library == lib & Benchmark == benchmark &
Test == test)
data.to.plot = data.to.plot %>% rowwise() %>%
mutate(CPUGPU=hosts.info[which(hosts.info$Host==Host), ifelse(lib!="cublas", "CPU", "GPU")])
if (benchmark != "gcbd")
{
if (lib!="cublas")
{
if (data.to.plot[which(hosts.info$CPU==HOST.REF), "Time"]!=Inf) {
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05),
PerfGain=data.to.plot[which(hosts.info$CPU==HOST.REF), "Time"]/Time)
} else {
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05),
PerfGain=data.to.plot[which(hosts.info$CPU==HOST.REF.SEC), "Time"]/Time)
}
} else {
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05),
PerfGain=data.to.plot[which(filter(hosts.info, !is.na(GPU))$GPU==HOST.REF.GPU), ][["Time"]]/Time)
}
} else {
if (lib!="cublas")
{
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05))
data.to.plot$PerfGain =
data.to.plot[which(data.to.plot$CPUGPU==HOST.REF), ][["Time"]]/data.to.plot$Time
} else {
data.to.plot = data.to.plot %>%
mutate(Time=replace(Time, Time==0, 5e-05))
data.to.plot$PerfGain =
data.to.plot[which(data.to.plot$CPUGPU==HOST.REF.GPU), ][["Time"]]/data.to.plot$Time
}
}
cat(paste0("#### ", # fix urbanek errors in names
gsub(" \\(.*\\)", "",
gsub("Linear regr. over a 3000x3000 matrix",
"Linear regr. over a 2000x2000 matrix",
gsub("Eigenvalues of a 640x640",
"Eigenvalues of a 600x600", test))
)
),
"\n\n")
if (any(is.na(data.to.plot$Time)))
{
cat(paste("Library crashes on", unique(as.character(as.data.frame(data.to.plot)[which(is.na(data.to.plot$Time)), "CPUGPU"]))), "in this test\n\n")
}
if (any(data.to.plot$Time == Inf, na.rm = TRUE))
{
cat(paste("Library hangs on", as.character(as.data.frame(data.to.plot)[which(data.to.plot$Time == Inf), "CPUGPU"])), "in this test\n\n")
}
data.to.plot = data.to.plot[data.to.plot$Time != Inf & !is.na(data.to.plot$Time), ]
image.path = file.path(IMAGES.DIR,
paste0("img_pl",
"_l", which(lib == LIBRARIES),
"_b", which(benchmark == BENCHMARKS),
"_t", i,
".png"))
if (benchmark != "gcbd")
cat(paste0("Time in seconds - ", data.to.plot$Runs[1], " runs - lower is better\n\n"))
else
cat(paste0("Performance gain regarding matrix size - reference: ", ifelse(lib!="cublas", HOST.REF, HOST.REF.GPU), " - from ", max(data.to.plot$Runs), " to ", min(data.to.plot$Runs), " runs - higher is better\n\n"))
myColors = c("#636363", "#636363", "#5AAC45", "#636363", "#636363", "#636363", "#636363", "#636363", "#636363", "#636363", "#E6191A")
if (lib=="cublas")
myColors = c("#5AAC45", "#636363", "#636363", "#E6191A")
colScale = scale_fill_manual(name = "Color", values = myColors)
data.to.plot = unique(select(data.to.plot, -Host))
if (benchmark != "gcbd")
{
png(image.path, width=600, height=50*length(unique(data.to.plot$CPUGPU))+ifelse(nrow(data.to.plot)>1, 0, 20))
print(ggplot(data.to.plot, aes(x=reorder(CPUGPU, -Time), y=Time,
fill=CPUGPU)) +
theme_classic() +
theme(
panel.border = element_blank(),
axis.title.x=element_blank(),
axis.title.y=element_blank(),
axis.text.x = element_text(colour="grey60"),
axis.ticks.x=element_line(color="grey60"),
axis.ticks.y=element_line(color="grey60"),
legend.position="none"
) +
scale_y_continuous(expand = c(0, 0),
limits = c(0, 1.20*max(data.to.plot$Time))) +
geom_bar(stat="identity", width=.7) +
coord_flip() +
geom_text(aes(y=Time, x=CPUGPU, label=format(Time, digits=2, nsmall=2)), hjust=-0.25, size=3, colour="grey45") +
geom_text(aes(y=1.2*max(data.to.plot$Time), x=CPUGPU, label=paste0("x", trimws(format(PerfGain, digits=1, nsmall=1)))), hjust=1, size=4) +
geom_hline(yintercept = 0, color="grey") +
geom_vline(xintercept = 0.4, color="grey") +
annotate("text", x=length(unique(data.to.plot$CPUGPU))+ifelse(nrow(data.to.plot)>1, 0.55, 0.45), y=1.2*max(data.to.plot$Time), label="Performance gain", hjust=1) +
colScale
)
dev.off()
cat(paste0("![](", image.path, ")\n\n\n\n"))
} else {
rbColors = c("#F40000","#FF8000","#0094FF","#7F00FF","#E900FF","#00DD0E","#B35807", "#7F006E", "#F4DD00", "#00AABB", "#000000")
png(image.path, width=700, height=400, type="cairo")
print(ggplot(data.to.plot,
aes(x=Size, y=PerfGain, group=CPUGPU, color=CPUGPU,
shape=CPUGPU, fill=CPUGPU)) +
theme_classic() +
theme(
panel.border = element_blank(),
axis.title.x=element_blank(),
axis.title.y=element_blank(),
axis.text.x = element_text(colour="grey60"),
axis.text.y = element_text(colour="grey60"),
axis.ticks.x=element_line(color="grey60"),
axis.ticks.y=element_line(color="grey60"),
legend.title=element_blank()
) +
geom_line(size=1) +
geom_point(size=2, color="grey30") +
scale_x_log10(expand=c(0,0),
breaks=c(100, 200, 400, 800, 1600, 3200, 5000),
limits=c(90, 5500)) +
scale_y_continuous(expand = c(0, 0)) +
geom_hline(yintercept = 0, color="grey") +
geom_vline(xintercept = 90, color="grey") +
scale_shape_manual(values=c(25,24,22,21,23,25,24,22,21,23,25)) +
scale_color_manual(values=rbColors) +
scale_fill_manual(values=rbColors)
)
dev.off()
cat(paste0("![](", image.path, ")\n\n\n\n"))
}
}
}
}
```