The Distributions package provides a comprehensive list of univariate, multivariate and matrix distributions and a set of generic functions that can be applied to them. See the documentation for details on the coverage.
Note that some methods refer to the distribution type (e.g. Normal) instead of a distribution instance (e.g. Normal(0.,1.))
In [1]:
using Distributions
d = Normal() # standard normal (Gaussian) distribution
Out[1]:
Distributions.Normal(μ=0.0, σ=1.0)
In [2]:
x = rand(d,20) # sample of size 20 from a standard normal
Out[2]:
20-element Array{Float64,1}:
-1.37163
0.108703
-0.614373
0.908453
-0.616237
1.30055
1.82147
1.56462
1.27457
-0.407733
-0.691858
-1.49719
0.850856
-0.250366
1.22701
-1.0103
-0.47893
0.512367
-0.433555
0.818587
In [3]:
de = fit_mle(Normal,x) # maximum likelihood estimates of normal dist. pars.
Out[3]:
Distributions.Normal(μ=0.15075083842683862, σ=0.9912678731753393)
In [4]:
mean(de)
Out[4]:
0.15075083842683862
In [5]:
std(de)
Out[5]:
0.9912678731753393
In [6]:
var(de)
Out[6]:
0.9826119963895605
In [7]:
kurtosis(de)
Out[7]:
0.0
In [8]:
skewness(de)
Out[8]:
0.0
In [9]:
loglikelihood(de,x)
Out[9]:
-28.203361159103117
In [10]:
ss = suffstats(Normal,x)
Out[10]:
Distributions.NormalStats(3.0150167685367726,0.15075083842683862,19.65223992779121,20.0)
In [11]:
fieldnames(ss)'
Out[11]:
1x4 Array{Symbol,2}:
:s :m :s2 :tw
In [12]:
fit_mle(Normal,ss) # can fit from sufficient statistics
Out[12]:
Distributions.Normal(μ=0.15075083842683862, σ=0.9912678731753393)
It is also possible to do map (maximum a posteriori) estimation using a conjugate prior. Again, see the documentation.
This is a lightweight package to define types that can contain NA's. It was split off from the DataFrames package because loading the whole of DataFrames takes a while. (This will change when pre-compiled packages are more easily constructed.)
The basic types defined in DataArrays are NA, used for literal NA input, the DataArray, like a numeric or integer vector in R, and the PooledDataVector, like a factor in R.
The concept of an NA is built into many of the R types. In Julia a DataArray or PooledDataArray is composed of the data and a separate bitarray of indicators of missingness.
In [2]:
using DataArrays
v = @data([2,1,NA,4])
Out[2]:
4-element DataArrays.DataArray{Int64,1}:
2
1
NA
4
In [14]:
fieldnames(v)
Out[14]:
2-element Array{Symbol,1}:
:data
:na
In [15]:
typeof(v).types
Out[15]:
svec(Array{Int64,1},BitArray{1})
In [16]:
v.data
Out[16]:
4-element Array{Int64,1}:
2
1
2
4
In [17]:
v.na
Out[17]:
4-element BitArray{1}:
false
false
true
false
In [18]:
isna(v)
Out[18]:
4-element BitArray{1}:
false
false
true
false
In [19]:
dropna(v)
Out[19]:
3-element Array{Int64,1}:
2
1
4
The PooledDataArray, generated with the @pdata macro call, consists of a pool array (similar to the levels in an R factor object) and a unsigned integer vector refs.
In [20]:
d = Bernoulli()
sex = @pdata [rand(d) ≠ 0 ? 'F' : 'M' for i in 1:1000]
Out[20]:
1000-element DataArrays.PooledDataArray{Char,UInt32,1}:
'M'
'F'
'M'
'M'
'M'
'F'
'F'
'F'
'M'
'F'
'M'
'F'
'F'
⋮
'M'
'F'
'M'
'F'
'F'
'F'
'M'
'F'
'F'
'F'
'F'
'M'
In [21]:
sex.pool
Out[21]:
2-element Array{Char,1}:
'F'
'M'
In [22]:
sex.refs
Out[22]:
1000-element Array{UInt32,1}:
0x00000002
0x00000001
0x00000002
0x00000002
0x00000002
0x00000001
0x00000001
0x00000001
0x00000002
0x00000001
0x00000002
0x00000001
0x00000001
⋮
0x00000002
0x00000001
0x00000002
0x00000001
0x00000001
0x00000001
0x00000002
0x00000001
0x00000001
0x00000001
0x00000001
0x00000002
In [23]:
sex = compact(sex) # provides a more compact representation, if possible
Out[23]:
1000-element DataArrays.PooledDataArray{Char,UInt8,1}:
'M'
'F'
'M'
'M'
'M'
'F'
'F'
'F'
'M'
'F'
'M'
'F'
'F'
⋮
'M'
'F'
'M'
'F'
'F'
'F'
'M'
'F'
'F'
'F'
'F'
'M'
In [24]:
sex.refs
Out[24]:
1000-element Array{UInt8,1}:
0x02
0x01
0x02
0x02
0x02
0x01
0x01
0x01
0x02
0x01
0x02
0x01
0x01
⋮
0x02
0x01
0x02
0x01
0x01
0x01
0x02
0x01
0x01
0x01
0x01
0x02
A few other functions common to an R programmer, like rep, are in the DataArrays package.
In [3]:
whos(DataArrays)
/ 38 KB Function
WARNING: both StatsBase and Base export "histrange"; uses of it in module DataArrays must be qualified
WARNING: both StatsBase and Base export "midpoints"; uses of it in module DataArrays must be qualified
@data 1533 bytes Function
@pdata 1249 bytes Function
AbstractDataArray 188 bytes DataType
AbstractDataMatrix 80 bytes TypeConstructor
AbstractDataVector 80 bytes TypeConstructor
AbstractHistogram 228 bytes DataType
CoefTable 284 bytes DataType
DataArray 220 bytes DataType
DataArrays 674 KB Module
DataMatrix 80 bytes TypeConstructor
DataVector 80 bytes TypeConstructor
EachDropNA 168 bytes DataType
EachFailNA 168 bytes DataType
EachReplaceNA 220 bytes DataType
FastPerm 284 bytes DataType
Histogram 272 bytes DataType
L1dist 1279 bytes Function
L2dist 577 bytes Function
Linfdist 1450 bytes Function
NA 0 bytes DataArrays.NAtype
NAException 112 bytes DataType
NAtype 92 bytes DataType
PooledDataArray 260 bytes DataType
PooledDataMatrix 120 bytes TypeConstructor
PooledDataVecs 8507 bytes Function
PooledDataVector 120 bytes TypeConstructor
RegressionModel 92 bytes DataType
StatisticalModel 92 bytes DataType
StatsBase 476 KB Module
WeightVec 284 bytes DataType
addcounts! 14 KB Function
allna 1744 bytes Function
anyna 1708 bytes Function
array 5595 bytes Function
autocor 1089 bytes Function
autocor! 3572 bytes Function
autocov 4814 bytes Function
autocov! 3572 bytes Function
coef 516 bytes Function
coeftable 516 bytes Function
compact 1438 bytes Function
competerank 649 bytes Function
confint 516 bytes Function
corkendall 5773 bytes Function
corspearman 3260 bytes Function
counteq 1287 bytes Function
countmap 2176 bytes Function
countne 1287 bytes Function
counts 8052 bytes Function
crosscor 8202 bytes Function
crosscor! 6952 bytes Function
crosscov 8202 bytes Function
crosscov! 6952 bytes Function
crossentropy 2134 bytes Function
cut 3992 bytes Function
data 504 bytes Function
denserank 647 bytes Function
describe 560 bytes Function
deviance 516 bytes Function
df_residual 516 bytes Function
dropna 2555 bytes Function
each_dropna 557 bytes Function
each_failNA 617 bytes Function
each_failna 557 bytes Function
each_replaceNA 629 bytes Function
each_replacena 1015 bytes Function
ecdf 948 bytes Function
entropy 1799 bytes Function
findat 538 bytes Function
fit 13 KB Function
fit! 548 bytes Function
fitted 516 bytes Function
geomean 1163 bytes Function
getpoolidx 2027 bytes Function
gkldiv 1559 bytes Function
gl 2271 bytes Function
harmmean 1153 bytes Function
head 592 bytes Function
hist 2683 bytes Function
indexmap 1184 bytes Function
indicatormat 4556 bytes Function
inverse_rle 1942 bytes Function
invsoftplus 5037 bytes Function
iqr 608 bytes Function
isna 4945 bytes Function
kldivergence 2138 bytes Function
kurtosis 5279 bytes Function
levels 1717 bytes Function
levelsmap 1320 bytes Function
logistic 4468 bytes Function
logit 4441 bytes Function
loglikelihood 516 bytes Function
logsumexp 2785 bytes Function
mad 3645 bytes Function
maxad 570 bytes Function
mean_and_cov 2938 bytes Function
mean_and_std 2120 bytes Function
mean_and_var 2120 bytes Function
meanad 585 bytes Function
middle 3053 bytes Function
mode 4046 bytes Function
model_response 516 bytes Function
modes 4963 bytes Function
moment 2360 bytes Function
msd 587 bytes Function
nobs 516 bytes Function
nquantile 590 bytes Function
ordinalrank 645 bytes Function
pacf 3226 bytes Function
pacf! 1893 bytes Function
padNA 1240 bytes Function
pdata 516 bytes Function
percent_change 1169 bytes Function
percentile 583 bytes Function
predict 516 bytes Function
predict! 516 bytes Function
proportionmap 1003 bytes Function
proportions 7036 bytes Function
psnr 655 bytes Function
reldiff 1140 bytes Function
removeNA 601 bytes Function
reorder 1040 bytes Function
rep 6024 bytes Function
replace! 4684 bytes Function
residuals 516 bytes Function
rle 6285 bytes Function
rmsd 1691 bytes Function
sample 9170 bytes Function
sample! 3510 bytes Function
samplepair 1447 bytes Function
scattermat 3208 bytes Function
sem 568 bytes Function
set_levels 611 bytes Function
set_levels! 615 bytes Function
setlevels 3164 bytes Function
setlevels! 4791 bytes Function
skewness 5199 bytes Function
softmax 560 bytes Function
softmax! 2515 bytes Function
softplus 5021 bytes Function
span 742 bytes Function
sqL2dist 1276 bytes Function
stderr 517 bytes Function
summarystats 1004 bytes Function
tail 607 bytes Function
tiedrank 646 bytes Function
trimmean 1904 bytes Function
variation 1035 bytes Function
vcov 516 bytes Function
view 4098 bytes Function
weights 1086 bytes Function
wmean 723 bytes Function
wmedian 1071 bytes Function
wquantile 2130 bytes Function
wsample 4621 bytes Function
wsample! 1945 bytes Function
wsum 1775 bytes Function
wsum! 1904 bytes Function
xlogx 4467 bytes Function
xlogy 5141 bytes Function
xtab 180 bytes DataType
xtabs 1041 bytes Function
zscore 3008 bytes Function
zscore! 2904 bytes Function
The DataFrame type and methods for working with it are defined in the DataFrames package. There is online documentation but, at least in my browser, the formatting is horrible. I would recommend reading the PDF file instead.
The DataFrames package is where the formula language and types like ModelFrame and ModelMatrix are defined. Many familiar examples of data frames are available in the RDatasets package.
In [26]:
using DataFrames, RDatasets
ds = dataset("lme4","Dyestuff")
Out[26]:
Batch Yield 1 A 1545 2 A 1440 3 A 1440 4 A 1520 5 A 1580 6 B 1540 7 B 1555 8 B 1490 9 B 1560 10 B 1495 11 C 1595 12 C 1550 13 C 1605 14 C 1510 15 C 1560 16 D 1445 17 D 1440 18 D 1595 19 D 1465 20 D 1545 21 E 1595 22 E 1630 23 E 1515 24 E 1635 25 E 1625 26 F 1520 27 F 1455 28 F 1450 29 F 1480 30 F 1445
@data 1533 bytes Function
@pdata 1545 bytes Function
AbstractDataArray 188 bytes DataType
AbstractDataMatrix 80 bytes TypeConstructor
AbstractDataVector 80 bytes TypeConstructor
AbstractHistogram 228 bytes DataType
CoefTable 284 bytes DataType
DataArray 220 bytes DataType
DataArrays 803 KB Module
DataMatrix 80 bytes TypeConstructor
DataVector 80 bytes TypeConstructor
EachDropNA 168 bytes DataType
EachFailNA 168 bytes DataType
EachReplaceNA 220 bytes DataType
FastPerm 284 bytes DataType
Histogram 272 bytes DataType
L1dist 1279 bytes Function
L2dist 577 bytes Function
Linfdist 1450 bytes Function
NA 0 bytes DataArrays.NAtype
NAException 112 bytes DataType
NAtype 92 bytes DataType
PooledDataArray 260 bytes DataType
PooledDataMatrix 120 bytes TypeConstructor
PooledDataVecs 8507 bytes Function
PooledDataVector 120 bytes TypeConstructor
RegressionModel 92 bytes DataType
StatisticalModel 92 bytes DataType
StatsBase 601 KB Module
WeightVec 284 bytes DataType
addcounts! 14 KB Function
allna 1744 bytes Function
anyna 1708 bytes Function
array 5595 bytes Function
autocor 1089 bytes Function
autocor! 3572 bytes Function
autocov 4814 bytes Function
autocov! 3572 bytes Function
coef 516 bytes Function
coeftable 516 bytes Function
compact 3324 bytes Function
competerank 649 bytes Function
confint 516 bytes Function
corkendall 5773 bytes Function
corspearman 3260 bytes Function
counteq 1287 bytes Function
countmap 2176 bytes Function
countne 1287 bytes Function
counts 8052 bytes Function
crosscor 8202 bytes Function
crosscor! 6952 bytes Function
crosscov 8202 bytes Function
crosscov! 6952 bytes Function
crossentropy 2134 bytes Function
cut 3992 bytes Function
data 504 bytes Function
denserank 647 bytes Function
describe 560 bytes Function
deviance 516 bytes Function
df_residual 516 bytes Function
dropna 3439 bytes Function
each_dropna 557 bytes Function
each_failNA 617 bytes Function
each_failna 557 bytes Function
each_replaceNA 629 bytes Function
each_replacena 1015 bytes Function
ecdf 948 bytes Function
entropy 31 KB Function
findat 538 bytes Function
fit 18 KB Function
fit! 548 bytes Function
fitted 516 bytes Function
geomean 1163 bytes Function
getpoolidx 2027 bytes Function
gkldiv 1559 bytes Function
gl 2271 bytes Function
harmmean 1153 bytes Function
head 592 bytes Function
hist 2683 bytes Function
indexmap 1184 bytes Function
indicatormat 4556 bytes Function
inverse_rle 1942 bytes Function
invsoftplus 5037 bytes Function
iqr 608 bytes Function
isna 5623 bytes Function
kldivergence 2638 bytes Function
kurtosis 38 KB Function
levels 1717 bytes Function
levelsmap 1320 bytes Function
logistic 4468 bytes Function
logit 4441 bytes Function
loglikelihood 2394 bytes Function
logsumexp 2785 bytes Function
mad 3645 bytes Function
maxad 570 bytes Function
mean_and_cov 2938 bytes Function
mean_and_std 2120 bytes Function
mean_and_var 2120 bytes Function
meanad 585 bytes Function
middle 3053 bytes Function
mode 31 KB Function
model_response 516 bytes Function
modes 14 KB Function
moment 2360 bytes Function
msd 587 bytes Function
nobs 516 bytes Function
nquantile 590 bytes Function
ordinalrank 645 bytes Function
pacf 3226 bytes Function
pacf! 1893 bytes Function
padNA 1240 bytes Function
pdata 516 bytes Function
percent_change 1169 bytes Function
percentile 583 bytes Function
predict 516 bytes Function
predict! 516 bytes Function
proportionmap 1003 bytes Function
proportions 7036 bytes Function
psnr 655 bytes Function
reldiff 1140 bytes Function
removeNA 601 bytes Function
reorder 1040 bytes Function
rep 6024 bytes Function
replace! 4684 bytes Function
residuals 516 bytes Function
rle 6285 bytes Function
rmsd 1691 bytes Function
sample 9170 bytes Function
sample! 3510 bytes Function
samplepair 1447 bytes Function
scattermat 3208 bytes Function
sem 568 bytes Function
set_levels 611 bytes Function
set_levels! 615 bytes Function
setlevels 3164 bytes Function
setlevels! 4791 bytes Function
skewness 36 KB Function
softmax 560 bytes Function
softmax! 2515 bytes Function
softplus 5021 bytes Function
span 742 bytes Function
sqL2dist 1276 bytes Function
stderr 517 bytes Function
summarystats 1004 bytes Function
tail 607 bytes Function
tiedrank 646 bytes Function
trimmean 1904 bytes Function
variation 1035 bytes Function
vcov 516 bytes Function
view 4098 bytes Function
weights 1086 bytes Function
wmean 723 bytes Function
wmedian 1071 bytes Function
wquantile 2130 bytes Function
wsample 4621 bytes Function
wsample! 1945 bytes Function
wsum 1775 bytes Function
wsum! 1904 bytes Function
xlogx 4467 bytes Function
xlogy 5141 bytes Function
xtab 180 bytes DataType
xtabs 1041 bytes Function
zscore 3008 bytes Function
zscore! 2904 bytes Function
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/bates/.julia/v0.4/RDatasets/src/dataset.jl:1
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/bates/.julia/v0.4/RDatasets/src/dataset.jl:1
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/bates/.julia/v0.4/RDatasets/src/datasets.jl:1
In [27]:
names(ds)
Out[27]:
2-element Array{Symbol,1}:
:Batch
:Yield
Indivual columns can be accessed by name using symbols (e.g. :Yield). This means that the column names should be valid Julia identifiers. Among other things, they cannot contain the dot or period character (.).
In [28]:
ds[:Yield]
Out[28]:
30-element DataArrays.DataArray{Int32,1}:
1545
1440
1440
1520
1580
1540
1555
1490
1560
1495
1595
1550
1605
⋮
1465
1545
1595
1630
1515
1635
1625
1520
1455
1450
1480
1445
The DataFrame constructor can be given <name>=<value> pairs.
In [29]:
x = 1.:10.;
ϵ = rand(Normal(0.,0.1),length(x));
β = [4.2,1.1];
ytrue = [ones(length(x)) x]*β;
dd = DataFrame(x=x,ytrue = ytrue, y = ytrue + ϵ)
Out[29]:
x ytrue y 1 1.0 5.300000000000001 5.4266459954573465 2 2.0 6.4 6.547618585779938 3 3.0 7.5 7.4126925420952325 4 4.0 8.600000000000001 8.502478506094308 5 5.0 9.7 9.459142933970893 6 6.0 10.8 10.798058744556116 7 7.0 11.900000000000002 11.791803744236113 8 8.0 13.0 13.131877566162375 9 9.0 14.100000000000001 14.145992654678988 10 10.0 15.2 15.120811027815394
In R many modeling functions that use a formula/data representation first apply model.frame then model.matrix. In the DataFrames package these are ModelFrame and ModelMatrix. A ModelFrame is the reduction of the original DataFrame to only those columns that are used in the model and after application of the NA action. It includes a Terms object, which describes the terms in the formula, again after some reduction and expansion. Finally, a record is kept of which rows in the original data frame are represented in the derived frame.
In [30]:
mf = ModelFrame(y ~ x, dd)
Out[30]:
DataFrames.ModelFrame(10x2 DataFrames.DataFrame
| Row | y | x |
|-----|---------|------|
| 1 | 5.42665 | 1.0 |
| 2 | 6.54762 | 2.0 |
| 3 | 7.41269 | 3.0 |
| 4 | 8.50248 | 4.0 |
| 5 | 9.45914 | 5.0 |
| 6 | 10.7981 | 6.0 |
| 7 | 11.7918 | 7.0 |
| 8 | 13.1319 | 8.0 |
| 9 | 14.146 | 9.0 |
| 10 | 15.1208 | 10.0 |,DataFrames.Terms(Any[:x],Any[:y,:x],2x2 Array{Int8,2}:
1 0
0 1,[1,1],true,true),Bool[true,true,true,true,true,true,true,true,true,true])
The ModelMatrix is constructed from the ModelFrame.
In [31]:
mm = ModelMatrix(mf)
Out[31]:
DataFrames.ModelMatrix{Float64}(10x2 Array{Float64,2}:
1.0 1.0
1.0 2.0
1.0 3.0
1.0 4.0
1.0 5.0
1.0 6.0
1.0 7.0
1.0 8.0
1.0 9.0
1.0 10.0,[0,1])
The assign vector in this object maps columns to terms. It is used when performing hypothesis tests, like anova. At present the model_response function returns the value of the expression on the left-hand side of the formula.
In [32]:
model_response(mf)
Out[32]:
10-element Array{Float64,1}:
5.42665
6.54762
7.41269
8.50248
9.45914
10.7981
11.7918
13.1319
14.146
15.1208
These facilities are not developed as fully as those in R.
The GLM package provides functions to fit and analyse the linear models and generalized linear models.
In [33]:
using GLM
fm = lm(y ~ x, dd)
Out[33]:
DataFrames.DataFrameRegressionModel{GLM.LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredQR{Float64}},Float64}:
Coefficients:
Estimate Std.Error t value Pr(>|t|)
(Intercept) 4.22575 0.0913301 46.269 <1e-10
x 1.09236 0.0147192 74.2132 <1e-11
In [34]:
fm = fit(LinearModel,y ~ x,dd)
Out[34]:
DataFrames.DataFrameRegressionModel{GLM.LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredQR{Float64}},Float64}:
Coefficients:
Estimate Std.Error t value Pr(>|t|)
(Intercept) 4.22575 0.0913301 46.269 <1e-10
x 1.09236 0.0147192 74.2132 <1e-11
The StatsBase package contains functions for sample statistics and many utilities. There is online documentation. Much of the design and implementation is by Dahua Lin who is a stickler for extracting every last ounce of performance.
In [1]:
using StatsBase
whos(StatsBase)
AbstractHistogram 228 bytes DataType
CoefTable 284 bytes DataType
Histogram 272 bytes DataType
L1dist 1279 bytes Function
L2dist 577 bytes Function
Linfdist 1450 bytes Function
RegressionModel 92 bytes DataType
StatisticalModel 92 bytes DataType
StatsBase 470 KB Module
WeightVec 284 bytes DataType
addcounts! 11 KB Function
autocor 4814 bytes Function
autocor! 3572 bytes Function
autocov 4814 bytes Function
autocov! 3572 bytes Function
coef 516 bytes Function
coeftable 516 bytes Function
competerank 649 bytes Function
confint 516 bytes Function
corkendall 5773 bytes Function
corspearman 2532 bytes Function
counteq 1287 bytes Function
countmap 1118 bytes Function
countne 1287 bytes Function
counts 8052 bytes Function
crosscor 8202 bytes Function
crosscor! 6952 bytes Function
crosscov 8202 bytes Function
crosscov! 6952 bytes Function
crossentropy 2134 bytes Function
denserank 647 bytes Function
describe 560 bytes Function
deviance 516 bytes Function
df_residual 516 bytes Function
ecdf 948 bytes Function
entropy 1799 bytes Function
findat 538 bytes Function
fit 13 KB Function
fit! 548 bytes Function
fitted 516 bytes Function
geomean 1163 bytes Function
gkldiv 1559 bytes Function
harmmean 1153 bytes Function
hist 2683 bytes Function
histrange 5943 bytes Function
indexmap 1184 bytes Function
indicatormat 4556 bytes Function
inverse_rle 1798 bytes Function
invsoftplus 5037 bytes Function
iqr 608 bytes Function
kldivergence 2138 bytes Function
kurtosis 4745 bytes Function
levelsmap 1320 bytes Function
logistic 4468 bytes Function
logit 4441 bytes Function
loglikelihood 516 bytes Function
logsumexp 2785 bytes Function
mad 3116 bytes Function
maxad 570 bytes Function
mean_and_cov 2938 bytes Function
mean_and_std 2120 bytes Function
mean_and_var 2120 bytes Function
meanad 585 bytes Function
middle 3053 bytes Function
midpoints 1657 bytes Function
mode 4046 bytes Function
model_response 516 bytes Function
modes 4963 bytes Function
moment 2360 bytes Function
msd 587 bytes Function
nobs 516 bytes Function
nquantile 590 bytes Function
ordinalrank 645 bytes Function
pacf 3226 bytes Function
pacf! 1893 bytes Function
percentile 583 bytes Function
predict 516 bytes Function
predict! 516 bytes Function
proportionmap 1003 bytes Function
proportions 7036 bytes Function
psnr 655 bytes Function
residuals 516 bytes Function
rle 1824 bytes Function
rmsd 1691 bytes Function
sample 9170 bytes Function
sample! 3510 bytes Function
samplepair 1447 bytes Function
scattermat 3208 bytes Function
sem 568 bytes Function
skewness 4665 bytes Function
softmax 560 bytes Function
softmax! 2515 bytes Function
softplus 5021 bytes Function
span 742 bytes Function
sqL2dist 1276 bytes Function
stderr 517 bytes Function
summarystats 1004 bytes Function
tiedrank 646 bytes Function
trimmean 1904 bytes Function
variation 1035 bytes Function
vcov 516 bytes Function
view 4098 bytes Function
weights 1086 bytes Function
wmean 723 bytes Function
wmedian 1071 bytes Function
wquantile 2130 bytes Function
wsample 4621 bytes Function
wsample! 1945 bytes Function
wsum 1775 bytes Function
wsum! 1904 bytes Function
xlogx 4467 bytes Function
xlogy 5141 bytes Function
zscore 3008 bytes Function
zscore! 2904 bytes Function
The MLBase package contains many functions for data manipulation and reduction. It uses the Machine Learning (ML) terminology.
In [5]:
using MLBase
whos(MLBase)
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/juser/.julia/v0.4/MLBase/src/modeltune.jl:5
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/juser/.julia/v0.4/MLBase/src/modeltune.jl:5
WARNING: Base.String is deprecated, use AbstractString instead.
likely near /home/juser/.julia/v0.4/MLBase/src/modeltune.jl:5
WARNING: Base.FloatingPoint is deprecated, use AbstractFloat instead.
likely near /home/juser/.julia/v0.4/MLBase/src/deprecated/datapre.jl:104
WARNING: Base.FloatingPoint is deprecated, use AbstractFloat instead.
likely near /home/juser/.julia/v0.4/MLBase/src/deprecated/datapre.jl:105
WARNING: Base.FloatingPoint is deprecated, use AbstractFloat instead.
likely near /home/juser/.julia/v0.4/MLBase/src/deprecated/datapre.jl:163
WARNING: Base.FloatingPoint is deprecated, use AbstractFloat instead.
likely near /home/juser/.julia/v0.4/MLBase/src/deprecated/datapre.jl:163
WARNING: Base.FloatingPoint is deprecated, use AbstractFloat instead.
likely near /home/juser/.julia/v0.4/MLBase/src/deprecated/datapre.jl:163
AbstractHistogram 228 bytes DataType
WARNING: both StatsBase and Base export "histrange"; uses of it in module MLBase must be qualified
WARNING: both StatsBase and Base export "midpoints"; uses of it in module MLBase must be qualified
CoefTable 284 bytes DataType
CrossValGenerator 92 bytes DataType
Forward 0 bytes Base.Order.ForwardOrdering
Histogram 272 bytes DataType
Kfold 136 bytes DataType
L1dist 1279 bytes Function
L2dist 577 bytes Function
LOOCV 112 bytes DataType
LabelMap 180 bytes DataType
Linfdist 1450 bytes Function
MLBase 369 KB Module
ROCNums 228 bytes DataType
RandomSub 136 bytes DataType
RegressionModel 92 bytes DataType
Reverse 0 bytes Base.Order.ReverseOrdering{Base.Or…
Standardize 136 bytes DataType
StatisticalModel 92 bytes DataType
StatsBase 470 KB Module
StratifiedKfold 148 bytes DataType
StratifiedRandomSub 148 bytes DataType
WeightVec 284 bytes DataType
addcounts! 11 KB Function
autocor 4814 bytes Function
autocor! 3572 bytes Function
autocov 4814 bytes Function
autocov! 3572 bytes Function
classify 4926 bytes Function
classify! 3564 bytes Function
classify_withscore 1934 bytes Function
classify_withscores 1325 bytes Function
classify_withscores! 2395 bytes Function
coef 516 bytes Function
coeftable 516 bytes Function
competerank 649 bytes Function
confint 516 bytes Function
confusmat 1518 bytes Function
corkendall 5773 bytes Function
correctrate 611 bytes Function
corspearman 2532 bytes Function
counteq 1287 bytes Function
counthits 4733 bytes Function
countmap 1118 bytes Function
countne 1287 bytes Function
counts 8052 bytes Function
cross_validate 2492 bytes Function
crosscor 8202 bytes Function
crosscor! 6952 bytes Function
crosscov 8202 bytes Function
crosscov! 6952 bytes Function
crossentropy 2134 bytes Function
denserank 647 bytes Function
describe 560 bytes Function
deviance 516 bytes Function
df_residual 516 bytes Function
ecdf 948 bytes Function
entropy 1799 bytes Function
errorrate 611 bytes Function
f1score 604 bytes Function
false_negative 496 bytes Function
false_negative_rate 521 bytes Function
false_positive 496 bytes Function
false_positive_rate 521 bytes Function
findat 538 bytes Function
fit 13 KB Function
fit! 548 bytes Function
fitted 516 bytes Function
geomean 1163 bytes Function
gkldiv 1559 bytes Function
gridtune 2063 bytes Function
groupindices 3382 bytes Function
harmmean 1153 bytes Function
hist 2683 bytes Function
hitrate 731 bytes Function
hitrates 1422 bytes Function
indexmap 1184 bytes Function
indicatormat 4556 bytes Function
inverse_rle 1798 bytes Function
invsoftplus 5037 bytes Function
iqr 608 bytes Function
kldivergence 2138 bytes Function
kurtosis 4745 bytes Function
labeldecode 1648 bytes Function
labelencode 1657 bytes Function
labelmap 1417 bytes Function
levelsmap 1320 bytes Function
logistic 4468 bytes Function
logit 4441 bytes Function
loglikelihood 516 bytes Function
logsumexp 2785 bytes Function
mad 3116 bytes Function
maxad 570 bytes Function
mean_and_cov 2938 bytes Function
mean_and_std 2120 bytes Function
mean_and_var 2120 bytes Function
meanad 585 bytes Function
middle 3053 bytes Function
mode 4046 bytes Function
model_response 516 bytes Function
modes 4963 bytes Function
moment 2360 bytes Function
msd 587 bytes Function
nobs 516 bytes Function
nquantile 590 bytes Function
ordinalrank 645 bytes Function
pacf 3226 bytes Function
pacf! 1893 bytes Function
percentile 583 bytes Function
precision 3287 bytes Function
predict 516 bytes Function
predict! 516 bytes Function
proportionmap 1003 bytes Function
proportions 7036 bytes Function
psnr 655 bytes Function
recall 506 bytes Function
repeach 3277 bytes Function
repeachcol 3354 bytes Function
repeachrow 4030 bytes Function
residuals 516 bytes Function
rle 1824 bytes Function
rmsd 1691 bytes Function
roc 15 KB Function
sample 9170 bytes Function
sample! 3510 bytes Function
samplepair 1447 bytes Function
scattermat 3208 bytes Function
sem 568 bytes Function
skewness 4665 bytes Function
softmax 560 bytes Function
softmax! 2515 bytes Function
softplus 5021 bytes Function
span 742 bytes Function
sqL2dist 1276 bytes Function
standardize 1819 bytes Function
standardize! 1821 bytes Function
stderr 517 bytes Function
summarystats 1004 bytes Function
tiedrank 646 bytes Function
transform 1086 bytes Function
trimmean 1904 bytes Function
true_negative 496 bytes Function
true_negative_rate 521 bytes Function
true_positive 496 bytes Function
true_positive_rate 521 bytes Function
variation 1035 bytes Function
vcov 516 bytes Function
view 4098 bytes Function
weights 1086 bytes Function
wmean 723 bytes Function
wmedian 1071 bytes Function
wquantile 2130 bytes Function
wsample 4621 bytes Function
wsample! 1945 bytes Function
wsum 1775 bytes Function
wsum! 1904 bytes Function
xlogx 4467 bytes Function
xlogy 5141 bytes Function
zscore 3008 bytes Function
zscore! 2904 bytes Function
In [7]:
using RCall
In [8]:
form = rcopy("Formaldehyde")
Out[8]:
carb optden 1 0.1 0.086 2 0.3 0.269 3 0.5 0.446 4 0.6 0.538 5 0.7 0.626 6 0.9 0.782
In [9]:
@rimport lme4
WARNING: RCall.jl Loading required package: Matrix
In [10]:
whos(lme4)
Arabidopsis 8 bytes RCall.RObject{RCall.VecSxp}
Cv_to_Sv 8 bytes RCall.RObject{RCall.ClosSxp}
Cv_to_Vv 8 bytes RCall.RObject{RCall.ClosSxp}
Dyestuff 8 bytes RCall.RObject{RCall.VecSxp}
Dyestuff2 8 bytes RCall.RObject{RCall.VecSxp}
GHrule 8 bytes RCall.RObject{RCall.ClosSxp}
GQN 8 bytes RCall.RObject{RCall.VecSxp}
GQdk 8 bytes RCall.RObject{RCall.ClosSxp}
InstEval 8 bytes RCall.RObject{RCall.VecSxp}
NelderMead 8 bytes RCall.RObject{RCall.ClosSxp}
Nelder_Mead 8 bytes RCall.RObject{RCall.ClosSxp}
Pastes 8 bytes RCall.RObject{RCall.VecSxp}
Penicillin 8 bytes RCall.RObject{RCall.VecSxp}
REMLcrit 8 bytes RCall.RObject{RCall.ClosSxp}
Sv_to_Cv 8 bytes RCall.RObject{RCall.ClosSxp}
VarCorr 8 bytes RCall.RObject{RCall.ClosSxp}
VerbAgg 8 bytes RCall.RObject{RCall.VecSxp}
Vv_to_Cv 8 bytes RCall.RObject{RCall.ClosSxp}
bootMer 8 bytes RCall.RObject{RCall.ClosSxp}
cake 8 bytes RCall.RObject{RCall.VecSxp}
cbpp 8 bytes RCall.RObject{RCall.VecSxp}
confint.merMod 8 bytes RCall.RObject{RCall.ClosSxp}
cov2sdcor 8 bytes RCall.RObject{RCall.ClosSxp}
devcomp 8 bytes RCall.RObject{RCall.ClosSxp}
dummy 8 bytes RCall.RObject{RCall.ClosSxp}
expandDoubleVerts 8 bytes RCall.RObject{RCall.ClosSxp}
factorize 8 bytes RCall.RObject{RCall.ClosSxp}
findbars 8 bytes RCall.RObject{RCall.ClosSxp}
fixef 8 bytes RCall.RObject{RCall.ClosSxp}
formatVC 8 bytes RCall.RObject{RCall.ClosSxp}
fortify.merMod 8 bytes RCall.RObject{RCall.ClosSxp}
getL 8 bytes RCall.RObject{RCall.ClosSxp}
getME 8 bytes RCall.RObject{RCall.ClosSxp}
glFormula 8 bytes RCall.RObject{RCall.ClosSxp}
glmFamily 8 bytes RCall.RObject{RCall.ClosSxp}
glmResp 8 bytes RCall.RObject{RCall.ClosSxp}
glmer 8 bytes RCall.RObject{RCall.ClosSxp}
glmer.nb 8 bytes RCall.RObject{RCall.ClosSxp}
glmerControl 8 bytes RCall.RObject{RCall.ClosSxp}
glmerLaplaceHandle 8 bytes RCall.RObject{RCall.ClosSxp}
golden 8 bytes RCall.RObject{RCall.ClosSxp}
grouseticks 8 bytes RCall.RObject{RCall.VecSxp}
grouseticks_agg 8 bytes RCall.RObject{RCall.VecSxp}
isGLMM 8 bytes RCall.RObject{RCall.ClosSxp}
isLMM 8 bytes RCall.RObject{RCall.ClosSxp}
isNLMM 8 bytes RCall.RObject{RCall.ClosSxp}
isNested 8 bytes RCall.RObject{RCall.ClosSxp}
isREML 8 bytes RCall.RObject{RCall.ClosSxp}
lFormula 8 bytes RCall.RObject{RCall.ClosSxp}
llikAIC 8 bytes RCall.RObject{RCall.ClosSxp}
lmList 8 bytes RCall.RObject{RCall.ClosSxp}
lmResp 8 bytes RCall.RObject{RCall.ClosSxp}
lme4 756 bytes Module
lmer 8 bytes RCall.RObject{RCall.ClosSxp}
lmerControl 8 bytes RCall.RObject{RCall.ClosSxp}
lmerResp 8 bytes RCall.RObject{RCall.ClosSxp}
logProf 8 bytes RCall.RObject{RCall.ClosSxp}
merPredD 8 bytes RCall.RObject{RCall.ClosSxp}
methTitle 8 bytes RCall.RObject{RCall.ClosSxp}
mkDataTemplate 8 bytes RCall.RObject{RCall.ClosSxp}
mkGlmerDevfun 8 bytes RCall.RObject{RCall.ClosSxp}
mkLmerDevfun 8 bytes RCall.RObject{RCall.ClosSxp}
mkMerMod 8 bytes RCall.RObject{RCall.ClosSxp}
mkParsTemplate 8 bytes RCall.RObject{RCall.ClosSxp}
mkReTrms 8 bytes RCall.RObject{RCall.ClosSxp}
mkRespMod 8 bytes RCall.RObject{RCall.ClosSxp}
mkVarCorr 8 bytes RCall.RObject{RCall.ClosSxp}
mlist2vec 8 bytes RCall.RObject{RCall.ClosSxp}
negative.binomial 8 bytes RCall.RObject{RCall.ClosSxp}
ngrps 8 bytes RCall.RObject{RCall.ClosSxp}
nlformula 8 bytes RCall.RObject{RCall.ClosSxp}
nlmer 8 bytes RCall.RObject{RCall.ClosSxp}
nlmerControl 8 bytes RCall.RObject{RCall.ClosSxp}
nloptwrap 8 bytes RCall.RObject{RCall.ClosSxp}
nlsResp 8 bytes RCall.RObject{RCall.ClosSxp}
nobars 8 bytes RCall.RObject{RCall.ClosSxp}
optimizeGlmer 8 bytes RCall.RObject{RCall.ClosSxp}
optimizeLmer 8 bytes RCall.RObject{RCall.ClosSxp}
ranef 8 bytes RCall.RObject{RCall.ClosSxp}
rePos 8 bytes RCall.RObject{RCall.ClosSxp}
refit 8 bytes RCall.RObject{RCall.ClosSxp}
refitML 8 bytes RCall.RObject{RCall.ClosSxp}
sdcor2cov 8 bytes RCall.RObject{RCall.ClosSxp}
show 8 bytes RCall.RObject{RCall.ClosSxp}
sigma 8 bytes RCall.RObject{RCall.ClosSxp}
sleepstudy 8 bytes RCall.RObject{RCall.VecSxp}
subbars 8 bytes RCall.RObject{RCall.ClosSxp}
updateGlmerDevfun 8 bytes RCall.RObject{RCall.ClosSxp}
varianceProf 8 bytes RCall.RObject{RCall.ClosSxp}
vcov.merMod 8 bytes RCall.RObject{RCall.ClosSxp}
vec2STlist 8 bytes RCall.RObject{RCall.ClosSxp}
vec2mlist 8 bytes RCall.RObject{RCall.ClosSxp}
In [11]:
lme4.grouseticks
Out[11]:
RCall.RObject{RCall.VecSxp}
INDEX TICKS BROOD HEIGHT YEAR LOCATION cHEIGHT
1 1 0 501 465 95 32 2.759305
2 2 0 501 465 95 32 2.759305
3 3 0 502 472 95 36 9.759305
4 4 0 503 475 95 37 12.759305
5 5 0 503 475 95 37 12.759305
6 6 3 503 475 95 37 12.759305
7 7 2 503 475 95 37 12.759305
8 8 0 504 488 95 44 25.759305
9 9 0 504 488 95 44 25.759305
10 10 2 504 488 95 44 25.759305
11 11 0 505 492 95 47 29.759305
12 12 0 505 492 95 47 29.759305
13 13 0 505 492 95 47 29.759305
14 14 0 506 490 95 45 27.759305
15 15 0 506 490 95 45 27.759305
16 16 0 506 490 95 45 27.759305
17 17 0 507 464 95 31 1.759305
18 18 0 507 464 95 31 1.759305
19 19 0 507 464 95 31 1.759305
20 20 1 507 464 95 31 1.759305
21 21 2 507 464 95 31 1.759305
22 22 1 509 457 95 28 -5.240695
23 23 0 510 457 95 28 -5.240695
24 24 0 511 457 95 28 -5.240695
25 25 5 511 457 95 28 -5.240695
26 26 8 512 451 95 26 -11.240695
27 27 3 512 451 95 26 -11.240695
28 28 4 512 451 95 26 -11.240695
29 29 7 513 437 95 17 -25.240695
30 30 0 513 437 95 17 -25.240695
31 31 4 513 437 95 17 -25.240695
32 32 4 514 430 95 14 -32.240695
33 33 1 514 430 95 14 -32.240695
34 34 0 514 430 95 14 -32.240695
35 35 0 514 430 95 14 -32.240695
36 36 3 514 430 95 14 -32.240695
37 37 1 514 430 95 14 -32.240695
38 38 6 515 427 95 13 -35.240695
39 39 0 515 427 95 13 -35.240695
40 40 1 515 427 95 13 -35.240695
41 41 0 515 427 95 13 -35.240695
42 42 2 516 419 95 7 -43.240695
43 43 7 516 419 95 7 -43.240695
44 44 31 516 419 95 7 -43.240695
45 45 34 517 411 95 4 -51.240695
46 46 17 517 411 95 4 -51.240695
47 47 16 517 411 95 4 -51.240695
48 48 66 518 419 95 7 -43.240695
49 49 49 518 419 95 7 -43.240695
50 50 82 518 419 95 7 -43.240695
51 51 85 518 419 95 7 -43.240695
52 52 64 518 419 95 7 -43.240695
53 53 11 519 424 95 11 -38.240695
54 54 14 519 424 95 11 -38.240695
55 55 4 519 424 95 11 -38.240695
56 56 10 519 424 95 11 -38.240695
57 57 3 520 427 95 13 -35.240695
58 58 15 520 427 95 13 -35.240695
59 59 8 520 427 95 13 -35.240695
60 60 9 521 422 95 9 -40.240695
61 61 11 521 422 95 9 -40.240695
62 62 7 521 422 95 9 -40.240695
63 63 13 521 422 95 9 -40.240695
64 64 3 522 503 95 53 40.759305
65 65 0 523 496 95 51 33.759305
66 66 0 523 496 95 51 33.759305
67 67 1 523 496 95 51 33.759305
68 68 1 523 496 95 51 33.759305
69 69 0 525 507 95 54 44.759305
70 70 0 525 507 95 54 44.759305
71 71 0 525 507 95 54 44.759305
72 72 0 525 507 95 54 44.759305
73 73 0 526 496 95 51 33.759305
74 74 0 526 496 95 51 33.759305
75 75 0 526 496 95 51 33.759305
76 76 1 526 496 95 51 33.759305
77 77 1 526 496 95 51 33.759305
78 78 0 526 496 95 51 33.759305
79 79 2 528 466 95 33 3.759305
80 80 0 528 466 95 33 3.759305
81 81 3 528 466 95 33 3.759305
82 82 1 531 488 95 44 25.759305
83 83 7 533 442 95 19 -20.240695
84 84 2 533 442 95 19 -20.240695
85 85 16 533 442 95 19 -20.240695
86 86 12 533 442 95 19 -20.240695
87 87 0 533 442 95 19 -20.240695
88 88 1 535 442 95 19 -20.240695
89 89 0 537 533 95 63 70.759305
90 90 0 537 533 95 63 70.759305
91 91 1 537 533 95 63 70.759305
92 92 0 537 533 95 63 70.759305
93 93 0 537 533 95 63 70.759305
94 94 1 537 533 95 63 70.759305
95 95 0 537 533 95 63 70.759305
96 96 0 538 533 95 63 70.759305
97 97 0 539 515 95 59 52.759305
98 98 0 539 515 95 59 52.759305
99 99 0 539 515 95 59 52.759305
100 100 0 539 515 95 59 52.759305
101 101 5 540 518 95 60 55.759305
102 102 2 540 518 95 60 55.759305
103 103 2 542 493 95 48 30.759305
104 104 1 542 493 95 48 30.759305
105 105 1 542 493 95 48 30.759305
106 106 0 548 468 95 34 5.759305
107 107 0 548 468 95 34 5.759305
108 108 1 548 468 95 34 5.759305
109 109 1 549 476 95 38 13.759305
110 110 1 549 476 95 38 13.759305
111 111 0 549 476 95 38 13.759305
112 112 0 549 476 95 38 13.759305
113 113 5 550 446 95 22 -16.240695
114 114 3 550 446 95 22 -16.240695
115 115 2 553 460 95 30 -2.240695
116 116 2 559 525 95 62 62.759305
117 117 1 559 525 95 62 62.759305
118 118 1 601 410 96 3 -52.240695
119 119 0 601 410 96 3 -52.240695
120 120 2 601 410 96 3 -52.240695
121 121 5 601 410 96 3 -52.240695
122 122 1 601 410 96 3 -52.240695
123 123 2 601 410 96 3 -52.240695
124 124 2 601 410 96 3 -52.240695
125 125 3 602 417 96 6 -45.240695
126 126 14 602 417 96 6 -45.240695
127 127 11 602 417 96 6 -45.240695
128 128 9 602 417 96 6 -45.240695
129 129 4 602 417 96 6 -45.240695
130 130 10 602 417 96 6 -45.240695
131 131 33 602 417 96 6 -45.240695
132 132 19 602 417 96 6 -45.240695
133 133 16 602 417 96 6 -45.240695
134 134 16 603 430 96 14 -32.240695
135 135 13 603 430 96 14 -32.240695
136 136 11 603 430 96 14 -32.240695
137 137 7 603 430 96 14 -32.240695
138 138 4 603 430 96 14 -32.240695
139 139 11 603 430 96 14 -32.240695
140 140 1 604 456 96 27 -6.240695
141 141 1 604 456 96 27 -6.240695
142 142 4 604 456 96 27 -6.240695
143 143 6 605 457 96 28 -5.240695
144 144 2 605 457 96 28 -5.240695
145 145 7 605 457 96 28 -5.240695
146 146 8 605 457 96 28 -5.240695
147 147 14 605 457 96 28 -5.240695
148 148 6 606 430 96 14 -32.240695
149 149 13 606 430 96 14 -32.240695
150 150 5 606 430 96 14 -32.240695
151 151 8 606 430 96 14 -32.240695
152 152 13 606 430 96 14 -32.240695
153 153 17 606 430 96 14 -32.240695
154 154 5 606 430 96 14 -32.240695
155 155 1 606 430 96 14 -32.240695
156 156 1 606 430 96 14 -32.240695
157 157 2 606 430 96 14 -32.240695
158 158 7 607 423 96 10 -39.240695
159 159 7 608 421 96 8 -41.240695
160 160 11 608 421 96 8 -41.240695
161 161 1 609 525 96 62 62.759305
162 162 0 609 525 96 62 62.759305
163 163 5 610 509 96 55 46.759305
164 164 4 610 509 96 55 46.759305
165 165 0 611 499 96 52 36.759305
166 166 0 611 499 96 52 36.759305
167 167 0 611 499 96 52 36.759305
168 168 7 612 503 96 53 40.759305
169 169 5 612 503 96 53 40.759305
170 170 3 612 503 96 53 40.759305
171 171 1 612 503 96 53 40.759305
172 172 6 612 503 96 53 40.759305
173 173 1 614 492 96 47 29.759305
174 174 2 614 492 96 47 29.759305
175 175 14 615 491 96 46 28.759305
176 176 5 615 491 96 46 28.759305
177 177 27 615 491 96 46 28.759305
178 178 1 616 475 96 37 12.759305
179 179 2 616 475 96 37 12.759305
180 180 3 616 475 96 37 12.759305
181 181 0 616 475 96 37 12.759305
182 182 1 617 479 96 40 16.759305
183 183 0 617 479 96 40 16.759305
184 184 5 617 479 96 40 16.759305
185 185 5 617 479 96 40 16.759305
186 186 8 617 479 96 40 16.759305
187 187 21 617 479 96 40 16.759305
188 188 15 618 472 96 36 9.759305
189 189 15 618 472 96 36 9.759305
190 190 6 618 472 96 36 9.759305
191 191 19 618 472 96 36 9.759305
192 192 14 618 472 96 36 9.759305
193 193 1 621 485 96 42 22.759305
194 194 1 621 485 96 42 22.759305
195 195 3 621 485 96 42 22.759305
196 196 2 621 485 96 42 22.759305
197 197 3 621 485 96 42 22.759305
198 198 2 623 495 96 50 32.759305
199 199 5 623 495 96 50 32.759305
200 200 0 624 472 96 36 9.759305
201 201 6 624 472 96 36 9.759305
202 202 3 624 472 96 36 9.759305
203 203 1 625 458 96 29 -4.240695
204 204 0 625 458 96 29 -4.240695
205 205 1 625 458 96 29 -4.240695
206 206 6 625 458 96 29 -4.240695
207 207 1 625 458 96 29 -4.240695
208 208 85 626 449 96 24 -13.240695
209 209 45 626 449 96 24 -13.240695
210 210 68 626 449 96 24 -13.240695
211 211 84 626 449 96 24 -13.240695
212 212 50 626 449 96 24 -13.240695
213 213 13 628 442 96 19 -20.240695
214 214 1 628 442 96 19 -20.240695
215 215 19 629 448 96 23 -14.240695
216 216 26 629 448 96 23 -14.240695
217 217 9 629 448 96 23 -14.240695
218 218 2 629 448 96 23 -14.240695
219 219 4 629 448 96 23 -14.240695
220 220 3 629 448 96 23 -14.240695
221 221 22 630 448 96 23 -14.240695
222 222 32 630 448 96 23 -14.240695
223 223 5 631 403 96 1 -59.240695
224 224 21 631 403 96 1 -59.240695
225 225 26 631 403 96 1 -59.240695
226 226 13 631 403 96 1 -59.240695
227 227 23 631 403 96 1 -59.240695
228 228 42 632 411 96 4 -51.240695
229 229 38 632 411 96 4 -51.240695
230 230 61 632 411 96 4 -51.240695
231 231 79 632 411 96 4 -51.240695
232 232 39 632 411 96 4 -51.240695
233 233 41 632 411 96 4 -51.240695
234 234 15 634 415 96 5 -47.240695
235 235 23 634 415 96 5 -47.240695
236 236 14 634 415 96 5 -47.240695
237 237 7 635 427 96 13 -35.240695
238 238 24 636 424 96 11 -38.240695
239 239 3 638 525 96 62 62.759305
240 240 1 638 525 96 62 62.759305
241 241 2 640 521 96 61 58.759305
242 242 1 640 521 96 61 58.759305
243 243 0 640 521 96 61 58.759305
244 244 3 641 518 96 60 55.759305
245 245 8 641 518 96 60 55.759305
246 246 1 642 495 96 50 32.759305
247 247 2 642 495 96 50 32.759305
248 248 0 642 495 96 50 32.759305
249 249 8 643 495 96 50 32.759305
250 250 3 643 495 96 50 32.759305
251 251 14 643 495 96 50 32.759305
252 252 16 643 495 96 50 32.759305
253 253 18 643 495 96 50 32.759305
254 254 11 643 495 96 50 32.759305
255 255 13 643 495 96 50 32.759305
256 256 6 645 460 96 30 -2.240695
257 257 7 645 460 96 30 -2.240695
258 258 10 645 460 96 30 -2.240695
259 259 5 647 442 96 19 -20.240695
260 260 7 647 442 96 19 -20.240695
261 261 25 648 443 96 20 -19.240695
262 262 11 648 443 96 20 -19.240695
263 263 6 648 443 96 20 -19.240695
264 264 4 648 443 96 20 -19.240695
265 265 7 648 443 96 20 -19.240695
266 266 4 650 425 96 12 -37.240695
267 267 6 650 425 96 12 -37.240695
268 268 2 650 425 96 12 -37.240695
269 269 5 651 439 96 18 -23.240695
270 270 3 651 439 96 18 -23.240695
271 271 7 651 439 96 18 -23.240695
272 272 3 652 444 96 21 -18.240695
273 273 1 701 450 97 25 -12.240695
274 274 4 701 450 97 25 -12.240695
275 275 4 701 450 97 25 -12.240695
276 276 2 701 450 97 25 -12.240695
277 277 5 701 450 97 25 -12.240695
278 278 3 702 446 97 22 -16.240695
279 279 0 702 446 97 22 -16.240695
280 280 3 702 446 97 22 -16.240695
281 281 1 702 446 97 22 -16.240695
282 282 2 702 446 97 22 -16.240695
283 283 3 702 446 97 22 -16.240695
284 284 1 704 472 97 36 9.759305
285 285 0 704 472 97 36 9.759305
286 286 4 704 472 97 36 9.759305
287 287 0 704 472 97 36 9.759305
288 288 0 704 472 97 36 9.759305
289 289 0 705 472 97 36 9.759305
290 290 0 706 460 97 30 -2.240695
291 291 0 706 460 97 30 -2.240695
292 292 0 706 460 97 30 -2.240695
293 293 1 708 442 97 19 -20.240695
294 294 3 708 442 97 19 -20.240695
295 295 4 708 442 97 19 -20.240695
296 296 0 708 442 97 19 -20.240695
297 297 4 708 442 97 19 -20.240695
298 298 2 708 442 97 19 -20.240695
299 299 0 709 525 97 62 62.759305
300 300 0 709 525 97 62 62.759305
301 301 1 709 525 97 62 62.759305
302 302 0 710 533 97 63 70.759305
303 303 1 710 533 97 63 70.759305
304 304 2 710 533 97 63 70.759305
305 305 0 710 533 97 63 70.759305
306 306 0 710 533 97 63 70.759305
307 307 0 710 533 97 63 70.759305
308 308 1 711 513 97 57 50.759305
309 309 0 711 513 97 57 50.759305
310 310 0 711 513 97 57 50.759305
311 311 1 711 513 97 57 50.759305
312 312 1 711 513 97 57 50.759305
313 313 0 711 513 97 57 50.759305
314 314 0 711 513 97 57 50.759305
315 315 0 712 514 97 58 51.759305
316 316 0 712 514 97 58 51.759305
317 317 0 713 511 97 56 48.759305
318 318 0 713 511 97 56 48.759305
319 319 1 713 511 97 56 48.759305
320 320 0 713 511 97 56 48.759305
321 321 0 713 511 97 56 48.759305
322 322 0 714 511 97 56 48.759305
323 323 0 714 511 97 56 48.759305
324 324 1 714 511 97 56 48.759305
325 325 0 714 511 97 56 48.759305
326 326 0 714 511 97 56 48.759305
327 327 0 714 511 97 56 48.759305
328 328 0 715 496 97 51 33.759305
329 329 0 715 496 97 51 33.759305
330 330 0 715 496 97 51 33.759305
331 331 0 715 496 97 51 33.759305
332 332 1 716 494 97 49 31.759305
333 333 0 716 494 97 49 31.759305
334 334 0 717 494 97 49 31.759305
335 335 0 717 494 97 49 31.759305
336 336 0 717 494 97 49 31.759305
337 337 2 718 411 97 4 -51.240695
338 338 4 718 411 97 4 -51.240695
339 339 4 718 411 97 4 -51.240695
340 340 1 718 411 97 4 -51.240695
341 341 2 718 411 97 4 -51.240695
342 342 2 719 411 97 4 -51.240695
343 343 1 719 411 97 4 -51.240695
344 344 4 719 411 97 4 -51.240695
345 345 1 719 411 97 4 -51.240695
346 346 3 719 411 97 4 -51.240695
347 347 3 719 411 97 4 -51.240695
348 348 2 720 423 97 10 -39.240695
349 349 0 720 423 97 10 -39.240695
350 350 3 721 424 97 11 -38.240695
351 351 2 722 403 97 1 -59.240695
352 352 0 722 403 97 1 -59.240695
353 353 1 722 403 97 1 -59.240695
354 354 0 723 409 97 2 -53.240695
355 355 3 723 409 97 2 -53.240695
356 356 1 723 409 97 2 -53.240695
357 357 10 724 434 97 16 -28.240695
358 358 4 724 434 97 16 -28.240695
359 359 1 724 434 97 16 -28.240695
360 360 2 725 477 97 39 14.759305
361 361 0 725 477 97 39 14.759305
362 362 1 725 477 97 39 14.759305
363 363 0 727 472 97 36 9.759305
364 364 0 728 468 97 34 5.759305
365 365 0 728 468 97 34 5.759305
366 366 0 729 470 97 35 7.759305
367 367 0 730 486 97 43 23.759305
368 368 0 731 495 97 50 32.759305
369 369 0 731 495 97 50 32.759305
370 370 0 731 495 97 50 32.759305
371 371 0 731 495 97 50 32.759305
372 372 0 731 495 97 50 32.759305
373 373 0 732 483 97 41 20.759305
374 374 0 732 483 97 41 20.759305
375 375 2 732 483 97 41 20.759305
376 376 2 733 442 97 19 -20.240695
377 377 2 733 442 97 19 -20.240695
378 378 0 734 457 97 28 -5.240695
379 379 4 736 457 97 28 -5.240695
380 380 5 736 457 97 28 -5.240695
381 381 2 737 457 97 28 -5.240695
382 382 3 737 457 97 28 -5.240695
383 383 2 737 457 97 28 -5.240695
384 384 2 737 457 97 28 -5.240695
385 385 1 737 457 97 28 -5.240695
386 386 2 737 457 97 28 -5.240695
387 387 0 737 457 97 28 -5.240695
388 388 2 738 464 97 31 1.759305
389 389 0 738 464 97 31 1.759305
390 390 1 738 464 97 31 1.759305
391 391 0 739 433 97 15 -29.240695
392 392 3 739 433 97 15 -29.240695
393 393 1 739 433 97 15 -29.240695
394 394 0 739 433 97 15 -29.240695
395 395 0 740 442 97 19 -20.240695
396 396 0 740 442 97 19 -20.240695
397 397 0 741 433 97 15 -29.240695
398 398 1 741 433 97 15 -29.240695
399 399 0 741 433 97 15 -29.240695
400 400 0 742 430 97 14 -32.240695
401 401 0 742 430 97 14 -32.240695
402 402 2 743 450 97 25 -12.240695
403 403 0 743 450 97 25 -12.240695
One of the areas in which Julia shines is optimization packages. I mostly do nonlinear optimization subject to box constraints and use the NLopt package. Many other types of optimization problems can be addressed with the JuMP package.
A recent addition is the JuliaDiff organization that provides several types of automatic differentiation packages for Julia.
Content source: dmbates/JuliaWorkshop
Similar notebooks: