# Quick Start Guide¶

## Intro¶

Let’s take a quick tour through Saddle to get a sense of the feature set. There are five major array-backed, specialized data structures:

Class Description
Vec 1D vector
Mat 2D matrix
Series 1D indexed vector
Frame 2D indexed matrix
Index Hashmap-like

All are designed with immutability in mind, although since they are backed by arrays and the library tries to be conservative in copying data, you should be careful not to let the backing arrays escape object construction.

Let’s look at each one in turn through examples. If you’ve got the source code and an SBT launcher, run the following (from the directory where you’ve got Saddle checked out):

\$ sbt console


If you’ve only got the Saddle jar in your classpath, the relevant import is:

import org.saddle._


(This should bring in all the implicits you need for the examples below.)

Note: by default, toString will print up to some number of data entries. If you would like to see more data, simply call the print() method on the relevant object with a larger number.

## Vec¶

Let’s walk through some examples in an sbt console session.

First, a few ways to create Vec instances:

scala> Vec(1, 2, 3)               // pass a sequence directly
scala> Vec(1 to 3 : _*)           // pass a sequence indirectly
scala> Vec(Array(1,2,3))          // wrap an array into a Vec
scala> Vec(Seq(1,2,3))            // not usually what you want!
scala> Vec(Seq(1,2,3) : _*)       // yes, usually what you want!
scala> Vec.empty[Double]          // create an empty Vec


There are also a few special factories:

scala> vec.ones(5)
scala> vec.zeros(5)


Sometimes random Vec instances are useful. There are a few ways to accomplish this:

scala> vec.rand(1000)             // 1000 random doubles, -1.0 to 1.0 (excluding 0)
scala> vec.randp(1000)            // a thousand random positive doubles
scala> vec.randi(1000)            // a thousand random ints
scala> vec.randpi(1000) % 10      // a thousand random positive ints, from 1 to 9
scala> vec.randn(100)             // 100 normally distributed observations
scala> vec.randn2(100, 2, 15)     // 100 obs normally distributed with mean 2 and stdev 15


Let’s take a quick look at some operations you can do on Vec instances. All the major arithmetic operations are supported between two Vec instances and between a Vec and a scalar.

scala> Vec(1,2,3) + Vec(4,5,6)
scala> Vec(1,2,3) * Vec(4,5,6)
scala> Vec(1,2,3) dot Vec(4,5,6)
scala> Vec(1,2,3) outer Vec(4,5,6)
scala> Vec(1,2,3) ** Vec(4,5,6)
scala> Vec(1,2,3) << 2
scala> Vec(1,2,3) & 0x1
scala> Vec(1,2,3) + 2             // Note: 2 must be on right hand side (it's Vec.+)


You can also slice out data from a Vec in various ways:

scala> val v = vec.rand(10)

scala> v.at(2)                        // wrapped in Scalar, in case of NA

res1: Double = -0.19816001024987906

scala> v(2,4,8)
scala> v(2 -> 4)
scala> v(* -> 3)
scala> v(8 -> * )
scala> v.slice(0,3)
scala> v.slice(0,8,2)


There are statistical functions available:

scala> val v = Vec(1,2,3)

scala> v.sum
res0: Int = 6

scala> v.prod
res1: Int = 6

scala> v.mean
res2: Double = 2.0

scala> v.median
res3: Double = 2.0

scala> v.max
res4: Option[Int] = Some(3)

scala> v.stdev
res5: Double = 1.0

scala> v.variance
res6: Double = 1.0

scala> v.skew
res7: Double = 0.0

scala> v.kurt
res8: Double = NaN

scala> v.geomean
res9: Double = 1.8171205928321394

// etc ...
scala> v.count
scala> v.countif(_ > 0)
scala> v.logsum
scala> v.argmin
scala> v.percentile(0.3, method=PctMethod.NIST)
scala> v.demeaned
scala> v.rank(tie=RankTie.Avg, ascending=true)


As well as a few specially-implemented rolling statistical functions:

scala> val v = vec.rand(10)

scala> v.rollingSum(5)            // with window size = 5
scala> v.rollingMean(5)           // etc.
scala> v.rollingMedian(5)
scala> v.rollingCount(5)


In fact, you can do any calculation you’d like over the rolling window:

scala> v.rolling(5, _.stdev)      // window size = 5, take stdev of vector input


Let’s take a quick look at some more advanced functionality:

scala> val v = vec.rand(10)

scala> v filter(_ > 0.5)          // these three commands are all the same!
scala> v where v > 0.5
scala> v.take(v.find(_ > 0.5))

scala> v.filterFoldLeft(_ > 0.5)(0d) { case (acc, d) => acc + d }

scala> v shift 1


Try out some of the following for yourself:

scala> v.reversed
scala> v.mapValues(_ + 1)
scala> v.foldLeft(0d) { case (acc, d) => acc + 1.0 / d }
scala> v.scanLeft(0d) { case (acc, d) => acc + 1.0 / d }
scala> v without v.find(_ < 0.5)
scala> v findOne(_ < 0.5)
scala> v.tail(2)
scala> v(0 -> 2).mask(Vec(true, false, true))
scala> v concat v


Note that NA (missing values) are handled within most calculations. Saddle tries to prevent accidentally using raw NA values; only two primitive types, Float and Double, have NA values that are safe to use in raw form: their NA representations are Float.NaN and Double.NaN, respectively.

scala> val v = Vec(1, na.to[Int], 2)
scala> v sum

res0: Int = 3

scala> v median
res1: Double = 1.5

scala> v prod
res2: Int = 2

scala> v dropNA                           // becomes [1 2]

scala> v.at(1)                            // boxed to prevent shooting yourself in foot

scala> v.raw(1)                           // you can do this, but be careful!
res5: Int = -2147483648

scala> v.fillNA(x => x)                   // becomes [1 1 2]; the argument is the index of the NA

scala> val d: Double = scalar.Scalar(1.0) // you can auto-unbox a double scalar


Also, a Scalar[T] can convert to Option[T] implicitly, so you may do everything with it that you may do with an Option; e.g., call map() or flatmap().

Finally, if you need to treat a Vec as a sequence, you may convert it to Seq, (specifically, an IndexedSeq). Also, you may access (a copy of) Vec as an array, by calling Vec.contents.

scala> v.toSeq
scala> v.contents


## Series¶

A Series combines a Vec with an Index that provides an ordered key-value mapping. We’ll talk more about the details of Index later. First, note a Vec[T] can convert implicitly to a Series[Int, T]. So for instance:

scala> val x: Series[Int, Double] = vec.rand(5)


The key type of a must have a natural ordering (ie, an Ordering of that type within the implicit scope). However, the Series maintains the order in which its data was supplied unless ordered othewise.

Let’s look at a few constructions:

// we already know we can convert a Vec
scala> Series(Vec(32, 12, 9))
[3 x 1]
0 -> 32
1 -> 12
2 -> 9

// we can pass a pair of tuples
scala> Series("a" -> 1, "b" -> 2, "c" -> 3)
[3 x 1]
a -> 1
b -> 2
c -> 3

// any series of tuples will work, eg:
scala> Series(List("a" -> 1, "b" -> 2, "c" -> 3) : _*)

// can pass data and index separately:
scala> Series(Vec(1,2,3), Index("a", "b", "c"))

// you can create an empty Series like so:
scala> Series.empty[String, Int]

// supplied order is maintained:
scala> Series(Vec(1,2,3), Index("c", "b", "a"))
[3 x 1]
c -> 1
b -> 2
a -> 3

// unlike map, multiple keys are entirely fine:
scala> Series(Vec(1,2,3,4), Index("c", "b", "a", "b"))
[4 x 1]
c -> 1
b -> 2
a -> 3
b -> 4


With construction out of the way, let’s look at a few ways we can get data out of a Series.

scala> val q = Series(Vec(1,3,2,4), Index("c", "b", "a", "b"))

// get the values or index
scala> q.values
scala> q.index

// extract value by numerical offset
scala> q.at(2)

scala> q.at(2,3,1)
[3 x 1]
2
4
3

// or extract key
scala> q.keyAt(2)

scala> q.keyAt(2,3,1)
[Index 3 x 1]
a
b
b

// sort by index ordering
scala> q.sortedIx
[4 x 1]
a -> 3
b -> 2
b -> 4
c -> 1

// sort by value ordering
scala> q.sorted
[4 x 1]
c -> 1
b -> 2
a -> 3
b -> 4

// extract elements matching the index
scala> q("b")
[2 x 1]
b -> 2
b -> 4

scala> q("a", "b")
[3 x 1]
a -> 2
b -> 3
b -> 4

// notice ordering subtleties:
scala> q("b", "a")
[3 x 1]
b -> 3
b -> 4
a -> 2

// get first or last values
scala> q.first
scala> q.last

// or key
scala> q.firstKey
scala> q.lastKey

// "reindex" to a new index:
scala> q.reindex(Index("a","c","d"))
[3 x 1]
a ->  2
c ->  1
d -> NA

// or just by a sequence of keys:
scala> q.reindex("a","c","d")

// notice that 'slicing' ignores unknown keys:
scala> q("a", "d")
[1 x 1]
a -> 2

// we cannot reindex with "b", because it isn't unique.
// (the problem is, which "b" would we choose?)
scala> q.reindex("a", "b")
java.lang.IllegalArgumentException: requirement failed: Could not reindex unambiguously
...

// we can "reset" the index to integer labels
scala> q.resetIndex

// or to a new index altogether
scala> q.setIndex(Index("w", "x", "y", "z"))

// to 'slice', we need a sorted index; slice is inclusive by default
scala> val s = q.sortedIx
scala> s.sliceBy("b", "c")
[3 x 1]
b -> 3
b -> 4
c -> 1

// syntactic sugar is provided:
scala> s.sliceBy("b" -> "c")
scala> s.sliceBy(* -> "b")

// where slice is by offset, exclusive by default, and the
// index doesn't have to be sorted:
scala> q.slice(0,2)
[2 x 1]
c -> 1
b -> 3

scala> q.tail(2)


Aside from extracting values, there are many fun ways to compute with Series. Try the following:

scala> val q = Series(Vec(1,3,2,4), Index("c", "b", "a", "b"))
scala> q.mapValues(_ + 1)
scala> q.mapIndex(_ + "x")
scala> q.shift(1)
scala> q.filter(_ > 2)
scala> q.filterIx(_ != "b")
scala> q.filterAt { case loc => loc != 1 && loc != 3 }
scala> q.find(_ == 2)
scala> q.findKey { case x => x == 2 || x == 3 }
scala> q.findOneKey { case x => x == 2 || x == 3 }
scala> q.minKey
scala> q.contains("a")
scala> q.scanLeft(0) { case (acc, v) => acc + v }
scala> q.reversed

scala> val m = q.mask(q.values > 2)
scala> m.hasNA
scala> m.dropNA

scala> q.rolling(2, _.minKey)
scala> q.splitAt(2)
scala> q.sortedIx.splitBy("b")


We can of course convert to a Vec or a Seq if we need to. The Series.toSeq method yields a sequence of key/value tuples.

scala> q.toVec
scala> q.toSeq


We can also group by key in order to transform or combine the groupings, which themselves are Series. For example:

scala> q.groupBy.combine(_.sum)
[3 x 1]
a -> 2
b -> 7
c -> 1

scala> q.groupBy.transform(s => s - s.mean)
[4 x 1]
c ->  0.0000
b -> -0.5000
a ->  0.0000
b ->  0.5000


You can also group by another index, or by a transformation of the current index, by passing an argument into groupBy. See the Saddle API for more info.

The expressive nature of working with Series becomes apparent when you need to align data:

scala> val a = Series(Vec(1,4,2,3), Index("a","b","c","d"))
scala> val b = Series(Vec(5,2,1,8,7), Index("b","c","d","e","f"))

scala> a + b
[6 x 1]
a -> NA
b ->  9
c ->  4
d ->  4
e -> NA
f -> NA


You see that the indexes have been aligned prior to operation being performed. Because there is a missing observation in each label of a, e, and f, the summation is not done and instead an NA value is inserted into the result.

Generally, a full-outer join is performed. So, for instance:

scala> val a = Series(Vec(1,4,2), Index("a","b","b"))
scala> val b = Series(Vec(5,2,1), Index("b","b","d"))

scala> a + b
[6 x 1]
a -> NA
b ->  9
b ->  6
b ->  7
b ->  4
d -> NA


Most basic math and boolean operations are supported between two Series, as well as between a Series and a scalar value.

We mentioned joins. Let’s look at a few join operations; the result is a Frame, which we will touch on a bit later. These are similar in nature to SQL joins.

scala> val a = Series(Vec(1,4,2), Index("a","b","b"))
scala> val b = Series(Vec(5,2,1), Index("b","b","d"))

scala> a.join(b, how=index.LeftJoin)
[4 x 2]
0  1
-- --
a ->  1 NA
b ->  4  5
b ->  4  2
b ->  2  5
b ->  2  2

scala> a.join(b, how=index.RightJoin)
[4 x 2]
0  1
-- --
b ->  4  5
b ->  2  5
b ->  4  2
b ->  2  2
d -> NA  1

scala> a.join(b, how=index.InnerJoin)
[3 x 2]
0  1
-- --
b ->  4  5
b ->  4  2
b ->  2  5
b ->  2  2

scala> a.join(b, how=index.OuterJoin)
[6 x 2]
0  1
-- --
a ->  1 NA
b ->  4  5
b ->  4  2
b ->  2  5
b ->  2  2
d -> NA  1


Finally, let’s take a look at a multiply indexed Series:

scala> val t = Series(Vec(1,2,3,4), Index((1,1),(1,2),(2,1),(2,2)))
[4 x 1]
1 1 -> 1
2 -> 2
2 1 -> 3
2 -> 4


Sometimes you want to move the innermost row label to be a column label instead. You can achieve this as follows:

scala> val f = t.pivot
[2 x 2]
1  2
-- --
1 ->  1  2
2 ->  3  4


And this is how you get back the original Series:

scala> f.melt
[4 x 1]
1 1 -> 1
2 -> 2
2 1 -> 3
2 -> 4


This generalizes to tuples of higher order.

## Mat¶

A Mat[T] represents a Matrix of values. Internally it is stored as a single contiguous array; sometimes, a duplicate array is created which stores the same values, but transposed, for speed of access having to do with memory locality.

This format was chosen to be compatible with DenseMatrix of EJML, a high performance linear algebra library which provides the default matrix multiply routine for Saddle. One or two properly placed implicit conversions can extend Saddle to be a powerful linear algebra system.

Let’s start off with construction:

scala> Mat(2,2, Array(1,2,3,4))
[2 x 2]
1 2
3 4

// all same:
scala> Mat(Array(1,3), Array(2,4))
scala> Mat(Array(Array(1,3), Array(2,4)))
scala> Mat(Vec(1,3), Vec(2,4))
scala> Mat(Array(Vec(1,3), Vec(2,4)))

// identity matrix:
scala> mat.ident(2)

// empty matrix:
scala> Mat.empty[Double]

// zeros:
scala> Mat[Int](2, 2)


Again, sometimes we want to create instances filled with random observations. As to Vec, we can do the following:

scala> mat.rand(2,2)       // random doubles from within [-1.0, 1.0] excluding 0
scala> mat.randp(2,2)      // random positive doubles
scala> mat.randn(2,2)      // random normally distributed doubles
scala> mat.randn(2,2,3,12) // random normally distributed with mean=3, stdev=12


There are a few other factory methods available:

scala> mat.ones(2,2)
scala> mat.zeros(2,2)
scala> mat.diag(Vec(1,2))


Let’s look at some basic operations with Mat. As with Vec, you may perform calculations on two Mat instances, or on a Mat and a scalar value.

// element-wise multiplication
scala> Mat(2,2,Array(1,2,3,4)) * Mat(2,2,Array(4,1,2,3))
[2 x 2]
4  2
6 12

// matrix multiplication; note implicit conversion to Double
// instead of dot, can also use mult
scala> Mat(2,2,Array(1,2,3,4)) dot Mat(2,2,Array(4,1,2,3))
[2 x 2]
8.0000  7.0000
20.0000 15.0000

// matrix-vector multiplication
scala> Mat(2,2,Array(1,2,3,4)) dot Vec(2,1)
[2 x 1]
4.0000
10.0000

// as expected
scala> Mat(2,2,Array(1,2,3,4)) * 2
scala> Mat(2,2,Array(1,2,3,4)) + 2
scala> Mat(2,2,Array(1,2,3,4)) << 2
// etc...

// transpose
scala> Mat(2,2,Array(1,2,3,4)).T
scala> Mat(2,2,Array(1,2,3,4)).transposed

// properties of Mat
scala> val m = Mat(2,2,Array(1,2,3,4))
scala> m.numRows
scala> m.numCols
scala> m.isSquare
scala> m.isEmpty


There are a few ways to extract values from a Mat.

scala> m.at(0,1)

// be careful with this one!
scala> m.raw(0,1)
res2: Int = 2

scala> m.takeRows(0)
[1 x 2]
1 2

scala> m.withoutRows(0)
[1 x 2]
3 4

scala> m.takeCols(0)
[2 x 1]
1
3

scala> m.col(0)
scala> m.row(0)
scala> m.rows()
scala> m.cols()


Some other interesting methods on Mat:

scala> val m = Mat(2,2,Array(1,2,na.to[Int],4))
[2 x 2]
1  2
NA  4

scala> m.rowsWithNA
res4: List[Int] = List(1)

scala> m.dropRowsWithNA

scala> m.reshape(1,4)
[1 x 4]
1  2 NA  4

scala> mat.rand(2,2).roundTo(2)
[2 x 2]
-0.3400  0.0000
-0.3800  0.2500


Finally, if you want to print, say, 100 rows and 10 columns:

scala> m.print(100, 10)


## Frame¶

A Frame combines a Mat with a row index and a column index which provides a way to index into the Mat. First, note a Mat[T] converts implicitly to a Frame[Int, Int, T]. So for instance

scala> val f: Frame[Int, Int, Double] = mat.rand(2, 2)


A Frame is represented internally as a sequence of column Vec instances all sharing the same row index; additionally a transpose of the data is created lazily if cross sections of data are requested.

Let’s look at some ways to instantiated a Frame:

scala> val v = Vec(1, 2)                              // given the following
scala> val u = Vec(3, 4)
scala> val s = Series("a" -> 1, "b" -> 2)
scala> val t = Series("b" -> 3, "c" -> 4)

scala> Frame(v, u)                                    // two-column frame

scala> Frame("x" -> v, "y" -> u)                      // with column index

scala> Frame(s, t)                                    // aligned along rows
[3 x 2]
0  1
-- --
a ->  1 NA
b ->  2  3
c -> NA  4

scala> Frame("x" -> s, "y" -> t)                      // with column index
[3 x 2]
x  y
-- --
a ->  1 NA
b ->  2  3
c -> NA  4

scala> Frame(Seq(s, t), Index("x", "y"))              // explicit column index

scala> Frame(Seq(v, u), Index(0, 1), Index("x", "y")) // row & col indexes specified explicitly

scala> Frame(Seq(v, u), Index("a", "b"))              // col index specified


You’ll notice that if an index is not provided, a default int index is set where the index ranges between 0 and the length of the data.

Frame elements are all recognized as the same type by the compiler. But if you want to work with frames whose columns contain heterogenous data, there are a few facilities to make it easier. You can construct Frame[_, _, Any] using the Panel() constructor, which mirrors the Frame() constructor, eg:

scala> val p = Panel(Vec(1,2,3), Vec("a","b","c"))


You may then extract columns of a particular type as follows:

scala> p.colType[Int]
scala> p.colType[Int, String]


Speaking of types, if you want to generate an empty row or column of the right type:

scala> f.emptyRow
scala> f.emptyCol


Back to homogenous Frames. If you want to set or reset the index, these methods are your friends:

scala> val f = Frame("x" -> s, "y" -> t)

scala> f.setRowIndex(Index(10, 20))
scala> f.setColIndex(Index("p", "q"))
scala> f.resetRowIndex()
scala> f.resetColIndex()


(Note: frame f will carry through the next examples.)

You also have the following index transformation tools at hand:

f.mapRowIndex { case rx => ... }
f.mapColIndex { case cx => ... }


Let’s next look at how to extract data from the Frame.

scala> f.rowAt(2)    // extract row at offset 2, as Series
scala> f.rowAt(1,2)  // extract frame of rows 1 & 2
scala> f.rowAt(1->2) // extract frame of rows 1 & 2

scala> f.colAt(1)    // extract col at offset 1, as Series
scala> f.colAt(0,1)  // extract frame of cols 1 & 2
scala> f.colAt(0->1) // extract frame of cols 1 & 2


rowAt and colAt are used under the hood for the at extractor:

scala> f.at(1,1)              // Scalar value
scala> f.at(Array(1,2), 0)    // extract rows 1,2 of column 0
scala> f.at(0->1, 1)          // extract rows 0,1 of column 1
scala> f.at(0->1, 0->1)       // extract rows 0,1 of columns 0, 1
// etc...


If you want more control over slicing, you can use these methods:

scala> f.colSlice(0,1)        // frame slice consisting of column 0
scala> f.rowSlice(0,3,2)      // row slice from 0 until 3, striding by 2


Of course, this is an bi-indexed data structure, so we can use its indexes to select out data using keys:

scala> f.row("a")             // row series 'a', with all columns
scala> f.col("x")             // col series 'x', with all rows
scala> f.row("a", "c")        // select two rows
scala> f.row("a"->"b")        // slice two rows (index must be sorted)
scala> f.row(Vec("a", "c"))   // another way to select


A more explict way to slice with keys is as follows, and you can specify whether the right bound is inclusive or exclusive. Again, to slice, the index keys must be ordered.

scala> f.rowSliceBy("a", "b", inclusive=false)
scala> f.colSliceBy("x", "x", inclusive=true)


The row and col methods are used under the hood for the apply method:

scala> f("a", "x")             // extract a one-element frame by keys
scala> f("a"->"b", "x")        // two-row, one-column frame
scala> f(Vec("a", "c"), "x")   // same as above, but extracting, not slicing


The methods of extracting multiple rows shown above can of course be done on columns as well.

You can also split up the Frame by key or index:

scala> f.colSplitAt(1)          // split into two frames at column 1
scala> f.colSplitBy("y")

scala> f.rowSplitAt(1)
scala> f.rowSplitBy("b")


You extract some number of rows or columns:

scala> f.head(2)                // operates on rows
scala> f.tail(2)
scala> f.headCol(1)             // operates on cols
scala> f.tailCol(1)


Or the first & last of some key (which is helpful when you’ve got a multi-key index):

scala> f.first("b")              // first row indexed by "b" key
scala> f.last("b")               // last row indexed by "b" key
scala> f.firstCol("x")
scala> f.lastCol("x")


There are a few other methods of extracting data:

scala> f.filter { case s => s.mean > 2.0 }  // any column whose series satisfies predicate
scala> f.filterIx { case x => x == "x" }    // col where index matches key "x"
scala> f.where(Vec(false, true))            // extract second column


There are analogous methods to operate on rows rather then columns:

• rfilter
• rfilterIx
• rwhere

etc... in general, methods operate on a column-wise basis, whereas the r-counterpart does so on a row-wise basis.

You can drop cols (rows) containing any NA values:

scala> f.dropNA
scala> f.rdropNA


Let’s take a look at some operations we can do with Frames. We can do all the normal binary math operations with Frames, with either a scalar value or with another Frame. When two frames are involved, they are reindexed along both axes to match the outer join of their indices, but any missing observation in either will carry through the calculations.

scala> f + 1
scala> f * f
scala> val g = Frame("y"->Series("b"->5, "d"->10))
scala> f + g                      // one non-NA entry, ("b", "y", 8)


You can effectively supply your own binary frame operation using joinMap, which lets you control the join style on rows and columns:

scala> f.joinMap(g, rhow=index.LeftJoin, chow=index.LeftJoin) { case (x, y) => x + y }


If you want simply to align one frame to another without performing an operation, use the following method:

scala> val (fNew, gNew) = f.align(g, rhow=index.LeftJoin, chow=index.OuterJoin)


If you want to treat a Frame as a matrix to use in linear algebraic fashion, call the toMat method.

We can sort a frame in various ways:

scala> f.sortedRIx                // sorted by row index
scala> f.sortedCIx                // sorted by col index
scala> f.sortedRows(0,1)          // sort rows by (primary) col 0 and (secondary) col 1
scala> f.sortedCols(1,0)          // sort cols by (primary) row 1 and (secondary) row 0


We can also sort by an ordering provided by the result of a function acting on rows or cols:

scala> f.sortedRowsBy { case r => r.at(0) }   // sort rows by first element of row
scala> f.sortedColsBy { case c => c.at(0) }   // sort cols by first element of col


There are several mapping functions:

scala> f.mapValues { case t => t + 1 }        // add one to each element of frame
scala> f.mapVec { case v => v.demeaned }      // map over each col vec of the frame
scala> f.reduce { case s => s.mean }          // collapse each col series to a single value
scala> f.transform { case s => s.reversed }   // transform each series; outerjoin results


scala> f.mask(_ > 2)                          // mask out values > 2
scala> f.mask(Vec(false, true, true))         // mask out rows 1 & 2 (keep row 0)


Columns (rows) containing only NA values can be dropped as follows:

scala> f.mask(Vec(true, false, false)).rsqueeze   // drop rows containing NA values
scala> f.rmask(Vec(false, true)).squeeze          // takes "x" column


We can groupBy in order to combine or transform:

scala> f.groupBy(_ == "a").combine(_.count)       // # obs in each column that have/not row key "a"
scala> f.groupBy(_ == "a").transform(_.demeaned)  // contrived, but you get the idea hopefully!


We can join against another frame, or against a series:

scala> f.join(g, how=index.LeftJoin)              // left joins on row index, drops col indexes
scala> f.join(s, how=index.LeftJoin)              // implicitly promotes s to Frame
scala> f.joinS(s, how=index.LeftJoin)             // use Series directly


Btw, to join a Frame to a series, the call looks like this:

scala> s.joinF(g, how=index.LeftJoin)


Of course, if you want to join along the column index instead, there is a rjoin method.

Let’s look at a few data reshaping commands. Try the following:

scala> f.melt
scala> f.melt.mapRowIndex { case (a, b) => (b, a) } colAt(0) pivot
scala> f.mapColIndex { case c => (1, c) } stack
scala> f.mapRowIndex { case r => (1, r) } unstack


There are statistics available on Frames on a column-wise basis that are NA-aware. They are provided via an implicit conversion to FrameStats; look there to see what’s available.

Finally, note that toSeq converts a Frame to a sequence of (row, col, value) triples.

## Index¶

Index provides constant-time lookup of a value within array-backed storage, and support for joining and slice operations. There are a few factory methods for creating an Index:

scala> Index("a", "b", "c")           // from seq of values
scala> Index(Vec("a", "b", "c"))      // from vec
scala> Index(Array("a", "b", "c"))    // from array


To create a multi-level index, you may do the following. In this example, the Index is comprised of (1,a), (2,b), and (3,c):

scala> Index.make(Vec(1, 2, 3), Vec("a", "b", "c"))


You likely do not want to utilize the methods of Index directly very often, but rather attach them to data (in Series and Frames) to achieve your goals in a more indirect manner. Still, there are a few useful tools:

scala> val x = Index("a", "a", "b", "b", "c", "c")
scala> val x.next("a")                                // returns "b"
scala> val x.prev("b")                                // returns "a"


For next and prev to work, the Index must be contiguous in values, although sortedness is unnecessary. By contiguous, we mean a-b-a-b would not be a valid ordering of data, but a-a-b-b would be.

For Index instances with Set semantics (ie, no duplicate keys), you have fast union and intersect methods.

For map-like functionality, there is contains and exists, although since Index is really a multi-map, the get function returns an array of locations within the backing array, and count gives you how many entries exist for a particular key. uniques allows you to get all the unique keys, and the methods getFirst and getLast retrieve the location offsets of a particular key. The API is worth exploring further.

## Dates/Times and Recurrences¶

The org.saddle.time._ module provides a useful factory method for joda DateTime objects: datetime. It provides vector manipulations on Vec and Index instances of type DateTime (via the implicit TimeAccessors).

As of Saddle 1.3, the library provides an implementation of recurrence rules (RRule), with a few default instances which may be found in the module RRules. To illustrate, the following code generates dates at business month ends for the first four months of 2013:

scala> import RRules._
import RRules._

scala> Index.make(bizEoms, datetime(2013,1,1), datetime(2013,5,1))
[Index 4 x 1]
2013-01-31 00:00:00.000-05:00
2013-02-28 00:00:00.000-05:00
2013-03-29 00:00:00.000-04:00
2013-04-30 00:00:00.000-04:00


An RRule object allows for complex recurrence rule generation following the RFC 2445 standard. (The implementation utilizes google-rfc-2445 under the hood, licensed under Apache 2.0.) RRule‘s can be combined with the Index.make factory method to instantiate indexes as above, or can be used independently to do complex date/time math. For example, the counting method of RRule provides syntactic sugar to do date offset calculation:

scala> RRule(MONTHLY) withInterval(2) counting 5 from datetime(2013,1,1)
res1: org.joda.time.DateTime = 2013-09-01T00:00:00.000-04:00


You may also generate iterators of DateTime‘s using RRule (here we take the first five generated values and convert to a list):

scala> weeklyOn(FR) withInterval(2) from datetime(2013,1,1) take 5 toList
res2: List[org.joda.time.DateTime] = List(2013-01-04T00:00:00.000-05:00,
2013-01-18T00:00:00.000-05:00, 2013-02-01T00:00:00.000-05:00,
2013-02-15T00:00:00.000-05:00, 2013-03-01T00:00:00.000-05:00)


You may conform a datetime instance forward or backward using the conform method:

scala> conform(weeklyOn(FR), datetime(2013,1,1), forward=false)
res10: org.joda.time.DateTime = 2012-12-28T00:00:00.000-05:00


## I/O¶

The org.saddle.io._ module provides some basic, and not-so-basic, I/O functionality, although there is still much to be developed. There is a fast csv file reader.

There is also HDF5 reading/writing available for Series and Frame objects that is essentially compatible with the basic pandas format (as of pandas 0.9), but note that it only supports certain primitive types like Int/Long/Double, and DateTime & String objects, but not all Serializable Java classes.

Please note that to use HDF5, you must include the dependency on saddle-hdf5, and have installed native HDF5 library from the HDF5 binaries so that the native shared library libjhdf5 is locatable in the java library path; you can check via:

println(System.getProperty("java.library.path"))


## Hello, Campaign Contributions¶

Let’s take a quick look at processing some real data with the latest snapshot version of Saddle. We’ll use data found at the FEC, the Federal Election Commission. Download a file... the ALL.zip file is fairly chunky at about 1Gb of unzipped text data, but let’s go for it! Unzip to a directory, and launch an SBT session with sufficient memory (eg, sbt -mem 4096).

import org.saddle.io._

// create reference to CSV file
val file = CsvFile("P00000001-ALL.csv")

// parse columns 2 and 9 of the CSV and convert the result to a Frame
// (we know in advance these cols are candidate name and donation amount)
// & set the first row as the col index
// & the first col (candidate names) as the row index
val frame = CsvParser.parse(List(2,9))(file).withRowIndex(0).withColIndex(0)

// convert frame body data to long primitives, mapping any parse errors to NA
val data = frame.mapValues(CsvParser.parseLong)

// look at the total contributions by candidate name, descending
data.groupBy.combine(_.sum).sortedRowsBy { case r => -r.raw(0) } print(14)


For fun, try looking at the mean and standard deviation of the campaign contribution of each candidate.

## Utilities¶

There some neat helper functions in the org.saddle.array._ module to work with arrays of primitives:

• range
• shuffle
• tile
• random array generators
• linspace
• filter
• flatten
• argsort
• argmin, argmax

The org.saddle.util.Random class provides a xorshift Marsiglia primitive value pseudorandom number generator the underlies the random number generation throughout Saddle.

## A note on optimization¶

The data structures above attempt to operate on primitives whenever possible, although the specialization is not to every primitive JVM data type as of yet. For example, Vec is specialized on Boolean, Int, Long, and Double; but not yet Float, yet, so Vec[Float] operations will (un)box.

Try to avoid looping through these structures; they were meant for terse lines of code which operate in a vectorized manner. If you find yourself looping through them, you’re probably doing it wrong!

What’s New

User Guide