Fast Row/Column Arithmetic for Matrix-Like Objects
arithmetic.RdFast operators to perform row- or column-wise replacing and sweeping operations of vectors on matrices, data frames, lists. See also setop for math by reference and setTRA for sweeping by reference.
Usage
## Perform the operation with v and each row of X
X %rr% v
X %r+% v
X %r-% v
X %r*% v
X %r/% v
## Perform a column-wise operation between V and X
X %cr% V
X %c+% V
X %c-% V
X %c*% V
X %c/% VArguments
- X
a vector, matrix, data frame or list like object (with rows (r) columns (c) matching
v/V).- v
for row operations: an atomic vector of matching
NCOL(X). IfXis a data frame,vcan also be a list of scalar atomic elements. It is also possible to sweep lists of vectorsvout of lists of matrices or data framesX.- V
for column operations: a suitable scalar, vector, or matrix / data frame matching
NROW(X).Xcan also be a list of vectors / matrices in which caseVcan be a scalar / vector / matrix or matching list of scalars / vectors / matrices.
Details
With a matrix or data frame X, the default behavior of R when calling X op v (such as multiplication X * v) is to perform the operation of v with each column of X. The equivalent operation is performed by X %cop% V, with the difference that it computes significantly faster if X/V is a data frame / list. A more complex but frequently required task is to perform an operation with v on each row of X. This is provided based on efficient C++ code by the %rop% set of functions, e.g. X %r*% v efficiently multiplies v to each row of X.
Value
X where the operation with v / V was performed on each row or column. All attributes of X are preserved.
Note
Computations and Output: These functions are all quite simple, they only work with X on the LHS i.e. v %op% X will likely fail. The row operations are simple wrappers around TRA which provides more operations including grouped replacing and sweeping (where v would be a matrix or data frame with less rows than X being mapped to the rows of X by grouping vectors). One consequence is that just like TRA, row-wise mathematical operations (+, -, *, /) always yield numeric output, even if both X and v may be integer. This is different for column- operations which depend on base R and may also preserve integer data.
Rules of Arithmetic: Since these operators are defined as simple infix functions, the normal rules of arithmetic are not respected. So a %c+% b %c*% c evaluates as (a %c+% b) %c*% c. As with all chained infix operations, they are just evaluated sequentially from left to right.
Performance Notes: The function setop and a related set of %op=% operators as well as the setTRA function can be used to perform these operations by reference, and are faster if copies of the output are not required!! Furthermore, for Fast Statistical Functions, using fmedian(X, TRA = "-") will be a tiny bit faster than X %r-% fmedian(X). Also use fwithin(X) for fast centering using the mean, and fscale(X) for fast scaling and centering or mean-preserving scaling.
Examples
## Using data frame's / lists
v <- mtcars$cyl
mtcars %cr% v
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 6 6 6 6 6 6 6 6 6 6 6
#> Mazda RX4 Wag 6 6 6 6 6 6 6 6 6 6 6
#> Datsun 710 4 4 4 4 4 4 4 4 4 4 4
#> Hornet 4 Drive 6 6 6 6 6 6 6 6 6 6 6
#> Hornet Sportabout 8 8 8 8 8 8 8 8 8 8 8
#> Valiant 6 6 6 6 6 6 6 6 6 6 6
#> Duster 360 8 8 8 8 8 8 8 8 8 8 8
#> Merc 240D 4 4 4 4 4 4 4 4 4 4 4
#> Merc 230 4 4 4 4 4 4 4 4 4 4 4
#> Merc 280 6 6 6 6 6 6 6 6 6 6 6
#> Merc 280C 6 6 6 6 6 6 6 6 6 6 6
#> Merc 450SE 8 8 8 8 8 8 8 8 8 8 8
#> Merc 450SL 8 8 8 8 8 8 8 8 8 8 8
#> Merc 450SLC 8 8 8 8 8 8 8 8 8 8 8
#> Cadillac Fleetwood 8 8 8 8 8 8 8 8 8 8 8
#> Lincoln Continental 8 8 8 8 8 8 8 8 8 8 8
#> Chrysler Imperial 8 8 8 8 8 8 8 8 8 8 8
#> Fiat 128 4 4 4 4 4 4 4 4 4 4 4
#> Honda Civic 4 4 4 4 4 4 4 4 4 4 4
#> Toyota Corolla 4 4 4 4 4 4 4 4 4 4 4
#> Toyota Corona 4 4 4 4 4 4 4 4 4 4 4
#> Dodge Challenger 8 8 8 8 8 8 8 8 8 8 8
#> AMC Javelin 8 8 8 8 8 8 8 8 8 8 8
#> Camaro Z28 8 8 8 8 8 8 8 8 8 8 8
#> Pontiac Firebird 8 8 8 8 8 8 8 8 8 8 8
#> Fiat X1-9 4 4 4 4 4 4 4 4 4 4 4
#> Porsche 914-2 4 4 4 4 4 4 4 4 4 4 4
#> Lotus Europa 4 4 4 4 4 4 4 4 4 4 4
#> Ford Pantera L 8 8 8 8 8 8 8 8 8 8 8
#> Ferrari Dino 6 6 6 6 6 6 6 6 6 6 6
#> Maserati Bora 8 8 8 8 8 8 8 8 8 8 8
#> Volvo 142E 4 4 4 4 4 4 4 4 4 4 4
mtcars %c-% v
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 15.0 0 154.0 104 -2.10 -3.380 10.46 -6 -5 -2 -2
#> Mazda RX4 Wag 15.0 0 154.0 104 -2.10 -3.125 11.02 -6 -5 -2 -2
#> Datsun 710 18.8 0 104.0 89 -0.15 -1.680 14.61 -3 -3 0 -3
#> Hornet 4 Drive 15.4 0 252.0 104 -2.92 -2.785 13.44 -5 -6 -3 -5
#> Hornet Sportabout 10.7 0 352.0 167 -4.85 -4.560 9.02 -8 -8 -5 -6
#> Valiant 12.1 0 219.0 99 -3.24 -2.540 14.22 -5 -6 -3 -5
#> Duster 360 6.3 0 352.0 237 -4.79 -4.430 7.84 -8 -8 -5 -4
#> Merc 240D 20.4 0 142.7 58 -0.31 -0.810 16.00 -3 -4 0 -2
#> Merc 230 18.8 0 136.8 91 -0.08 -0.850 18.90 -3 -4 0 -2
#> Merc 280 13.2 0 161.6 117 -2.08 -2.560 12.30 -5 -6 -2 -2
#> Merc 280C 11.8 0 161.6 117 -2.08 -2.560 12.90 -5 -6 -2 -2
#> Merc 450SE 8.4 0 267.8 172 -4.93 -3.930 9.40 -8 -8 -5 -5
#> Merc 450SL 9.3 0 267.8 172 -4.93 -4.270 9.60 -8 -8 -5 -5
#> Merc 450SLC 7.2 0 267.8 172 -4.93 -4.220 10.00 -8 -8 -5 -5
#> Cadillac Fleetwood 2.4 0 464.0 197 -5.07 -2.750 9.98 -8 -8 -5 -4
#> Lincoln Continental 2.4 0 452.0 207 -5.00 -2.576 9.82 -8 -8 -5 -4
#> Chrysler Imperial 6.7 0 432.0 222 -4.77 -2.655 9.42 -8 -8 -5 -4
#> Fiat 128 28.4 0 74.7 62 0.08 -1.800 15.47 -3 -3 0 -3
#> Honda Civic 26.4 0 71.7 48 0.93 -2.385 14.52 -3 -3 0 -2
#> Toyota Corolla 29.9 0 67.1 61 0.22 -2.165 15.90 -3 -3 0 -3
#> Toyota Corona 17.5 0 116.1 93 -0.30 -1.535 16.01 -3 -4 -1 -3
#> Dodge Challenger 7.5 0 310.0 142 -5.24 -4.480 8.87 -8 -8 -5 -6
#> AMC Javelin 7.2 0 296.0 142 -4.85 -4.565 9.30 -8 -8 -5 -6
#> Camaro Z28 5.3 0 342.0 237 -4.27 -4.160 7.41 -8 -8 -5 -4
#> Pontiac Firebird 11.2 0 392.0 167 -4.92 -4.155 9.05 -8 -8 -5 -6
#> Fiat X1-9 23.3 0 75.0 62 0.08 -2.065 14.90 -3 -3 0 -3
#> Porsche 914-2 22.0 0 116.3 87 0.43 -1.860 12.70 -4 -3 1 -2
#> Lotus Europa 26.4 0 91.1 109 -0.23 -2.487 12.90 -3 -3 1 -2
#> Ford Pantera L 7.8 0 343.0 256 -3.78 -4.830 6.50 -8 -7 -3 -4
#> Ferrari Dino 13.7 0 139.0 169 -2.38 -3.230 9.50 -6 -5 -1 0
#> Maserati Bora 7.0 0 293.0 327 -4.46 -4.430 6.60 -8 -7 -3 0
#> Volvo 142E 17.4 0 117.0 105 0.11 -1.220 14.60 -3 -3 0 -2
mtcars %r-% seq_col(mtcars)
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 20.0 4 157.0 106 -1.10 -3.380 9.46 -8 -8 -6 -7
#> Mazda RX4 Wag 20.0 4 157.0 106 -1.10 -3.125 10.02 -8 -8 -6 -7
#> Datsun 710 21.8 2 105.0 89 -1.15 -3.680 11.61 -7 -8 -6 -10
#> Hornet 4 Drive 20.4 4 255.0 106 -1.92 -2.785 12.44 -7 -9 -7 -10
#> Hornet Sportabout 17.7 6 357.0 171 -1.85 -2.560 10.02 -8 -9 -7 -9
#> Valiant 17.1 4 222.0 101 -2.24 -2.540 13.22 -7 -9 -7 -10
#> Duster 360 13.3 6 357.0 241 -1.79 -2.430 8.84 -8 -9 -7 -7
#> Merc 240D 23.4 2 143.7 58 -1.31 -2.810 13.00 -7 -9 -6 -9
#> Merc 230 21.8 2 137.8 91 -1.08 -2.850 15.90 -7 -9 -6 -9
#> Merc 280 18.2 4 164.6 119 -1.08 -2.560 11.30 -7 -9 -6 -7
#> Merc 280C 16.8 4 164.6 119 -1.08 -2.560 11.90 -7 -9 -6 -7
#> Merc 450SE 15.4 6 272.8 176 -1.93 -1.930 10.40 -8 -9 -7 -8
#> Merc 450SL 16.3 6 272.8 176 -1.93 -2.270 10.60 -8 -9 -7 -8
#> Merc 450SLC 14.2 6 272.8 176 -1.93 -2.220 11.00 -8 -9 -7 -8
#> Cadillac Fleetwood 9.4 6 469.0 201 -2.07 -0.750 10.98 -8 -9 -7 -7
#> Lincoln Continental 9.4 6 457.0 211 -2.00 -0.576 10.82 -8 -9 -7 -7
#> Chrysler Imperial 13.7 6 437.0 226 -1.77 -0.655 10.42 -8 -9 -7 -7
#> Fiat 128 31.4 2 75.7 62 -0.92 -3.800 12.47 -7 -8 -6 -10
#> Honda Civic 29.4 2 72.7 48 -0.07 -4.385 11.52 -7 -8 -6 -9
#> Toyota Corolla 32.9 2 68.1 61 -0.78 -4.165 12.90 -7 -8 -6 -10
#> Toyota Corona 20.5 2 117.1 93 -1.30 -3.535 13.01 -7 -9 -7 -10
#> Dodge Challenger 14.5 6 315.0 146 -2.24 -2.480 9.87 -8 -9 -7 -9
#> AMC Javelin 14.2 6 301.0 146 -1.85 -2.565 10.30 -8 -9 -7 -9
#> Camaro Z28 12.3 6 347.0 241 -1.27 -2.160 8.41 -8 -9 -7 -7
#> Pontiac Firebird 18.2 6 397.0 171 -1.92 -2.155 10.05 -8 -9 -7 -9
#> Fiat X1-9 26.3 2 76.0 62 -0.92 -4.065 11.90 -7 -8 -6 -10
#> Porsche 914-2 25.0 2 117.3 87 -0.57 -3.860 9.70 -8 -8 -5 -9
#> Lotus Europa 29.4 2 92.1 109 -1.23 -4.487 9.90 -7 -8 -5 -9
#> Ford Pantera L 14.8 6 348.0 260 -0.78 -2.830 7.50 -8 -8 -5 -7
#> Ferrari Dino 18.7 4 142.0 171 -1.38 -3.230 8.50 -8 -8 -5 -5
#> Maserati Bora 14.0 6 298.0 331 -1.46 -2.430 7.60 -8 -8 -5 -3
#> Volvo 142E 20.4 2 118.0 105 -0.89 -3.220 11.60 -7 -8 -6 -9
mtcars %r-% lapply(mtcars, quantile, 0.28)
#> mpg cyl disp hp drat wt qsec vs am gear
#> Mazda RX4 5.296 2 25.536 7.56 0.7724 -0.102 -0.5216 0 1 1
#> Mazda RX4 Wag 5.296 2 25.536 7.56 0.7724 0.153 0.0384 0 1 1
#> Datsun 710 7.096 0 -26.464 -9.44 0.7224 -0.402 1.6284 1 1 1
#> Hornet 4 Drive 5.696 2 123.536 7.56 -0.0476 0.493 2.4584 1 0 0
#> Hornet Sportabout 2.996 4 225.536 72.56 0.0224 0.718 0.0384 0 0 0
#> Valiant 2.396 2 90.536 2.56 -0.3676 0.738 3.2384 1 0 0
#> Duster 360 -1.404 4 225.536 142.56 0.0824 0.848 -1.1416 0 0 0
#> Merc 240D 8.696 0 12.236 -40.44 0.5624 0.468 3.0184 1 0 1
#> Merc 230 7.096 0 6.336 -7.44 0.7924 0.428 5.9184 1 0 1
#> Merc 280 3.496 2 33.136 20.56 0.7924 0.718 1.3184 1 0 1
#> Merc 280C 2.096 2 33.136 20.56 0.7924 0.718 1.9184 1 0 1
#> Merc 450SE 0.696 4 141.336 77.56 -0.0576 1.348 0.4184 0 0 0
#> Merc 450SL 1.596 4 141.336 77.56 -0.0576 1.008 0.6184 0 0 0
#> Merc 450SLC -0.504 4 141.336 77.56 -0.0576 1.058 1.0184 0 0 0
#> Cadillac Fleetwood -5.304 4 337.536 102.56 -0.1976 2.528 0.9984 0 0 0
#> Lincoln Continental -5.304 4 325.536 112.56 -0.1276 2.702 0.8384 0 0 0
#> Chrysler Imperial -1.004 4 305.536 127.56 0.1024 2.623 0.4384 0 0 0
#> Fiat 128 16.696 0 -55.764 -36.44 0.9524 -0.522 2.4884 1 1 1
#> Honda Civic 14.696 0 -58.764 -50.44 1.8024 -1.107 1.5384 1 1 1
#> Toyota Corolla 18.196 0 -63.364 -37.44 1.0924 -0.887 2.9184 1 1 1
#> Toyota Corona 5.796 0 -14.364 -5.44 0.5724 -0.257 3.0284 1 0 0
#> Dodge Challenger -0.204 4 183.536 47.56 -0.3676 0.798 -0.1116 0 0 0
#> AMC Javelin -0.504 4 169.536 47.56 0.0224 0.713 0.3184 0 0 0
#> Camaro Z28 -2.404 4 215.536 142.56 0.6024 1.118 -1.5716 0 0 0
#> Pontiac Firebird 3.496 4 265.536 72.56 -0.0476 1.123 0.0684 0 0 0
#> Fiat X1-9 11.596 0 -55.464 -36.44 0.9524 -0.787 1.9184 1 1 1
#> Porsche 914-2 10.296 0 -14.164 -11.44 1.3024 -0.582 -0.2816 0 1 2
#> Lotus Europa 14.696 0 -39.364 10.56 0.6424 -1.209 -0.0816 1 1 2
#> Ford Pantera L 0.096 4 216.536 161.56 1.0924 0.448 -2.4816 0 1 2
#> Ferrari Dino 3.996 2 10.536 72.56 0.4924 0.048 -1.4816 0 1 2
#> Maserati Bora -0.704 4 166.536 232.56 0.4124 0.848 -2.3816 0 1 2
#> Volvo 142E 5.696 0 -13.464 6.56 0.9824 0.058 1.6184 1 1 1
#> carb
#> Mazda RX4 2
#> Mazda RX4 Wag 2
#> Datsun 710 -1
#> Hornet 4 Drive -1
#> Hornet Sportabout 0
#> Valiant -1
#> Duster 360 2
#> Merc 240D 0
#> Merc 230 0
#> Merc 280 2
#> Merc 280C 2
#> Merc 450SE 1
#> Merc 450SL 1
#> Merc 450SLC 1
#> Cadillac Fleetwood 2
#> Lincoln Continental 2
#> Chrysler Imperial 2
#> Fiat 128 -1
#> Honda Civic 0
#> Toyota Corolla -1
#> Toyota Corona -1
#> Dodge Challenger 0
#> AMC Javelin 0
#> Camaro Z28 2
#> Pontiac Firebird 0
#> Fiat X1-9 -1
#> Porsche 914-2 0
#> Lotus Europa 0
#> Ford Pantera L 2
#> Ferrari Dino 4
#> Maserati Bora 6
#> Volvo 142E 0
mtcars %c*% 5 # Significantly faster than mtcars * 5
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 105.0 30 800.0 550 19.50 13.100 82.30 0 5 20 20
#> Mazda RX4 Wag 105.0 30 800.0 550 19.50 14.375 85.10 0 5 20 20
#> Datsun 710 114.0 20 540.0 465 19.25 11.600 93.05 5 5 20 5
#> Hornet 4 Drive 107.0 30 1290.0 550 15.40 16.075 97.20 5 0 15 5
#> Hornet Sportabout 93.5 40 1800.0 875 15.75 17.200 85.10 0 0 15 10
#> Valiant 90.5 30 1125.0 525 13.80 17.300 101.10 5 0 15 5
#> Duster 360 71.5 40 1800.0 1225 16.05 17.850 79.20 0 0 15 20
#> Merc 240D 122.0 20 733.5 310 18.45 15.950 100.00 5 0 20 10
#> Merc 230 114.0 20 704.0 475 19.60 15.750 114.50 5 0 20 10
#> Merc 280 96.0 30 838.0 615 19.60 17.200 91.50 5 0 20 20
#> Merc 280C 89.0 30 838.0 615 19.60 17.200 94.50 5 0 20 20
#> Merc 450SE 82.0 40 1379.0 900 15.35 20.350 87.00 0 0 15 15
#> Merc 450SL 86.5 40 1379.0 900 15.35 18.650 88.00 0 0 15 15
#> Merc 450SLC 76.0 40 1379.0 900 15.35 18.900 90.00 0 0 15 15
#> Cadillac Fleetwood 52.0 40 2360.0 1025 14.65 26.250 89.90 0 0 15 20
#> Lincoln Continental 52.0 40 2300.0 1075 15.00 27.120 89.10 0 0 15 20
#> Chrysler Imperial 73.5 40 2200.0 1150 16.15 26.725 87.10 0 0 15 20
#> Fiat 128 162.0 20 393.5 330 20.40 11.000 97.35 5 5 20 5
#> Honda Civic 152.0 20 378.5 260 24.65 8.075 92.60 5 5 20 10
#> Toyota Corolla 169.5 20 355.5 325 21.10 9.175 99.50 5 5 20 5
#> Toyota Corona 107.5 20 600.5 485 18.50 12.325 100.05 5 0 15 5
#> Dodge Challenger 77.5 40 1590.0 750 13.80 17.600 84.35 0 0 15 10
#> AMC Javelin 76.0 40 1520.0 750 15.75 17.175 86.50 0 0 15 10
#> Camaro Z28 66.5 40 1750.0 1225 18.65 19.200 77.05 0 0 15 20
#> Pontiac Firebird 96.0 40 2000.0 875 15.40 19.225 85.25 0 0 15 10
#> Fiat X1-9 136.5 20 395.0 330 20.40 9.675 94.50 5 5 20 5
#> Porsche 914-2 130.0 20 601.5 455 22.15 10.700 83.50 0 5 25 10
#> Lotus Europa 152.0 20 475.5 565 18.85 7.565 84.50 5 5 25 10
#> Ford Pantera L 79.0 40 1755.0 1320 21.10 15.850 72.50 0 5 25 20
#> Ferrari Dino 98.5 30 725.0 875 18.10 13.850 77.50 0 5 25 30
#> Maserati Bora 75.0 40 1505.0 1675 17.70 17.850 73.00 0 5 25 40
#> Volvo 142E 107.0 20 605.0 545 20.55 13.900 93.00 5 5 20 10
mtcars %c*% mtcars # Significantly faster than mtcars * mtcars
#> mpg cyl disp hp drat wt qsec vs
#> Mazda RX4 441.00 36 25600.00 12100 15.2100 6.864400 270.9316 0
#> Mazda RX4 Wag 441.00 36 25600.00 12100 15.2100 8.265625 289.6804 0
#> Datsun 710 519.84 16 11664.00 8649 14.8225 5.382400 346.3321 1
#> Hornet 4 Drive 457.96 36 66564.00 12100 9.4864 10.336225 377.9136 1
#> Hornet Sportabout 349.69 64 129600.00 30625 9.9225 11.833600 289.6804 0
#> Valiant 327.61 36 50625.00 11025 7.6176 11.971600 408.8484 1
#> Duster 360 204.49 64 129600.00 60025 10.3041 12.744900 250.9056 0
#> Merc 240D 595.36 16 21520.89 3844 13.6161 10.176100 400.0000 1
#> Merc 230 519.84 16 19824.64 9025 15.3664 9.922500 524.4100 1
#> Merc 280 368.64 36 28089.76 15129 15.3664 11.833600 334.8900 1
#> Merc 280C 316.84 36 28089.76 15129 15.3664 11.833600 357.2100 1
#> Merc 450SE 268.96 64 76065.64 32400 9.4249 16.564900 302.7600 0
#> Merc 450SL 299.29 64 76065.64 32400 9.4249 13.912900 309.7600 0
#> Merc 450SLC 231.04 64 76065.64 32400 9.4249 14.288400 324.0000 0
#> Cadillac Fleetwood 108.16 64 222784.00 42025 8.5849 27.562500 323.2804 0
#> Lincoln Continental 108.16 64 211600.00 46225 9.0000 29.419776 317.5524 0
#> Chrysler Imperial 216.09 64 193600.00 52900 10.4329 28.569025 303.4564 0
#> Fiat 128 1049.76 16 6193.69 4356 16.6464 4.840000 379.0809 1
#> Honda Civic 924.16 16 5730.49 2704 24.3049 2.608225 342.9904 1
#> Toyota Corolla 1149.21 16 5055.21 4225 17.8084 3.367225 396.0100 1
#> Toyota Corona 462.25 16 14424.01 9409 13.6900 6.076225 400.4001 1
#> Dodge Challenger 240.25 64 101124.00 22500 7.6176 12.390400 284.5969 0
#> AMC Javelin 231.04 64 92416.00 22500 9.9225 11.799225 299.2900 0
#> Camaro Z28 176.89 64 122500.00 60025 13.9129 14.745600 237.4681 0
#> Pontiac Firebird 368.64 64 160000.00 30625 9.4864 14.784025 290.7025 0
#> Fiat X1-9 745.29 16 6241.00 4356 16.6464 3.744225 357.2100 1
#> Porsche 914-2 676.00 16 14472.09 8281 19.6249 4.579600 278.8900 0
#> Lotus Europa 924.16 16 9044.01 12769 14.2129 2.289169 285.6100 1
#> Ford Pantera L 249.64 64 123201.00 69696 17.8084 10.048900 210.2500 0
#> Ferrari Dino 388.09 36 21025.00 30625 13.1044 7.672900 240.2500 0
#> Maserati Bora 225.00 64 90601.00 112225 12.5316 12.744900 213.1600 0
#> Volvo 142E 457.96 16 14641.00 11881 16.8921 7.728400 345.9600 1
#> am gear carb
#> Mazda RX4 1 16 16
#> Mazda RX4 Wag 1 16 16
#> Datsun 710 1 16 1
#> Hornet 4 Drive 0 9 1
#> Hornet Sportabout 0 9 4
#> Valiant 0 9 1
#> Duster 360 0 9 16
#> Merc 240D 0 16 4
#> Merc 230 0 16 4
#> Merc 280 0 16 16
#> Merc 280C 0 16 16
#> Merc 450SE 0 9 9
#> Merc 450SL 0 9 9
#> Merc 450SLC 0 9 9
#> Cadillac Fleetwood 0 9 16
#> Lincoln Continental 0 9 16
#> Chrysler Imperial 0 9 16
#> Fiat 128 1 16 1
#> Honda Civic 1 16 4
#> Toyota Corolla 1 16 1
#> Toyota Corona 0 9 1
#> Dodge Challenger 0 9 4
#> AMC Javelin 0 9 4
#> Camaro Z28 0 9 16
#> Pontiac Firebird 0 9 4
#> Fiat X1-9 1 16 1
#> Porsche 914-2 1 25 4
#> Lotus Europa 1 25 4
#> Ford Pantera L 1 25 16
#> Ferrari Dino 1 25 36
#> Maserati Bora 1 25 64
#> Volvo 142E 1 16 4
## Using matrices
X <- qM(mtcars)
X %cr% v
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 6 6 6 6 6 6 6 6 6 6 6
#> Mazda RX4 Wag 6 6 6 6 6 6 6 6 6 6 6
#> Datsun 710 4 4 4 4 4 4 4 4 4 4 4
#> Hornet 4 Drive 6 6 6 6 6 6 6 6 6 6 6
#> Hornet Sportabout 8 8 8 8 8 8 8 8 8 8 8
#> Valiant 6 6 6 6 6 6 6 6 6 6 6
#> Duster 360 8 8 8 8 8 8 8 8 8 8 8
#> Merc 240D 4 4 4 4 4 4 4 4 4 4 4
#> Merc 230 4 4 4 4 4 4 4 4 4 4 4
#> Merc 280 6 6 6 6 6 6 6 6 6 6 6
#> Merc 280C 6 6 6 6 6 6 6 6 6 6 6
#> Merc 450SE 8 8 8 8 8 8 8 8 8 8 8
#> Merc 450SL 8 8 8 8 8 8 8 8 8 8 8
#> Merc 450SLC 8 8 8 8 8 8 8 8 8 8 8
#> Cadillac Fleetwood 8 8 8 8 8 8 8 8 8 8 8
#> Lincoln Continental 8 8 8 8 8 8 8 8 8 8 8
#> Chrysler Imperial 8 8 8 8 8 8 8 8 8 8 8
#> Fiat 128 4 4 4 4 4 4 4 4 4 4 4
#> Honda Civic 4 4 4 4 4 4 4 4 4 4 4
#> Toyota Corolla 4 4 4 4 4 4 4 4 4 4 4
#> Toyota Corona 4 4 4 4 4 4 4 4 4 4 4
#> Dodge Challenger 8 8 8 8 8 8 8 8 8 8 8
#> AMC Javelin 8 8 8 8 8 8 8 8 8 8 8
#> Camaro Z28 8 8 8 8 8 8 8 8 8 8 8
#> Pontiac Firebird 8 8 8 8 8 8 8 8 8 8 8
#> Fiat X1-9 4 4 4 4 4 4 4 4 4 4 4
#> Porsche 914-2 4 4 4 4 4 4 4 4 4 4 4
#> Lotus Europa 4 4 4 4 4 4 4 4 4 4 4
#> Ford Pantera L 8 8 8 8 8 8 8 8 8 8 8
#> Ferrari Dino 6 6 6 6 6 6 6 6 6 6 6
#> Maserati Bora 8 8 8 8 8 8 8 8 8 8 8
#> Volvo 142E 4 4 4 4 4 4 4 4 4 4 4
X %c-% v
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 15.0 0 154.0 104 -2.10 -3.380 10.46 -6 -5 -2 -2
#> Mazda RX4 Wag 15.0 0 154.0 104 -2.10 -3.125 11.02 -6 -5 -2 -2
#> Datsun 710 18.8 0 104.0 89 -0.15 -1.680 14.61 -3 -3 0 -3
#> Hornet 4 Drive 15.4 0 252.0 104 -2.92 -2.785 13.44 -5 -6 -3 -5
#> Hornet Sportabout 10.7 0 352.0 167 -4.85 -4.560 9.02 -8 -8 -5 -6
#> Valiant 12.1 0 219.0 99 -3.24 -2.540 14.22 -5 -6 -3 -5
#> Duster 360 6.3 0 352.0 237 -4.79 -4.430 7.84 -8 -8 -5 -4
#> Merc 240D 20.4 0 142.7 58 -0.31 -0.810 16.00 -3 -4 0 -2
#> Merc 230 18.8 0 136.8 91 -0.08 -0.850 18.90 -3 -4 0 -2
#> Merc 280 13.2 0 161.6 117 -2.08 -2.560 12.30 -5 -6 -2 -2
#> Merc 280C 11.8 0 161.6 117 -2.08 -2.560 12.90 -5 -6 -2 -2
#> Merc 450SE 8.4 0 267.8 172 -4.93 -3.930 9.40 -8 -8 -5 -5
#> Merc 450SL 9.3 0 267.8 172 -4.93 -4.270 9.60 -8 -8 -5 -5
#> Merc 450SLC 7.2 0 267.8 172 -4.93 -4.220 10.00 -8 -8 -5 -5
#> Cadillac Fleetwood 2.4 0 464.0 197 -5.07 -2.750 9.98 -8 -8 -5 -4
#> Lincoln Continental 2.4 0 452.0 207 -5.00 -2.576 9.82 -8 -8 -5 -4
#> Chrysler Imperial 6.7 0 432.0 222 -4.77 -2.655 9.42 -8 -8 -5 -4
#> Fiat 128 28.4 0 74.7 62 0.08 -1.800 15.47 -3 -3 0 -3
#> Honda Civic 26.4 0 71.7 48 0.93 -2.385 14.52 -3 -3 0 -2
#> Toyota Corolla 29.9 0 67.1 61 0.22 -2.165 15.90 -3 -3 0 -3
#> Toyota Corona 17.5 0 116.1 93 -0.30 -1.535 16.01 -3 -4 -1 -3
#> Dodge Challenger 7.5 0 310.0 142 -5.24 -4.480 8.87 -8 -8 -5 -6
#> AMC Javelin 7.2 0 296.0 142 -4.85 -4.565 9.30 -8 -8 -5 -6
#> Camaro Z28 5.3 0 342.0 237 -4.27 -4.160 7.41 -8 -8 -5 -4
#> Pontiac Firebird 11.2 0 392.0 167 -4.92 -4.155 9.05 -8 -8 -5 -6
#> Fiat X1-9 23.3 0 75.0 62 0.08 -2.065 14.90 -3 -3 0 -3
#> Porsche 914-2 22.0 0 116.3 87 0.43 -1.860 12.70 -4 -3 1 -2
#> Lotus Europa 26.4 0 91.1 109 -0.23 -2.487 12.90 -3 -3 1 -2
#> Ford Pantera L 7.8 0 343.0 256 -3.78 -4.830 6.50 -8 -7 -3 -4
#> Ferrari Dino 13.7 0 139.0 169 -2.38 -3.230 9.50 -6 -5 -1 0
#> Maserati Bora 7.0 0 293.0 327 -4.46 -4.430 6.60 -8 -7 -3 0
#> Volvo 142E 17.4 0 117.0 105 0.11 -1.220 14.60 -3 -3 0 -2
X %r-% dapply(X, quantile, 0.28)
#> mpg cyl disp hp drat wt qsec vs am gear
#> Mazda RX4 5.296 2 25.536 7.56 0.7724 -0.102 -0.5216 0 1 1
#> Mazda RX4 Wag 5.296 2 25.536 7.56 0.7724 0.153 0.0384 0 1 1
#> Datsun 710 7.096 0 -26.464 -9.44 0.7224 -0.402 1.6284 1 1 1
#> Hornet 4 Drive 5.696 2 123.536 7.56 -0.0476 0.493 2.4584 1 0 0
#> Hornet Sportabout 2.996 4 225.536 72.56 0.0224 0.718 0.0384 0 0 0
#> Valiant 2.396 2 90.536 2.56 -0.3676 0.738 3.2384 1 0 0
#> Duster 360 -1.404 4 225.536 142.56 0.0824 0.848 -1.1416 0 0 0
#> Merc 240D 8.696 0 12.236 -40.44 0.5624 0.468 3.0184 1 0 1
#> Merc 230 7.096 0 6.336 -7.44 0.7924 0.428 5.9184 1 0 1
#> Merc 280 3.496 2 33.136 20.56 0.7924 0.718 1.3184 1 0 1
#> Merc 280C 2.096 2 33.136 20.56 0.7924 0.718 1.9184 1 0 1
#> Merc 450SE 0.696 4 141.336 77.56 -0.0576 1.348 0.4184 0 0 0
#> Merc 450SL 1.596 4 141.336 77.56 -0.0576 1.008 0.6184 0 0 0
#> Merc 450SLC -0.504 4 141.336 77.56 -0.0576 1.058 1.0184 0 0 0
#> Cadillac Fleetwood -5.304 4 337.536 102.56 -0.1976 2.528 0.9984 0 0 0
#> Lincoln Continental -5.304 4 325.536 112.56 -0.1276 2.702 0.8384 0 0 0
#> Chrysler Imperial -1.004 4 305.536 127.56 0.1024 2.623 0.4384 0 0 0
#> Fiat 128 16.696 0 -55.764 -36.44 0.9524 -0.522 2.4884 1 1 1
#> Honda Civic 14.696 0 -58.764 -50.44 1.8024 -1.107 1.5384 1 1 1
#> Toyota Corolla 18.196 0 -63.364 -37.44 1.0924 -0.887 2.9184 1 1 1
#> Toyota Corona 5.796 0 -14.364 -5.44 0.5724 -0.257 3.0284 1 0 0
#> Dodge Challenger -0.204 4 183.536 47.56 -0.3676 0.798 -0.1116 0 0 0
#> AMC Javelin -0.504 4 169.536 47.56 0.0224 0.713 0.3184 0 0 0
#> Camaro Z28 -2.404 4 215.536 142.56 0.6024 1.118 -1.5716 0 0 0
#> Pontiac Firebird 3.496 4 265.536 72.56 -0.0476 1.123 0.0684 0 0 0
#> Fiat X1-9 11.596 0 -55.464 -36.44 0.9524 -0.787 1.9184 1 1 1
#> Porsche 914-2 10.296 0 -14.164 -11.44 1.3024 -0.582 -0.2816 0 1 2
#> Lotus Europa 14.696 0 -39.364 10.56 0.6424 -1.209 -0.0816 1 1 2
#> Ford Pantera L 0.096 4 216.536 161.56 1.0924 0.448 -2.4816 0 1 2
#> Ferrari Dino 3.996 2 10.536 72.56 0.4924 0.048 -1.4816 0 1 2
#> Maserati Bora -0.704 4 166.536 232.56 0.4124 0.848 -2.3816 0 1 2
#> Volvo 142E 5.696 0 -13.464 6.56 0.9824 0.058 1.6184 1 1 1
#> carb
#> Mazda RX4 2
#> Mazda RX4 Wag 2
#> Datsun 710 -1
#> Hornet 4 Drive -1
#> Hornet Sportabout 0
#> Valiant -1
#> Duster 360 2
#> Merc 240D 0
#> Merc 230 0
#> Merc 280 2
#> Merc 280C 2
#> Merc 450SE 1
#> Merc 450SL 1
#> Merc 450SLC 1
#> Cadillac Fleetwood 2
#> Lincoln Continental 2
#> Chrysler Imperial 2
#> Fiat 128 -1
#> Honda Civic 0
#> Toyota Corolla -1
#> Toyota Corona -1
#> Dodge Challenger 0
#> AMC Javelin 0
#> Camaro Z28 2
#> Pontiac Firebird 0
#> Fiat X1-9 -1
#> Porsche 914-2 0
#> Lotus Europa 0
#> Ford Pantera L 2
#> Ferrari Dino 4
#> Maserati Bora 6
#> Volvo 142E 0
## Chained Operations
library(magrittr) # Needed here to evaluate infix operators in sequence
mtcars %>% fwithin() %r-% rnorm(11) %c*% 5 %>%
tfm(mpg = fsum(mpg)) %>% qsu()
#> N Mean SD Min Max
#> mpg 32 182.082 0 182.082 182.082
#> cyl 32 2.7901 8.9296 -8.1474 11.8526
#> disp 32 -5.2627 619.6935 -803.3721 1201.1279
#> hp 32 -3.3884 342.8143 -476.8259 938.1741
#> drat 32 -0.1925 2.6734 -4.3753 6.4747
#> wt 32 1.7819 4.8923 -6.7393 12.8157
#> qsec 32 -3.9142 8.9347 -20.658 21.342
#> vs 32 -4.0221 2.5201 -6.2096 -1.2096
#> am 32 9.5003 2.495 7.4691 12.4691
#> gear 32 -4.6789 3.689 -8.1164 1.8836
#> carb 32 1.5453 8.076 -7.5172 27.4828