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 # Replace rows of X with v
X %r+% v # Add v to each row of X
X %r-% v # Subtract v from each row of X
X %r*% v # Multiply each row of X with v
X %r/% v # Divide each row of X by v
## Perform a column-wise operation between V and X
X %cr% V # Replace columns of X with V
X %c+% V # Add V to columns of X
X %c-% V # Subtract V from columns of X
X %c*% V # Multiply columns of X with V
X %c/% V # Divide columns of X by 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
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
mtcars %c-% v
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 15.0 0 154 104 -2.10 -3.380 10.46 -6 -5 -2 -2
#> Mazda RX4 Wag 15.0 0 154 104 -2.10 -3.125 11.02 -6 -5 -2 -2
#> Datsun 710 18.8 0 104 89 -0.15 -1.680 14.61 -3 -3 0 -3
#> Hornet 4 Drive 15.4 0 252 104 -2.92 -2.785 13.44 -5 -6 -3 -5
#> Hornet Sportabout 10.7 0 352 167 -4.85 -4.560 9.02 -8 -8 -5 -6
#> Valiant 12.1 0 219 99 -3.24 -2.540 14.22 -5 -6 -3 -5
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
mtcars %r-% seq_col(mtcars)
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 20.0 4 157 106 -1.10 -3.380 9.46 -8 -8 -6 -7
#> Mazda RX4 Wag 20.0 4 157 106 -1.10 -3.125 10.02 -8 -8 -6 -7
#> Datsun 710 21.8 2 105 89 -1.15 -3.680 11.61 -7 -8 -6 -10
#> Hornet 4 Drive 20.4 4 255 106 -1.92 -2.785 12.44 -7 -9 -7 -10
#> Hornet Sportabout 17.7 6 357 171 -1.85 -2.560 10.02 -8 -9 -7 -9
#> Valiant 17.1 4 222 101 -2.24 -2.540 13.22 -7 -9 -7 -10
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
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
#> carb
#> Mazda RX4 2
#> Mazda RX4 Wag 2
#> Datsun 710 -1
#> Hornet 4 Drive -1
#> Hornet Sportabout 0
#> Valiant -1
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
mtcars %c*% 5 # Significantly faster than mtcars * 5
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> Mazda RX4 105.0 30 800 550 19.50 13.100 82.30 0 5 20 20
#> Mazda RX4 Wag 105.0 30 800 550 19.50 14.375 85.10 0 5 20 20
#> Datsun 710 114.0 20 540 465 19.25 11.600 93.05 5 5 20 5
#> Hornet 4 Drive 107.0 30 1290 550 15.40 16.075 97.20 5 0 15 5
#> Hornet Sportabout 93.5 40 1800 875 15.75 17.200 85.10 0 0 15 10
#> Valiant 90.5 30 1125 525 13.80 17.300 101.10 5 0 15 5
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
mtcars %c*% mtcars # Significantly faster than mtcars * mtcars
#> mpg cyl disp hp drat wt qsec vs am gear
#> Mazda RX4 441.00 36 25600 12100 15.2100 6.864400 270.9316 0 1 16
#> Mazda RX4 Wag 441.00 36 25600 12100 15.2100 8.265625 289.6804 0 1 16
#> Datsun 710 519.84 16 11664 8649 14.8225 5.382400 346.3321 1 1 16
#> Hornet 4 Drive 457.96 36 66564 12100 9.4864 10.336225 377.9136 1 0 9
#> Hornet Sportabout 349.69 64 129600 30625 9.9225 11.833600 289.6804 0 0 9
#> Valiant 327.61 36 50625 11025 7.6176 11.971600 408.8484 1 0 9
#> carb
#> Mazda RX4 16
#> Mazda RX4 Wag 16
#> Datsun 710 1
#> Hornet 4 Drive 1
#> Hornet Sportabout 4
#> Valiant 1
#> [ reached 'max' / getOption("max.print") -- omitted 26 rows ]
## 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
#> [ reached getOption("max.print") -- omitted 26 rows ]
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
#> [ reached getOption("max.print") -- omitted 26 rows ]
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
#> carb
#> Mazda RX4 2
#> Mazda RX4 Wag 2
#> Datsun 710 -1
#> Hornet 4 Drive -1
#> Hornet Sportabout 0
#> Valiant -1
#> [ reached getOption("max.print") -- omitted 26 rows ]
## 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 -245.2386 0 -245.2386 -245.2386
#> cyl 32 -2.1457 8.9296 -13.0832 6.9168
#> disp 32 -0.6105 619.6935 -798.7199 1205.7801
#> hp 32 5.6901 342.8143 -467.7474 947.2526
#> drat 32 2.7901 2.6734 -1.3927 9.4573
#> wt 32 -5.2627 4.8923 -13.7839 5.7711
#> qsec 32 -3.3884 8.9347 -20.1322 21.8678
#> vs 32 -0.1925 2.5201 -2.38 2.62
#> am 32 1.7819 2.495 -0.2493 4.7507
#> gear 32 -3.9142 3.689 -7.3517 2.6483
#> carb 32 -4.0221 8.076 -13.0846 21.9154