`calculate`

```
library(lans2r)
library(dplyr)
library(knitr)
```

The `?calculate`

function is intended to make it easy and
efficient to calculate sets of derived quantities (e.g. ratios from
`13C`

and `12C`

data but also from
`15N12C`

and `14N12C`

data). It allows defining
exactly how the derived quantities should be calculated but also makes
it possible to calculate derived errors and how to go about naming the
newly derived quantities. Due to its structure it allows for a large
amount of flexibility to cover all possible use cases. This vignettes
illustrates some basic examples how this may be used to calculate
derived quantities from measured ion currents. The functions
`?calculate_ratios`

, `?calculate_abundances`

,
`?calculate_sums`

are all pre-implemented examples of using
`calculate`

to achieve a specific task and work out of the
box without additional specifications as illustrated in the main
vignette.

For simple illustration, this is a completely contrived artifical data set:

```
set.seed(123) # set random seed
<-
test_data tibble(
ROI = rep(1:5, times = 4),
variable = rep(LETTERS[1:4], each = 5),
value = rpois(20,lambda = 10),
sigma = sqrt(value),
data_type = "raw"
)kable(test_data, d = 2)
```

ROI | variable | value | sigma | data_type |
---|---|---|---|---|

1 | A | 8 | 2.83 | raw |

2 | A | 9 | 3.00 | raw |

3 | A | 14 | 3.74 | raw |

4 | A | 10 | 3.16 | raw |

5 | A | 10 | 3.16 | raw |

1 | B | 15 | 3.87 | raw |

2 | B | 11 | 3.32 | raw |

3 | B | 5 | 2.24 | raw |

4 | B | 4 | 2.00 | raw |

5 | B | 13 | 3.61 | raw |

1 | C | 11 | 3.32 | raw |

2 | C | 11 | 3.32 | raw |

3 | C | 10 | 3.16 | raw |

4 | C | 8 | 2.83 | raw |

5 | C | 15 | 3.87 | raw |

1 | D | 11 | 3.32 | raw |

2 | D | 3 | 1.73 | raw |

3 | D | 7 | 2.65 | raw |

4 | D | 6 | 2.45 | raw |

5 | D | 8 | 2.83 | raw |

As a first example, using `calculate`

to calculate
different column products and propagate the error by standard error
propagation (assuming no covariance).

```
# functions to calculate values and errors and derive names from the names of the variables used
# note that they all have to take the same parameters (even if they are not used)
<- function(x, y, x.err, y.err) x*y
my_value_fun <- function(x, y, x.err, y.err) my_value_fun(x, y, x.err, y.err) * sqrt((x.err/x)^2 + (y.err/y)^2)
my_error_fun <- function(x, y, x.err, y.err) paste0(deparse(substitute(x)), "*", deparse(substitute(y)))
my_name_fun
<-
derived_data %>%
test_data calculate(
# data type of the derived quantities (can be anything descriptive)
data_type = "derived",
# which sets of variables to use for calculations
c(D, C, `D sigma`, `C sigma`), c(B, A, `B sigma`, `A sigma`), c(B, C, `B sigma`, `C sigma`),
# the function to make the calculations
value_fun = my_value_fun, error_fun = my_error_fun, name_fun = my_name_fun)
```

```
## INFO: 15 'derived' values + errors calculated, 15 added (subset: all)
## values added (stored in 'variable' column): 'B*A' (5x), 'B*C' (5x), 'D*C' (5x)
```

`kable(derived_data, d = 2)`

ROI | variable | value | sigma | data_type |
---|---|---|---|---|

1 | A | 8 | 2.83 | raw |

2 | A | 9 | 3.00 | raw |

3 | A | 14 | 3.74 | raw |

4 | A | 10 | 3.16 | raw |

5 | A | 10 | 3.16 | raw |

1 | B | 15 | 3.87 | raw |

2 | B | 11 | 3.32 | raw |

3 | B | 5 | 2.24 | raw |

4 | B | 4 | 2.00 | raw |

5 | B | 13 | 3.61 | raw |

1 | C | 11 | 3.32 | raw |

2 | C | 11 | 3.32 | raw |

3 | C | 10 | 3.16 | raw |

4 | C | 8 | 2.83 | raw |

5 | C | 15 | 3.87 | raw |

1 | D | 11 | 3.32 | raw |

2 | D | 3 | 1.73 | raw |

3 | D | 7 | 2.65 | raw |

4 | D | 6 | 2.45 | raw |

5 | D | 8 | 2.83 | raw |

1 | D*C | 121 | 51.59 | derived |

2 | D*C | 33 | 21.49 | derived |

3 | D*C | 70 | 34.50 | derived |

4 | D*C | 48 | 25.92 | derived |

5 | D*C | 120 | 52.54 | derived |

1 | B*A | 120 | 52.54 | derived |

2 | B*A | 99 | 44.50 | derived |

3 | B*A | 70 | 36.47 | derived |

4 | B*A | 40 | 23.66 | derived |

5 | B*A | 130 | 54.68 | derived |

1 | B*C | 165 | 65.50 | derived |

2 | B*C | 121 | 51.59 | derived |

3 | B*C | 50 | 27.39 | derived |

4 | B*C | 32 | 19.60 | derived |

5 | B*C | 195 | 73.89 | derived |

As a second example, build on the derived quantities to generate custom sums (again with standard error propagation):

```
<- function(x, y, x.err, y.err) x+y
my_value_fun <- function(x, y, x.err, y.err) sqrt(x.err^2 + y.err^2)
my_error_fun <- function(x, y, x.err, y.err) paste0(deparse(substitute(x)), "+", deparse(substitute(y)))
my_name_fun
<-
derived_data2 %>%
derived_data calculate(
# data type of the derived quantities (can be anything descriptive)
data_type = "derived2",
# which sets of variables to use for calculations
c(D, C, `D sigma`, `C sigma`), c(`B*A`, `C`, `B*A sigma`, `C sigma`),
# the function to make the calculations
value_fun = my_value_fun, error_fun = my_error_fun, name_fun = my_name_fun)
```

```
## INFO: 10 'derived2' values + errors calculated, 10 added (subset: all)
## values added (stored in 'variable' column): 'B*A+C' (5x), 'D+C' (5x)
```

`kable(derived_data2, d = 2)`

ROI | variable | value | sigma | data_type |
---|---|---|---|---|

1 | A | 8 | 2.83 | raw |

2 | A | 9 | 3.00 | raw |

3 | A | 14 | 3.74 | raw |

4 | A | 10 | 3.16 | raw |

5 | A | 10 | 3.16 | raw |

1 | B | 15 | 3.87 | raw |

2 | B | 11 | 3.32 | raw |

3 | B | 5 | 2.24 | raw |

4 | B | 4 | 2.00 | raw |

5 | B | 13 | 3.61 | raw |

1 | C | 11 | 3.32 | raw |

2 | C | 11 | 3.32 | raw |

3 | C | 10 | 3.16 | raw |

4 | C | 8 | 2.83 | raw |

5 | C | 15 | 3.87 | raw |

1 | D | 11 | 3.32 | raw |

2 | D | 3 | 1.73 | raw |

3 | D | 7 | 2.65 | raw |

4 | D | 6 | 2.45 | raw |

5 | D | 8 | 2.83 | raw |

1 | D*C | 121 | 51.59 | derived |

2 | D*C | 33 | 21.49 | derived |

3 | D*C | 70 | 34.50 | derived |

4 | D*C | 48 | 25.92 | derived |

5 | D*C | 120 | 52.54 | derived |

1 | B*A | 120 | 52.54 | derived |

2 | B*A | 99 | 44.50 | derived |

3 | B*A | 70 | 36.47 | derived |

4 | B*A | 40 | 23.66 | derived |

5 | B*A | 130 | 54.68 | derived |

1 | B*C | 165 | 65.50 | derived |

2 | B*C | 121 | 51.59 | derived |

3 | B*C | 50 | 27.39 | derived |

4 | B*C | 32 | 19.60 | derived |

5 | B*C | 195 | 73.89 | derived |

1 | D+C | 22 | 4.69 | derived2 |

2 | D+C | 14 | 3.74 | derived2 |

3 | D+C | 17 | 4.12 | derived2 |

4 | D+C | 14 | 3.74 | derived2 |

5 | D+C | 23 | 4.80 | derived2 |

1 | B*A+C | 131 | 52.64 | derived2 |

2 | B*A+C | 110 | 44.62 | derived2 |

3 | B*A+C | 80 | 36.61 | derived2 |

4 | B*A+C | 48 | 23.83 | derived2 |

5 | B*A+C | 145 | 54.82 | derived2 |

To calculate a derived quantity without calculating errors, simply
don’t supply an error function. Also illustrated here is a simple way to
provide specific variable names and defining the functions in line. Note
the use of `sum(x)`

as well, this can easily be used for
calculating normalized derived quantities.

```
<-
derived_data3 %>%
derived_data2 calculate(
# data type of the derived quantities (can be anything descriptive)
data_type = "special",
# which sets of variables to use for calculations
c("my_var", A, B, C),
# the function to make the calculations
value_fun = function(name, x, y, z) x+y^2+z^3/sum(x),
name_fun = function(name, x, y, z) name)
```

```
## INFO: 5 'special' values + errors calculated, 5 added (subset: all)
## values added (stored in 'variable' column): 'my_var' (5x)
```

`kable(derived_data3, d = 2)`

ROI | variable | value | sigma | data_type |
---|---|---|---|---|

1 | A | 8.00 | 2.83 | raw |

2 | A | 9.00 | 3.00 | raw |

3 | A | 14.00 | 3.74 | raw |

4 | A | 10.00 | 3.16 | raw |

5 | A | 10.00 | 3.16 | raw |

1 | B | 15.00 | 3.87 | raw |

2 | B | 11.00 | 3.32 | raw |

3 | B | 5.00 | 2.24 | raw |

4 | B | 4.00 | 2.00 | raw |

5 | B | 13.00 | 3.61 | raw |

1 | C | 11.00 | 3.32 | raw |

2 | C | 11.00 | 3.32 | raw |

3 | C | 10.00 | 3.16 | raw |

4 | C | 8.00 | 2.83 | raw |

5 | C | 15.00 | 3.87 | raw |

1 | D | 11.00 | 3.32 | raw |

2 | D | 3.00 | 1.73 | raw |

3 | D | 7.00 | 2.65 | raw |

4 | D | 6.00 | 2.45 | raw |

5 | D | 8.00 | 2.83 | raw |

1 | D*C | 121.00 | 51.59 | derived |

2 | D*C | 33.00 | 21.49 | derived |

3 | D*C | 70.00 | 34.50 | derived |

4 | D*C | 48.00 | 25.92 | derived |

5 | D*C | 120.00 | 52.54 | derived |

1 | B*A | 120.00 | 52.54 | derived |

2 | B*A | 99.00 | 44.50 | derived |

3 | B*A | 70.00 | 36.47 | derived |

4 | B*A | 40.00 | 23.66 | derived |

5 | B*A | 130.00 | 54.68 | derived |

1 | B*C | 165.00 | 65.50 | derived |

2 | B*C | 121.00 | 51.59 | derived |

3 | B*C | 50.00 | 27.39 | derived |

4 | B*C | 32.00 | 19.60 | derived |

5 | B*C | 195.00 | 73.89 | derived |

1 | D+C | 22.00 | 4.69 | derived2 |

2 | D+C | 14.00 | 3.74 | derived2 |

3 | D+C | 17.00 | 4.12 | derived2 |

4 | D+C | 14.00 | 3.74 | derived2 |

5 | D+C | 23.00 | 4.80 | derived2 |

1 | B*A+C | 131.00 | 52.64 | derived2 |

2 | B*A+C | 110.00 | 44.62 | derived2 |

3 | B*A+C | 80.00 | 36.61 | derived2 |

4 | B*A+C | 48.00 | 23.83 | derived2 |

5 | B*A+C | 145.00 | 54.82 | derived2 |

1 | my_var | 259.10 | NA | special |

2 | my_var | 156.10 | NA | special |

3 | my_var | 58.61 | NA | special |

4 | my_var | 36.04 | NA | special |

5 | my_var | 245.18 | NA | special |

This data format makes it easy to have arbitrarily elaborate derived quantities and dynamically include the same calculation for multiple sets of variables. It is also a format that lends itself very well to visualization:

```
library(ggplot2)
%>%
derived_data3 ggplot() +
aes(x = ROI, y = value, ymin = value-sigma, ymax = value+sigma, color = variable) +
geom_errorbar() +
geom_point() +
facet_wrap(~data_type, scales = "free")
```

Lastly, it can be very useful to have data converted to a wide format
with all variables and errors next to each other (e.g. for summary
tables or export to Excel). This is easily accomplished with
*lans2r*’s `spread_data`

function:

`%>% spread_data() %>% kable(d = 2) derived_data3 `

ROI | A | B | B*A | B*A+C | B*C | C | D | D*C | D+C | my_var | A sigma | B sigma | B*A sigma | B*A+C sigma | B*C sigma | C sigma | D sigma | D*C sigma | D+C sigma | my_var sigma |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 8 | 15 | 120 | 131 | 165 | 11 | 11 | 121 | 22 | 259.10 | 2.83 | 3.87 | 52.54 | 52.64 | 65.50 | 3.32 | 3.32 | 51.59 | 4.69 | NA |

2 | 9 | 11 | 99 | 110 | 121 | 11 | 3 | 33 | 14 | 156.10 | 3.00 | 3.32 | 44.50 | 44.62 | 51.59 | 3.32 | 1.73 | 21.49 | 3.74 | NA |

3 | 14 | 5 | 70 | 80 | 50 | 10 | 7 | 70 | 17 | 58.61 | 3.74 | 2.24 | 36.47 | 36.61 | 27.39 | 3.16 | 2.65 | 34.50 | 4.12 | NA |

4 | 10 | 4 | 40 | 48 | 32 | 8 | 6 | 48 | 14 | 36.04 | 3.16 | 2.00 | 23.66 | 23.83 | 19.60 | 2.83 | 2.45 | 25.92 | 3.74 | NA |

5 | 10 | 13 | 130 | 145 | 195 | 15 | 8 | 120 | 23 | 245.18 | 3.16 | 3.61 | 54.68 | 54.82 | 73.89 | 3.87 | 2.83 | 52.54 | 4.80 | NA |

`%>% spread_data(errors = FALSE) %>% kable(d = 2) derived_data3 `

ROI | A | B | B*A | B*A+C | B*C | C | D | D*C | D+C | my_var |
---|---|---|---|---|---|---|---|---|---|---|

1 | 8 | 15 | 120 | 131 | 165 | 11 | 11 | 121 | 22 | 259.10 |

2 | 9 | 11 | 99 | 110 | 121 | 11 | 3 | 33 | 14 | 156.10 |

3 | 14 | 5 | 70 | 80 | 50 | 10 | 7 | 70 | 17 | 58.61 |

4 | 10 | 4 | 40 | 48 | 32 | 8 | 6 | 48 | 14 | 36.04 |

5 | 10 | 13 | 130 | 145 | 195 | 15 | 8 | 120 | 23 | 245.18 |