Philipp Baumann // [email protected] July 25, 2018
- Getting started
- Reading spectra from OPUS spectrometer files: prerequisites
- Reading spectrometer data into the R environment
- Session info
For a html version of this tutorial, see here. You can also download this tutorial as pdf.
- First, you need to be familar how to work into R. Here I give some recommendations to start mastering spectroscopy analysis tasks.
- You need to need to now that there are R basic data structures used for analysis. Have a first read here in the Advanced R book of Hadley Wickham.
-
You will learn how to use different R base data structures and basic operations such as subsetting to explore and transform spectral data.
-
This hands-on tutorial teaches you the technical skills how to work with data structures in R by the example of manipulating spectral data.
- Use the
Clone or Downloadbutton and clone/download this tutorial repository from github to your computer. - Unzip the folder.
- Double-click the
.RProjfile and the tutorial is loaded as R project (no need to usesetwd()andpath = "yourverylonganduniquedirectoryonyourpc"or other nasty hard-coded approaches to set the working directory, which makes your projects not reproducible for others; kindly follow these instructions to learn how to work with RStudio self-contained projects. - For working with this R markdown notebooks for reproducible and interactive analysis, see here.
- Have fun reproducing.
Spectroscopy modeling requires that we first organize our spectra well. In particular, a proper and reproducible data management of spectral data, metadata, and data from reference chemical analyses is key for all the subsequent data processing and modeling workflow.
The Sustainable Agroecosystems group at ETH relies on Diffuse Reflectance Fourier Transform (DRIFT) infrared spectrometers manufactured by the company Bruker (see Figure ). The manufacturer relies on a proprietary binary format called OPUS to store an extensive amount of data that includes different types of intermediary spectra. For each sample that was measured a single OPUS file is produced.
First, we load the set of packages of tidyverse (see here for details) and the simplerspec package (see here). Simplerspec contains a universal file reader that allows to read selected parameters (e.g. instrument, optic and acquisition parameters) and all types of spectra from a single OPUS binary file or a list of files.
# Load collection of packages that work together seamlessly for efficient
# analysis workflows
library("tidyverse")## ── Attaching packages ─────────────────────────────────────────────── tidyverse 1.2.1 ──
## âś” ggplot2 3.0.0 âś” purrr 0.2.5
## âś” tibble 1.4.2 âś” dplyr 0.7.6
## âś” tidyr 0.8.1 âś” stringr 1.3.1
## âś” readr 1.1.1 âś” forcats 0.3.0
## ── Conflicts ────────────────────────────────────────────────── tidyverse_conflicts() ──
## âś– dplyr::filter() masks stats::filter()
## âś– dplyr::lag() masks stats::lag()
# Package that facilitates spectral data handling, processing and modeling
library("simplerspec")## Loading required package: foreach
##
## Attaching package: 'foreach'
## The following objects are masked from 'package:purrr':
##
## accumulate, when
I recommended that you set up a self-contained directory where all R scripts, data (spectra and chemical reference data), models, outputs (figures and text files of data and model summaries), and predictions live. Further, you can use the folder structure depicted in figure to organize your spectroscopy-related research projects.
When you have spectra that cover separate experiments and/or different locations and times, you might prefer to organize your spectra as sub-folders within data/spectra. This hands-on is based on spectral data that were used to build and evaluate the YAMSYS spectroscopy reference models. Besides these reference spectra measured with a Bruker ALPHA mid-IR spectrometer at the Sustainable Agroecosystems group at ETH ZĂĽrich, there are other spectra that have been acquired to test different questions such as spectrometer cross-comparisons. Therefore, other comparison spectra are in separate paths, e.g. data/spectra/soilspec_eth_bin.
In the Figure below you can see a file explorer screenshot showing OPUS files of three replicate scans for each of the first three reference soil samples. OPUS have the extension .n where n represents an integer of repeated sample measurements starting from 0.
We aim to read all the reference spectra contained within this folder. First, we get the full path names of the file names, which we subsequently assign to the object files:
# Extract data from OPUS binary files; list of file paths
files <- list.files("data/spectra", full.names = TRUE)Note that you need to set the full.names argument to TRUE (default is FALSE to get the path of all OPUS spectra files contained within the target directory, otherwise R will not be able to find the files when using the universal simplerspec OPUS reader.
You can compactly display the internal structure of the files object:
str(files)## chr [1:284] "data/spectra/BF_lo_01_soil_cal.0" ...
The object files has the data structure atomic vector. Atomic vectors have six possible basic (atomic) vector types. These are logical, integer, real, complex, string (or character) and raw. Vector types can be returned by the R base function typeof(x), which returns the type or internal storage mode an object x. For the files object it is
# Check type of files object
typeof(files)## [1] "character"
We get the length of the vector or the number of elements by
# How many files are listed to read? length of vector
length(files)## [1] 284
Base R has subsetting operations that allow you to extract pieces of data structures you are interested in. One of the three base subsetting operators is [.
We subset the character vector files as follows:
# Use character subsetting to return the first element
# Subsetting can be seen as complement to str()
# (1) Subsetting with positive integers (position)
files[1:3]## [1] "data/spectra/BF_lo_01_soil_cal.0" "data/spectra/BF_lo_01_soil_cal.1"
## [3] "data/spectra/BF_lo_01_soil_cal.2"
# (2) Subsetting with negative integers (remove values)
head(files[-c(1:3)], n = 5L) # show only first 5 values## [1] "data/spectra/BF_lo_02_soil_cal.0" "data/spectra/BF_lo_02_soil_cal.1"
## [3] "data/spectra/BF_lo_02_soil_cal.2" "data/spectra/BF_lo_03_soil_cal.0"
## [5] "data/spectra/BF_lo_03_soil_cal.1"
# The first three elements of the character vector are removedBruker FTIR spectrometers produce binary files in the OPUS format that can contain different types of spectra and many parameters such as instrument type and settings that were used at the time of data acquisition and internal processing (e.g. Fourier transform operations). Basically, the entire set of Setup Measurement Parameters, selected spectra, supplementary metadata such as the time of measurement are written into OPUS binary files. In contrast to simple text files that contain only plain text with a defined character encoding, binary files can contain any type of data represented as sequences of bytes (a single byte is sequence of 8 bits and 1 bit either represents 0 or 1).
Figure shows graphical representation from the OPUS viewer software to get familiarize with types of parameters OPUS files may contain.
You can download the OPUS viewer software from this Bruker webpage for free. However, Bruker only provides a Windows version and the free version is limited to visualize only final spectra. The remaining spectral blocks can be checked choosing the menu Window > New Report Window and opening OPUS by the menu File > Load File.
The types of spectra and associated data parameters that are saved after a single measurement depend on the options that are selected in the OPUS software. For data acquisition, the values under the tab Advanced of the Setup Measurement Parameters menu window in the OPUS software.
Depending on the standard of a binary file, different regions in a file can be interpreted differently by a program. For example, some information at some block positions need to be interpreted as a certain type of number representation whereas others are text. Hence, the interpretation of different bit positions in the file requires either a priori knowledge provided by some file specifications or extensive reverse-engineering.
Instead of sharing the full binary file specification, Bruker ships the OPUS macro programming language or Microsoft Visual Basic scripts for automated data acquisition and processing. However, this approaches are very inflexible and not transparent, and therefore not reproducible. Hence, the idea of implementing a file reader that is integrated in the R statistical programming environment was targeted first in the soil.spec R package created by Andrew Sila (ICRAF, Nairobi), Tomislav Hengl (ISRIC -- World Soil Information) and Thomas Terhoeven-Urselmans (former member of ICRAF, Nairobi). soil.spec was created based on the African Soil Information Services (AfSIS) project (see here for more information). Because this reader worked only when applying a restricted set of settings and procedures in OPUS, the idea came up to modify and extend the previously mentioned soil.spec::read.opus() function. This restriction is mainly due to the fact that positions where spectra occur are not fixed and there is no evident accessible information about the sequence of spectra and data parameters and the type of present spectra. Therefore, I have been working extensively on a universal Bruker OPUS format file reader that can correctly assign and read out different spectra types from any type of Bruker FTIR spectrometer with different blocks saved and with and without atmospheric compensation.
Simplerspec comes with reader function written in R, that is intended to be a universal Bruker OPUS file reader that extract spectra and key metadata from files. Usually, one is mostly interested to extract the final absorbance spectra (shown as AB in the OPUS viewer software).
## Register parallel backend for using multiple cores
# Allows to tune the models using parallel processing (e.g. use all available
# cores of a CPU); caret package automatically detects the registered backend
library("doParallel")
# Make a cluster with all possible threads (more than physical cores)
cl <- makeCluster(detectCores())
# Register backend
registerDoParallel(cl)
# Return number of parallel workers
getDoParWorkers() # 8 threads on MacBook Pro (Retina, 15-inch, Mid 2015);## [1] 8
# Quadcore processor
# Read spectra and metadata of all binary OPUS files into a list
spc_list <- read_opus_univ(fnames = files, extract = c("spc"), parallel = TRUE)The extracted spectra and metadata data are within a list. A list is a very flexible R data structure that can contain any other type of R objects. You can think of lists as containers that help to save and transform objects. Lists can contain hierarchically nested elements, e.g. a list can contain lists. In this case, the list contains the following elements:
# Return the names of a list; names() returns a character vector
# of the elemelement names and `[` extracts the first 10 names
names(spc_list)[1:10]## [1] "BF_lo_01_soil_cal.0" "BF_lo_01_soil_cal.1" "BF_lo_01_soil_cal.2"
## [4] "BF_lo_02_soil_cal.0" "BF_lo_02_soil_cal.1" "BF_lo_02_soil_cal.2"
## [7] "BF_lo_03_soil_cal.0" "BF_lo_03_soil_cal.1" "BF_lo_03_soil_cal.2"
## [10] "BF_lo_04_soil_cal.0"
# The names from the spectral data list are identical to the
# files that were read (file names without path of folder where data
# are contained)
files[1:10]## [1] "data/spectra/BF_lo_01_soil_cal.0" "data/spectra/BF_lo_01_soil_cal.1"
## [3] "data/spectra/BF_lo_01_soil_cal.2" "data/spectra/BF_lo_02_soil_cal.0"
## [5] "data/spectra/BF_lo_02_soil_cal.1" "data/spectra/BF_lo_02_soil_cal.2"
## [7] "data/spectra/BF_lo_03_soil_cal.0" "data/spectra/BF_lo_03_soil_cal.1"
## [9] "data/spectra/BF_lo_03_soil_cal.2" "data/spectra/BF_lo_04_soil_cal.0"
List subsetting/extraction of components: Lists can be subsetted similar to atomic vectors by the [ and [[ operators. The most important difference is that [ returns a list (sub-list of list) and [[ returns the content of a single component of the list (note that a single components can still contain sub-lists). Based on the [ operator we can extract spectra and metadata from a single replicate measurement of a sample:
# Display structure
str(spc_list["BF_lo_01_soil_cal.0"])## List of 1
## $ BF_lo_01_soil_cal.0:List of 10
## ..$ metadata :Classes 'tbl_df', 'tbl' and 'data.frame': 1 obs. of 20 variables:
## .. ..$ unique_id : chr "BF_lo_01_soil_cal.0_2015-11-06 14:34:10"
## .. ..$ file_id : chr "BF_lo_01_soil_cal.0"
## .. ..$ sample_id : chr "BF_lo_01_soil_cal"
## .. ..$ rep_no : num 0
## .. ..$ date_time_sm : POSIXct[1:1], format: "2015-11-06 14:34:10"
## .. ..$ date_time_rf : POSIXct[1:1], format: "2015-11-06 14:30:10"
## .. ..$ sample_name : chr "BF_lo_01_soil_cal"
## .. ..$ instr_name_range: chr "alpha-mir"
## .. ..$ resolution_wn : int 4
## .. ..$ result_spc : chr "AB"
## .. ..$ beamspl : chr "ZnS"
## .. ..$ laser_wn : num 11602
## .. ..$ spc_in_file : chr "ScSm;ScRf;spc_nocomp;spc"
## .. ..$ zero_filling : int 2
## .. ..$ temp_scanner_sm : num 33.7
## .. ..$ temp_scanner_rf : num 33.6
## .. ..$ hum_rel_sm : int 25
## .. ..$ hum_rel_rf : int 25
## .. ..$ hum_abs_sm : num 9.5
## .. ..$ hum_abs_rf : num 9.49
## ..$ spc :Classes 'data.table' and 'data.frame': 1 obs. of 1716 variables:
## .. ..$ 3997.4: num 0.112
## .. ..$ 3995.4: num 0.111
## .. ..$ 3993.3: num 0.11
## .. ..$ 3991.3: num 0.111
## .. ..$ 3989.2: num 0.111
## .. ..$ 3987.2: num 0.112
## .. ..$ 3985.2: num 0.112
## .. ..$ 3983.1: num 0.112
## .. ..$ 3981.1: num 0.111
## .. ..$ 3979 : num 0.111
## .. ..$ 3977 : num 0.111
## .. ..$ 3975 : num 0.11
## .. ..$ 3972.9: num 0.109
## .. ..$ 3970.9: num 0.109
## .. ..$ 3968.8: num 0.11
## .. ..$ 3966.8: num 0.111
## .. ..$ 3964.8: num 0.111
## .. ..$ 3962.7: num 0.111
## .. ..$ 3960.7: num 0.111
## .. ..$ 3958.6: num 0.11
## .. ..$ 3956.6: num 0.11
## .. ..$ 3954.6: num 0.109
## .. ..$ 3952.5: num 0.108
## .. ..$ 3950.5: num 0.107
## .. ..$ 3948.4: num 0.107
## .. ..$ 3946.4: num 0.106
## .. ..$ 3944.4: num 0.106
## .. ..$ 3942.3: num 0.108
## .. ..$ 3940.3: num 0.108
## .. ..$ 3938.3: num 0.11
## .. ..$ 3936.2: num 0.11
## .. ..$ 3934.2: num 0.109
## .. ..$ 3932.1: num 0.107
## .. ..$ 3930.1: num 0.103
## .. ..$ 3928.1: num 0.102
## .. ..$ 3926 : num 0.104
## .. ..$ 3924 : num 0.104
## .. ..$ 3921.9: num 0.104
## .. ..$ 3919.9: num 0.106
## .. ..$ 3917.9: num 0.108
## .. ..$ 3915.8: num 0.109
## .. ..$ 3913.8: num 0.11
## .. ..$ 3911.7: num 0.113
## .. ..$ 3909.7: num 0.112
## .. ..$ 3907.7: num 0.107
## .. ..$ 3905.6: num 0.102
## .. ..$ 3903.6: num 0.0946
## .. ..$ 3901.5: num 0.0903
## .. ..$ 3899.5: num 0.093
## .. ..$ 3897.5: num 0.0965
## .. ..$ 3895.4: num 0.1
## .. ..$ 3893.4: num 0.107
## .. ..$ 3891.3: num 0.108
## .. ..$ 3889.3: num 0.104
## .. ..$ 3887.3: num 0.105
## .. ..$ 3885.2: num 0.105
## .. ..$ 3883.2: num 0.101
## .. ..$ 3881.1: num 0.103
## .. ..$ 3879.1: num 0.104
## .. ..$ 3877.1: num 0.103
## .. ..$ 3875 : num 0.103
## .. ..$ 3873 : num 0.0997
## .. ..$ 3870.9: num 0.0971
## .. ..$ 3868.9: num 0.0937
## .. ..$ 3866.9: num 0.0923
## .. ..$ 3864.8: num 0.0978
## .. ..$ 3862.8: num 0.102
## .. ..$ 3860.8: num 0.101
## .. ..$ 3858.7: num 0.1
## .. ..$ 3856.7: num 0.103
## .. ..$ 3854.6: num 0.107
## .. ..$ 3852.6: num 0.0999
## .. ..$ 3850.6: num 0.0927
## .. ..$ 3848.5: num 0.0989
## .. ..$ 3846.5: num 0.109
## .. ..$ 3844.4: num 0.11
## .. ..$ 3842.4: num 0.101
## .. ..$ 3840.4: num 0.0939
## .. ..$ 3838.3: num 0.093
## .. ..$ 3836.3: num 0.0941
## .. ..$ 3834.2: num 0.0988
## .. ..$ 3832.2: num 0.106
## .. ..$ 3830.2: num 0.11
## .. ..$ 3828.1: num 0.11
## .. ..$ 3826.1: num 0.108
## .. ..$ 3824 : num 0.105
## .. ..$ 3822 : num 0.103
## .. ..$ 3820 : num 0.0964
## .. ..$ 3817.9: num 0.0978
## .. ..$ 3815.9: num 0.11
## .. ..$ 3813.8: num 0.116
## .. ..$ 3811.8: num 0.118
## .. ..$ 3809.8: num 0.122
## .. ..$ 3807.7: num 0.122
## .. ..$ 3805.7: num 0.111
## .. ..$ 3803.6: num 0.105
## .. ..$ 3801.6: num 0.107
## .. ..$ 3799.6: num 0.105
## .. ..$ 3797.5: num 0.11
## .. .. [list output truncated]
## .. ..- attr(*, ".internal.selfref")=<externalptr>
## ..$ spc_nocomp : NULL
## ..$ sc_sm : NULL
## ..$ sc_rf : NULL
## ..$ ig_sm : NULL
## ..$ ig_rf : NULL
## ..$ wavenumbers : num [1:1716] 3997 3995 3993 3991 3989 ...
## ..$ wavenumbers_sc_sm: NULL
## ..$ wavenumbers_sc_rf: NULL
The above code extracts a list with one element that is named BF_lo_01_soil_cal.0, whereas using [[ shows the content of the subsetted list and the name is not shown anymore. The content contains again 9 elements, as str() reveals:
str(spc_list[["BF_lo_01_soil_cal.0"]])## List of 10
## $ metadata :Classes 'tbl_df', 'tbl' and 'data.frame': 1 obs. of 20 variables:
## ..$ unique_id : chr "BF_lo_01_soil_cal.0_2015-11-06 14:34:10"
## ..$ file_id : chr "BF_lo_01_soil_cal.0"
## ..$ sample_id : chr "BF_lo_01_soil_cal"
## ..$ rep_no : num 0
## ..$ date_time_sm : POSIXct[1:1], format: "2015-11-06 14:34:10"
## ..$ date_time_rf : POSIXct[1:1], format: "2015-11-06 14:30:10"
## ..$ sample_name : chr "BF_lo_01_soil_cal"
## ..$ instr_name_range: chr "alpha-mir"
## ..$ resolution_wn : int 4
## ..$ result_spc : chr "AB"
## ..$ beamspl : chr "ZnS"
## ..$ laser_wn : num 11602
## ..$ spc_in_file : chr "ScSm;ScRf;spc_nocomp;spc"
## ..$ zero_filling : int 2
## ..$ temp_scanner_sm : num 33.7
## ..$ temp_scanner_rf : num 33.6
## ..$ hum_rel_sm : int 25
## ..$ hum_rel_rf : int 25
## ..$ hum_abs_sm : num 9.5
## ..$ hum_abs_rf : num 9.49
## $ spc :Classes 'data.table' and 'data.frame': 1 obs. of 1716 variables:
## ..$ 3997.4: num 0.112
## ..$ 3995.4: num 0.111
## ..$ 3993.3: num 0.11
## ..$ 3991.3: num 0.111
## ..$ 3989.2: num 0.111
## ..$ 3987.2: num 0.112
## ..$ 3985.2: num 0.112
## ..$ 3983.1: num 0.112
## ..$ 3981.1: num 0.111
## ..$ 3979 : num 0.111
## ..$ 3977 : num 0.111
## ..$ 3975 : num 0.11
## ..$ 3972.9: num 0.109
## ..$ 3970.9: num 0.109
## ..$ 3968.8: num 0.11
## ..$ 3966.8: num 0.111
## ..$ 3964.8: num 0.111
## ..$ 3962.7: num 0.111
## ..$ 3960.7: num 0.111
## ..$ 3958.6: num 0.11
## ..$ 3956.6: num 0.11
## ..$ 3954.6: num 0.109
## ..$ 3952.5: num 0.108
## ..$ 3950.5: num 0.107
## ..$ 3948.4: num 0.107
## ..$ 3946.4: num 0.106
## ..$ 3944.4: num 0.106
## ..$ 3942.3: num 0.108
## ..$ 3940.3: num 0.108
## ..$ 3938.3: num 0.11
## ..$ 3936.2: num 0.11
## ..$ 3934.2: num 0.109
## ..$ 3932.1: num 0.107
## ..$ 3930.1: num 0.103
## ..$ 3928.1: num 0.102
## ..$ 3926 : num 0.104
## ..$ 3924 : num 0.104
## ..$ 3921.9: num 0.104
## ..$ 3919.9: num 0.106
## ..$ 3917.9: num 0.108
## ..$ 3915.8: num 0.109
## ..$ 3913.8: num 0.11
## ..$ 3911.7: num 0.113
## ..$ 3909.7: num 0.112
## ..$ 3907.7: num 0.107
## ..$ 3905.6: num 0.102
## ..$ 3903.6: num 0.0946
## ..$ 3901.5: num 0.0903
## ..$ 3899.5: num 0.093
## ..$ 3897.5: num 0.0965
## ..$ 3895.4: num 0.1
## ..$ 3893.4: num 0.107
## ..$ 3891.3: num 0.108
## ..$ 3889.3: num 0.104
## ..$ 3887.3: num 0.105
## ..$ 3885.2: num 0.105
## ..$ 3883.2: num 0.101
## ..$ 3881.1: num 0.103
## ..$ 3879.1: num 0.104
## ..$ 3877.1: num 0.103
## ..$ 3875 : num 0.103
## ..$ 3873 : num 0.0997
## ..$ 3870.9: num 0.0971
## ..$ 3868.9: num 0.0937
## ..$ 3866.9: num 0.0923
## ..$ 3864.8: num 0.0978
## ..$ 3862.8: num 0.102
## ..$ 3860.8: num 0.101
## ..$ 3858.7: num 0.1
## ..$ 3856.7: num 0.103
## ..$ 3854.6: num 0.107
## ..$ 3852.6: num 0.0999
## ..$ 3850.6: num 0.0927
## ..$ 3848.5: num 0.0989
## ..$ 3846.5: num 0.109
## ..$ 3844.4: num 0.11
## ..$ 3842.4: num 0.101
## ..$ 3840.4: num 0.0939
## ..$ 3838.3: num 0.093
## ..$ 3836.3: num 0.0941
## ..$ 3834.2: num 0.0988
## ..$ 3832.2: num 0.106
## ..$ 3830.2: num 0.11
## ..$ 3828.1: num 0.11
## ..$ 3826.1: num 0.108
## ..$ 3824 : num 0.105
## ..$ 3822 : num 0.103
## ..$ 3820 : num 0.0964
## ..$ 3817.9: num 0.0978
## ..$ 3815.9: num 0.11
## ..$ 3813.8: num 0.116
## ..$ 3811.8: num 0.118
## ..$ 3809.8: num 0.122
## ..$ 3807.7: num 0.122
## ..$ 3805.7: num 0.111
## ..$ 3803.6: num 0.105
## ..$ 3801.6: num 0.107
## ..$ 3799.6: num 0.105
## ..$ 3797.5: num 0.11
## .. [list output truncated]
## ..- attr(*, ".internal.selfref")=<externalptr>
## $ spc_nocomp : NULL
## $ sc_sm : NULL
## $ sc_rf : NULL
## $ ig_sm : NULL
## $ ig_rf : NULL
## $ wavenumbers : num [1:1716] 3997 3995 3993 3991 3989 ...
## $ wavenumbers_sc_sm: NULL
## $ wavenumbers_sc_rf: NULL
head(spc_list[["BF_lo_01_soil_cal.0"]][["wavenumbers"]])## [1] 3997.397 3995.357 3993.318 3991.278 3989.239 3987.199
Using the function ls() returns a vector of character strings giving the names of the list:
# Show names of first hierarchy of list
ls(spc_list[["BF_lo_01_soil_cal.0"]])## [1] "ig_rf" "ig_sm" "metadata"
## [4] "sc_rf" "sc_sm" "spc"
## [7] "spc_nocomp" "wavenumbers" "wavenumbers_sc_rf"
## [10] "wavenumbers_sc_sm"
To extract nested elements from a list, you can repeatedly apply subsetting operators. Besides using name subsetting for named data structures that contain a name attribute you can also use integers as index or logical vectors (TRUE and FALSE).
names(spc_list["BF_lo_01_soil_cal.0"]) # subset by name of first element## [1] "BF_lo_01_soil_cal.0"
# subset by integer index, result is identical
names(spc_list[1]) == names(spc_list["BF_lo_01_soil_cal.0"])## [1] TRUE
For logical subsetting we create a new vector containing TRUE or FALSE that is of same length as the spectra list spc_list. Usually logical type vectors are returned when testing conditions using binary operators that allow the comparison of values in atomic vectors (see R help for relational operators by entering ?Comparision in the R console; e.g. <, >, ==). Here, we create a logical vector logical_subset manually in order to illustrate that subsetting also works with vectors of type logical:
# repeat FALSE length(spc_list) times
logical_subset <- rep(FALSE, length(spc_list))
# Print subsetting vector
logical_subset## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [23] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [67] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [78] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [89] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [111] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [122] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [144] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [155] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [166] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [177] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [188] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [199] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [210] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [221] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [232] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [243] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [254] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [276] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# Check type
typeof(logical_subset)## [1] "logical"
Subsetting and assignment can be combined to replace the third element with FALSE:
# Replace the 3rd element with TRUE; use subsetting and assignment
logical_subset[3] <- TRUESubsequently, we can use the newly created logical vector for subsetting the spectral data list
# Extract list with `[`; use str() to show a compact output that
# is nicely printed
str(spc_list[logical_subset]) # Returns positions that are TRUE, element 3## List of 1
## $ BF_lo_01_soil_cal.2:List of 10
## ..$ metadata :Classes 'tbl_df', 'tbl' and 'data.frame': 1 obs. of 20 variables:
## .. ..$ unique_id : chr "BF_lo_01_soil_cal.2_2015-11-06 14:40:55"
## .. ..$ file_id : chr "BF_lo_01_soil_cal.2"
## .. ..$ sample_id : chr "BF_lo_01_soil_cal"
## .. ..$ rep_no : num 2
## .. ..$ date_time_sm : POSIXct[1:1], format: "2015-11-06 14:40:55"
## .. ..$ date_time_rf : POSIXct[1:1], format: "2015-11-06 14:30:10"
## .. ..$ sample_name : chr "BF_lo_01_soil_cal"
## .. ..$ instr_name_range: chr "alpha-mir"
## .. ..$ resolution_wn : int 4
## .. ..$ result_spc : chr "AB"
## .. ..$ beamspl : chr "ZnS"
## .. ..$ laser_wn : num 11602
## .. ..$ spc_in_file : chr "ScSm;ScRf;spc_nocomp;spc"
## .. ..$ zero_filling : int 2
## .. ..$ temp_scanner_sm : num 33.7
## .. ..$ temp_scanner_rf : num 33.6
## .. ..$ hum_rel_sm : int 25
## .. ..$ hum_rel_rf : int 25
## .. ..$ hum_abs_sm : num 9.51
## .. ..$ hum_abs_rf : num 9.49
## ..$ spc :Classes 'data.table' and 'data.frame': 1 obs. of 1716 variables:
## .. ..$ 3997.4: num 0.136
## .. ..$ 3995.4: num 0.135
## .. ..$ 3993.3: num 0.135
## .. ..$ 3991.3: num 0.135
## .. ..$ 3989.2: num 0.135
## .. ..$ 3987.2: num 0.136
## .. ..$ 3985.2: num 0.136
## .. ..$ 3983.1: num 0.136
## .. ..$ 3981.1: num 0.136
## .. ..$ 3979 : num 0.135
## .. ..$ 3977 : num 0.135
## .. ..$ 3975 : num 0.134
## .. ..$ 3972.9: num 0.133
## .. ..$ 3970.9: num 0.134
## .. ..$ 3968.8: num 0.135
## .. ..$ 3966.8: num 0.135
## .. ..$ 3964.8: num 0.135
## .. ..$ 3962.7: num 0.136
## .. ..$ 3960.7: num 0.135
## .. ..$ 3958.6: num 0.134
## .. ..$ 3956.6: num 0.133
## .. ..$ 3954.6: num 0.133
## .. ..$ 3952.5: num 0.131
## .. ..$ 3950.5: num 0.132
## .. ..$ 3948.4: num 0.131
## .. ..$ 3946.4: num 0.13
## .. ..$ 3944.4: num 0.131
## .. ..$ 3942.3: num 0.132
## .. ..$ 3940.3: num 0.132
## .. ..$ 3938.3: num 0.133
## .. ..$ 3936.2: num 0.134
## .. ..$ 3934.2: num 0.134
## .. ..$ 3932.1: num 0.132
## .. ..$ 3930.1: num 0.128
## .. ..$ 3928.1: num 0.126
## .. ..$ 3926 : num 0.129
## .. ..$ 3924 : num 0.129
## .. ..$ 3921.9: num 0.127
## .. ..$ 3919.9: num 0.13
## .. ..$ 3917.9: num 0.133
## .. ..$ 3915.8: num 0.134
## .. ..$ 3913.8: num 0.135
## .. ..$ 3911.7: num 0.137
## .. ..$ 3909.7: num 0.135
## .. ..$ 3907.7: num 0.131
## .. ..$ 3905.6: num 0.126
## .. ..$ 3903.6: num 0.12
## .. ..$ 3901.5: num 0.116
## .. ..$ 3899.5: num 0.118
## .. ..$ 3897.5: num 0.119
## .. ..$ 3895.4: num 0.122
## .. ..$ 3893.4: num 0.131
## .. ..$ 3891.3: num 0.133
## .. ..$ 3889.3: num 0.128
## .. ..$ 3887.3: num 0.13
## .. ..$ 3885.2: num 0.13
## .. ..$ 3883.2: num 0.125
## .. ..$ 3881.1: num 0.128
## .. ..$ 3879.1: num 0.128
## .. ..$ 3877.1: num 0.126
## .. ..$ 3875 : num 0.127
## .. ..$ 3873 : num 0.126
## .. ..$ 3870.9: num 0.124
## .. ..$ 3868.9: num 0.119
## .. ..$ 3866.9: num 0.116
## .. ..$ 3864.8: num 0.122
## .. ..$ 3862.8: num 0.126
## .. ..$ 3860.8: num 0.124
## .. ..$ 3858.7: num 0.122
## .. ..$ 3856.7: num 0.128
## .. ..$ 3854.6: num 0.138
## .. ..$ 3852.6: num 0.131
## .. ..$ 3850.6: num 0.117
## .. ..$ 3848.5: num 0.12
## .. ..$ 3846.5: num 0.131
## .. ..$ 3844.4: num 0.133
## .. ..$ 3842.4: num 0.126
## .. ..$ 3840.4: num 0.119
## .. ..$ 3838.3: num 0.119
## .. ..$ 3836.3: num 0.119
## .. ..$ 3834.2: num 0.122
## .. ..$ 3832.2: num 0.13
## .. ..$ 3830.2: num 0.134
## .. ..$ 3828.1: num 0.135
## .. ..$ 3826.1: num 0.131
## .. ..$ 3824 : num 0.128
## .. ..$ 3822 : num 0.129
## .. ..$ 3820 : num 0.121
## .. ..$ 3817.9: num 0.122
## .. ..$ 3815.9: num 0.135
## .. ..$ 3813.8: num 0.139
## .. ..$ 3811.8: num 0.139
## .. ..$ 3809.8: num 0.145
## .. ..$ 3807.7: num 0.147
## .. ..$ 3805.7: num 0.135
## .. ..$ 3803.6: num 0.128
## .. ..$ 3801.6: num 0.132
## .. ..$ 3799.6: num 0.13
## .. ..$ 3797.5: num 0.134
## .. .. [list output truncated]
## .. ..- attr(*, ".internal.selfref")=<externalptr>
## ..$ spc_nocomp : NULL
## ..$ sc_sm : NULL
## ..$ sc_rf : NULL
## ..$ ig_sm : NULL
## ..$ ig_rf : NULL
## ..$ wavenumbers : num [1:1716] 3997 3995 3993 3991 3989 ...
## ..$ wavenumbers_sc_sm: NULL
## ..$ wavenumbers_sc_rf: NULL
We can also test if the spectral list contains certain characters in the file name by using pattern matching functions. If one has used the string "_tb_" as part of the sample identifier to specify the sampling region in the file names, we might be interested in selecting only spectra and metadata of these region ("_tb_" stands for the site Tieningboué in Côte d'Ivoire for YAMSYS spectroscopy reference samples).
# Samples from site abbreviation "tb" (Tieningboué)
contains_tb <- grepl(pattern = "tb", x = names(spc_list))
# Show names of spectral data list elements that are returned by
# looking for "CI"
names(spc_list[contains_tb])## [1] "CI_tb_01_soil_cal.0" "CI_tb_01_soil_cal.1" "CI_tb_01_soil_cal.2"
## [4] "CI_tb_02_soil_cal.0" "CI_tb_02_soil_cal.1" "CI_tb_02_soil_cal.2"
## [7] "CI_tb_02_soil_cal.3" "CI_tb_02_soil_cal.4" "CI_tb_02_soil_cal.5"
## [10] "CI_tb_03_soil_cal.0" "CI_tb_03_soil_cal.1" "CI_tb_03_soil_cal.2"
## [13] "CI_tb_04_soil_cal.0" "CI_tb_04_soil_cal.1" "CI_tb_04_soil_cal.2"
## [16] "CI_tb_05_soil_cal.0" "CI_tb_05_soil_cal.1" "CI_tb_05_soil_cal.2"
## [19] "CI_tb_06_soil_cal.0" "CI_tb_06_soil_cal.1" "CI_tb_06_soil_cal.2"
## [22] "CI_tb_07_soil_cal.0" "CI_tb_07_soil_cal.1" "CI_tb_07_soil_cal.2"
## [25] "CI_tb_08_soil_cal.0" "CI_tb_08_soil_cal.1" "CI_tb_08_soil_cal.2"
## [28] "CI_tb_09_soil_cal.0" "CI_tb_09_soil_cal.1" "CI_tb_09_soil_cal.2"
## [31] "CI_tb_10_soil_cal.0" "CI_tb_10_soil_cal.1" "CI_tb_10_soil_cal.2"
## [34] "CI_tb_11_soil_cal.0" "CI_tb_11_soil_cal.1" "CI_tb_11_soil_cal.2"
## [37] "CI_tb_12_soil_cal.0" "CI_tb_12_soil_cal.1" "CI_tb_12_soil_cal.2"
## [40] "CI_tb_13_soil_cal.0" "CI_tb_13_soil_cal.1" "CI_tb_13_soil_cal.2"
## [43] "CI_tb_14_soil_cal.0" "CI_tb_14_soil_cal.1" "CI_tb_14_soil_cal.2"
## [46] "CI_tb_15_soil_cal.0" "CI_tb_15_soil_cal.1" "CI_tb_15_soil_cal.2"
## [49] "CI_tb_16_soil_cal.0" "CI_tb_16_soil_cal.1" "CI_tb_16_soil_cal.2"
## [52] "CI_tb_17_soil_cal.0" "CI_tb_17_soil_cal.1" "CI_tb_17_soil_cal.2"
## [55] "CI_tb_18_soil_cal.0" "CI_tb_18_soil_cal.1" "CI_tb_18_soil_cal.2"
## [58] "CI_tb_19_soil_cal.0" "CI_tb_19_soil_cal.1" "CI_tb_19_soil_cal.2"
## [61] "CI_tb_20_soil_cal.0" "CI_tb_20_soil_cal.1" "CI_tb_20_soil_cal.2"
As the above example illustrates, only spectral data from files containing the string "tb" are selected.
Data frames are one of the basic R data structures.
When first reading spectral data from binary OPUS files, simplerspec returns ̀data.tabless of final spectra (AB block in OPUS viewer software).
# Extract spectrum from file "BF_lo_01_soil_cal.0"
# and get overview of the data structure
str(spc_list[["BF_lo_01_soil_cal.0"]][["spc"]])## Classes 'data.table' and 'data.frame': 1 obs. of 1716 variables:
## $ 3997.4: num 0.112
## $ 3995.4: num 0.111
## $ 3993.3: num 0.11
## $ 3991.3: num 0.111
## $ 3989.2: num 0.111
## $ 3987.2: num 0.112
## $ 3985.2: num 0.112
## $ 3983.1: num 0.112
## $ 3981.1: num 0.111
## $ 3979 : num 0.111
## $ 3977 : num 0.111
## $ 3975 : num 0.11
## $ 3972.9: num 0.109
## $ 3970.9: num 0.109
## $ 3968.8: num 0.11
## $ 3966.8: num 0.111
## $ 3964.8: num 0.111
## $ 3962.7: num 0.111
## $ 3960.7: num 0.111
## $ 3958.6: num 0.11
## $ 3956.6: num 0.11
## $ 3954.6: num 0.109
## $ 3952.5: num 0.108
## $ 3950.5: num 0.107
## $ 3948.4: num 0.107
## $ 3946.4: num 0.106
## $ 3944.4: num 0.106
## $ 3942.3: num 0.108
## $ 3940.3: num 0.108
## $ 3938.3: num 0.11
## $ 3936.2: num 0.11
## $ 3934.2: num 0.109
## $ 3932.1: num 0.107
## $ 3930.1: num 0.103
## $ 3928.1: num 0.102
## $ 3926 : num 0.104
## $ 3924 : num 0.104
## $ 3921.9: num 0.104
## $ 3919.9: num 0.106
## $ 3917.9: num 0.108
## $ 3915.8: num 0.109
## $ 3913.8: num 0.11
## $ 3911.7: num 0.113
## $ 3909.7: num 0.112
## $ 3907.7: num 0.107
## $ 3905.6: num 0.102
## $ 3903.6: num 0.0946
## $ 3901.5: num 0.0903
## $ 3899.5: num 0.093
## $ 3897.5: num 0.0965
## $ 3895.4: num 0.1
## $ 3893.4: num 0.107
## $ 3891.3: num 0.108
## $ 3889.3: num 0.104
## $ 3887.3: num 0.105
## $ 3885.2: num 0.105
## $ 3883.2: num 0.101
## $ 3881.1: num 0.103
## $ 3879.1: num 0.104
## $ 3877.1: num 0.103
## $ 3875 : num 0.103
## $ 3873 : num 0.0997
## $ 3870.9: num 0.0971
## $ 3868.9: num 0.0937
## $ 3866.9: num 0.0923
## $ 3864.8: num 0.0978
## $ 3862.8: num 0.102
## $ 3860.8: num 0.101
## $ 3858.7: num 0.1
## $ 3856.7: num 0.103
## $ 3854.6: num 0.107
## $ 3852.6: num 0.0999
## $ 3850.6: num 0.0927
## $ 3848.5: num 0.0989
## $ 3846.5: num 0.109
## $ 3844.4: num 0.11
## $ 3842.4: num 0.101
## $ 3840.4: num 0.0939
## $ 3838.3: num 0.093
## $ 3836.3: num 0.0941
## $ 3834.2: num 0.0988
## $ 3832.2: num 0.106
## $ 3830.2: num 0.11
## $ 3828.1: num 0.11
## $ 3826.1: num 0.108
## $ 3824 : num 0.105
## $ 3822 : num 0.103
## $ 3820 : num 0.0964
## $ 3817.9: num 0.0978
## $ 3815.9: num 0.11
## $ 3813.8: num 0.116
## $ 3811.8: num 0.118
## $ 3809.8: num 0.122
## $ 3807.7: num 0.122
## $ 3805.7: num 0.111
## $ 3803.6: num 0.105
## $ 3801.6: num 0.107
## $ 3799.6: num 0.105
## $ 3797.5: num 0.11
## [list output truncated]
## - attr(*, ".internal.selfref")=<externalptr>
You can test if the above output has the class data.frame with
is.data.frame(spc_list[["BF_lo_01_soil_cal.0"]][["spc"]])## [1] TRUE
As the output TRUE indicates, the selected spectrum from the list is a data frame.
You can get the number of rows and columns of a data.table by
# Assign data.table to object
spc_dt <- spc_list[["BF_lo_01_soil_cal.0"]][["spc"]]
nrow(spc_dt)## [1] 1
ncol(spc_dt)## [1] 1716
The spectral data.table within the file "BF_lo_01_soil_cal.0" has 1 rows and 1716 columns. The columns correspond to wavenumber variables.
Data frames have a dimnames attribute that names columns and rows:
# Show row name and only first and last 10 column names
rownames(spc_dt)## [1] "1"
idx_firstandlast10 <- c(1:10, seq(from = ncol(spc_dt) - 10, ncol(spc_dt), 1))
colnames(spc_dt)[idx_firstandlast10]## [1] "3997.4" "3995.4" "3993.3" "3991.3" "3989.2" "3987.2" "3985.2"
## [8] "3983.1" "3981.1" "3979" "520.1" "518" "516" "514"
## [15] "511.9" "509.9" "507.8" "505.8" "503.8" "501.7" "499.7"
You can also get dimension names in list form
# Show row and column names as list
str(dimnames(spc_dt))## List of 2
## $ : NULL
## $ : chr [1:1716] "3997.4" "3995.4" "3993.3" "3991.3" ...
Subsetting data frames : Data frame subsetting operations allow you to extract parts of values stored within a data frame that you are interested in. The basic syntax is that you can use [ and supply a 1D index for both rows and columns, separated by a comma. Blank subsetting without an index value keeps all rows or columns:
# Show columns 2, 3 and 6
spc_dt[, c(2, 3, 6)]## 3995.4 3993.3 3987.2
## 1: 0.1110472 0.1104522 0.1115582
The first index before the comma is the row index and the second the column index. Omitting the row index shows all rows. In the case of data.table spc_dt there is only one row. For exemplifying the subsetting behavior of matrices we can duplicate the data.table spc_dt and copy the same content into a second row using rbind(), which is a generic function to combine objects by rows (equivalent for columns is cbind()):
spc_dt2 <- rbind(spc_dt, spc_dt)
# Check dimensions
dim(spc_dt2)## [1] 2 1716
Now we can e.g. replace the first value in the second row by first selecting the value in the second row of the first column by 1 and then assigning the number 1 to it. This will modify the value at the selection position in the previous data frame in place.
spc_dt2[2, 1] # extract 2nd row and first column## 3997.4
## 1: 0.1116138
# Subset and modify by assignment
spc_dt2[2, 1] <- 1
# Check if value at selected position has been replaced
spc_dt2[2, 1]## 3997.4
## 1: 1
The above code shows that the selected value has been correctly replaced. It is also possible to only show the first row of spc_dt2, by leaving the column index empty:
head(spc_dt[1, ]) # Show only first 10 values (default of head())## 3997.4 3995.4 3993.3 3991.3 3989.2 3987.2 3985.2
## 1: 0.1116138 0.1110472 0.1104522 0.1107337 0.1113628 0.1115582 0.1116115
## 3983.1 3981.1 3979 3977 3975 3972.9 3970.9
## 1: 0.1116768 0.1113948 0.1110339 0.1107579 0.109912 0.1089011 0.1090422
## 3968.8 3966.8 3964.8 3962.7 3960.7 3958.6 3956.6
## 1: 0.1099667 0.1105003 0.1109353 0.1112978 0.1105624 0.1098195 0.1098699
## 3954.6 3952.5 3950.5 3948.4 3946.4 3944.4 3942.3
## 1: 0.1092134 0.1078505 0.1072382 0.1066292 0.1056538 0.1063747 0.1077091
## 3940.3 3938.3 3936.2 3934.2 3932.1 3930.1 3928.1
## 1: 0.1084273 0.1096656 0.1101731 0.1092632 0.1068086 0.1033797 0.1024289
## 3926 3924 3921.9 3919.9 3917.9 3915.8 3913.8
## 1: 0.1039596 0.1039926 0.1035535 0.1058372 0.1082846 0.1088962 0.11031
## 3911.7 3909.7 3907.7 3905.6 3903.6 3901.5 3899.5
## 1: 0.1126094 0.1115171 0.1073066 0.1019541 0.09455585 0.09026368 0.0930251
## 3897.5 3895.4 3893.4 3891.3 3889.3 3887.3 3885.2
## 1: 0.09647838 0.1002236 0.1065465 0.1080022 0.1044163 0.1052921 0.104677
## 3883.2 3881.1 3879.1 3877.1 3875 3873 3870.9
## 1: 0.1006632 0.102958 0.1044673 0.1030064 0.1025012 0.09970551 0.0971354
## 3868.9 3866.9 3864.8 3862.8 3860.8 3858.7 3856.7
## 1: 0.09369191 0.09233829 0.097812 0.1017904 0.1012478 0.09999011 0.1029824
## 3854.6 3852.6 3850.6 3848.5 3846.5 3844.4 3842.4
## 1: 0.1070663 0.09993207 0.09267305 0.098864 0.1089062 0.1100293 0.101408
## 3840.4 3838.3 3836.3 3834.2 3832.2 3830.2
## 1: 0.09394594 0.09304497 0.09413817 0.09882298 0.1061592 0.1099934
## 3828.1 3826.1 3824 3822 3820 3817.9 3815.9
## 1: 0.1104877 0.107561 0.1046565 0.1031307 0.09639382 0.09775814 0.1102891
## 3813.8 3811.8 3809.8 3807.7 3805.7 3803.6 3801.6
## 1: 0.1161217 0.1178017 0.122399 0.1221272 0.1113749 0.1050898 0.1065325
## 3799.6 3797.5 3795.5 3793.4 3791.4 3789.4 3787.3
## 1: 0.1051933 0.1098949 0.1206683 0.1290725 0.1349746 0.137058 0.1360136
## 3785.3 3783.3 3781.2 3779.2 3777.1 3775.1 3773.1
## 1: 0.134024 0.1321631 0.1341237 0.1378448 0.1387957 0.1398433 0.1425246
## 3771 3769 3766.9 3764.9 3762.9 3760.8 3758.8
## 1: 0.1438005 0.1416286 0.1409272 0.1428057 0.1447936 0.1481354 0.148438
## 3756.7 3754.7 3752.7 3750.6 3748.6 3746.5 3744.5
## 1: 0.1438407 0.142666 0.1452873 0.1412795 0.1345256 0.1467782 0.1670109
## 3742.5 3740.4 3738.4 3736.3 3734.3 3732.3 3730.2
## 1: 0.1698551 0.1683959 0.1752269 0.1832757 0.1916004 0.2045362 0.2196238
## 3728.2 3726.1 3724.1 3722.1 3720 3718 3715.9
## 1: 0.2355921 0.2515314 0.2675849 0.2890549 0.3161238 0.343578 0.3706079
## 3713.9 3711.9 3709.8 3707.8 3705.8 3703.7 3701.7
## 1: 0.404244 0.4496876 0.5026801 0.5598037 0.6234682 0.6987669 0.7819785
## 3699.6 3697.6 3695.6 3693.5 3691.5 3689.4 3687.4
## 1: 0.855344 0.9035529 0.9179483 0.8980334 0.8533946 0.7960867 0.7427536
## 3685.4 3683.3 3681.3 3679.2 3677.2 3675.2 3673.1
## 1: 0.7079352 0.687908 0.6708944 0.6567918 0.6553099 0.6605251 0.6698021
## 3671.1 3669 3667 3665 3662.9 3660.9 3658.8
## 1: 0.6929669 0.711397 0.7123793 0.71206 0.7149729 0.7191647 0.7290136
## 3656.8 3654.8 3652.7 3650.7 3648.6 3646.6 3644.6
## 1: 0.7397532 0.7387432 0.7297438 0.7138904 0.6853508 0.6612893 0.6531969
## 3642.5 3640.5 3638.4 3636.4 3634.4 3632.3 3630.3
## 1: 0.6528124 0.6513506 0.6481165 0.6458585 0.6446651 0.6500137 0.6743921
## 3628.2 3626.2 3624.2 3622.1 3620.1 3618.1 3616
## 1: 0.7154637 0.7650172 0.8259271 0.8828155 0.8908083 0.8285634 0.7421793
## 3614 3611.9 3609.9 3607.9 3605.8 3603.8 3601.7
## 1: 0.673768 0.6267841 0.5968329 0.5779265 0.565888 0.5626228 0.5643913
## 3599.7 3597.7 3595.6 3593.6 3591.5 3589.5 3587.5
## 1: 0.5631593 0.5582041 0.5510668 0.5404087 0.5300417 0.5245773 0.5191186
## 3585.4 3583.4 3581.3 3579.3 3577.3 3575.2 3573.2
## 1: 0.5123681 0.5112181 0.5143472 0.5151356 0.5134943 0.511289 0.507393
## 3571.1 3569.1 3567.1 3565 3563 3560.9 3558.9
## 1: 0.5021104 0.4969654 0.4907912 0.4861864 0.4897577 0.4987744 0.505169
## 3556.9 3554.8 3552.8 3550.7 3548.7 3546.7 3544.6
## 1: 0.506789 0.5063753 0.5048466 0.5019996 0.5005469 0.5010287 0.5011958
## 3542.6 3540.6 3538.5 3536.5 3534.4 3532.4 3530.4
## 1: 0.5025658 0.5061851 0.5095251 0.5102621 0.5089468 0.5078958 0.5070646
## 3528.3 3526.3 3524.2 3522.2 3520.2 3518.1 3516.1
## 1: 0.5051079 0.503341 0.5036097 0.5052959 0.5080728 0.51164 0.514064
## 3514 3512 3510 3507.9 3505.9 3503.8 3501.8
## 1: 0.5145297 0.5139735 0.5129235 0.5114836 0.5116599 0.5134345 0.5139225
## 3499.8 3497.7 3495.7 3493.6 3491.6 3489.6 3487.5
## 1: 0.5145717 0.5174403 0.5200608 0.5208555 0.5211441 0.5215181 0.5212984
## 3485.5 3483.4 3481.4 3479.4 3477.3 3475.3 3473.2
## 1: 0.5208611 0.5211357 0.5209543 0.520404 0.5219475 0.5248185 0.5266916
## 3471.2 3469.2 3467.1 3465.1 3463.1 3461 3459
## 1: 0.528021 0.5295117 0.529994 0.5294459 0.5294614 0.5295542 0.5291033
## 3456.9 3454.9 3452.9 3450.8 3448.8 3446.7 3444.7
## 1: 0.5293549 0.5306885 0.5320562 0.5322884 0.531772 0.530844 0.5305933
## 3442.7 3440.6 3438.6 3436.5 3434.5 3432.5 3430.4
## 1: 0.532656 0.5355729 0.5383387 0.5407725 0.5418113 0.5417949 0.5415865
## 3428.4 3426.3 3424.3 3422.3 3420.2 3418.2 3416.1
## 1: 0.5410931 0.5400733 0.5390592 0.5386636 0.5384083 0.538309 0.5391221
## 3414.1 3412.1 3410 3408 3405.9 3403.9 3401.9
## 1: 0.540336 0.5409092 0.5404803 0.5400574 0.5406018 0.5413219 0.541763
## 3399.8 3397.8 3395.7 3393.7 3391.7 3389.6 3387.6
## 1: 0.5432697 0.5428165 0.5424205 0.5431384 0.543209 0.5422207 0.5421394
## 3385.6 3383.5 3381.5 3379.4 3377.4 3375.4 3373.3
## 1: 0.5425027 0.542112 0.5419476 0.5423765 0.5426027 0.5426469 0.5432032
## 3371.3 3369.2 3367.2 3365.2 3363.1 3361.1 3359
## 1: 0.5443523 0.5452251 0.5448565 0.5431483 0.5419671 0.5421976 0.5419435
## 3357 3355 3352.9 3350.9 3348.8 3346.8 3344.8
## 1: 0.5409678 0.5408535 0.5415211 0.5418525 0.5416046 0.5411514 0.5408642
## 3342.7 3340.7 3338.6 3336.6 3334.6 3332.5 3330.5
## 1: 0.5410772 0.541231 0.5407252 0.5399434 0.5388844 0.5375247 0.5367965
## 3328.4 3326.4 3324.4 3322.3 3320.3 3318.2 3316.2
## 1: 0.5370393 0.5374069 0.5375454 0.5378051 0.5380245 0.5378212 0.5372844
## 3314.2 3312.1 3310.1 3308 3306 3304 3301.9
## 1: 0.5367095 0.5364211 0.5366427 0.5367549 0.5363613 0.5358801 0.535311
## 3299.9 3297.9 3295.8 3293.8 3291.7 3289.7 3287.7
## 1: 0.5347087 0.5342708 0.5338174 0.5332146 0.5324051 0.5316291 0.5315127
## 3285.6 3283.6 3281.5 3279.5 3277.5 3275.4 3273.4
## 1: 0.5318202 0.5315689 0.530727 0.5300602 0.5298554 0.529889 0.5297794
## 3271.3 3269.3 3267.3 3265.2 3263.2 3261.1 3259.1
## 1: 0.5292903 0.528484 0.5276083 0.5270485 0.5267999 0.5263633 0.5257509
## 3257.1 3255 3253 3250.9 3248.9 3246.9 3244.8
## 1: 0.5253119 0.5249451 0.5242097 0.5229785 0.521868 0.5214114 0.5207522
## 3242.8 3240.7 3238.7 3236.7 3234.6 3232.6 3230.5
## 1: 0.5193753 0.5183725 0.518406 0.5189752 0.5192338 0.5185085 0.5168555
## 3228.5 3226.5 3224.4 3222.4 3220.4 3218.3 3216.3
## 1: 0.5151792 0.5143575 0.5142948 0.5141286 0.5132591 0.5117249 0.510248
## 3214.2 3212.2 3210.2 3208.1 3206.1 3204 3202
## 1: 0.5092981 0.5084108 0.5074376 0.5066918 0.5061628 0.5052173 0.5036492
## 3200 3197.9 3195.9 3193.8 3191.8 3189.8 3187.7
## 1: 0.5021023 0.5007395 0.4998238 0.499485 0.4987416 0.4974239 0.4962434
## 3185.7 3183.6 3181.6 3179.6 3177.5 3175.5 3173.4
## 1: 0.4952952 0.4942829 0.4929222 0.4914428 0.4897038 0.4875807 0.485836
## 3171.4 3169.4 3167.3 3165.3 3163.2 3161.2 3159.2
## 1: 0.4846831 0.4837314 0.4826354 0.4812084 0.479837 0.478722 0.4774536
## 3157.1 3155.1 3153 3151 3149 3146.9 3144.9
## 1: 0.4762946 0.4755839 0.4744931 0.472665 0.4706939 0.4689855 0.4677578
## 3142.9 3140.8 3138.8 3136.7 3134.7 3132.7 3130.6
## 1: 0.4668166 0.4657238 0.4642204 0.4622339 0.4601486 0.4582447 0.4567231
## 3128.6 3126.5 3124.5 3122.5 3120.4 3118.4 3116.3
## 1: 0.4554727 0.4539556 0.4526301 0.4517795 0.450786 0.4495825 0.4482124
## 3114.3 3112.3 3110.2 3108.2 3106.1 3104.1 3102.1
## 1: 0.4466802 0.4455313 0.4448372 0.4437627 0.4417416 0.4393316 0.437277
## 3100 3098 3095.9 3093.9 3091.9 3089.8 3087.8
## 1: 0.4355066 0.4340266 0.4327925 0.4315788 0.4306334 0.4297255 0.4283357
## 3085.7 3083.7 3081.7 3079.6 3077.6 3075.5 3073.5
## 1: 0.4268396 0.4256024 0.4242012 0.4222257 0.4199938 0.4181655 0.4166711
## 3071.5 3069.4 3067.4 3065.4 3063.3 3061.3 3059.2
## 1: 0.4152657 0.4141215 0.4128367 0.4110576 0.4092566 0.4076953 0.406259
## 3057.2 3055.2 3053.1 3051.1 3049 3047 3045
## 1: 0.4047865 0.4031602 0.40165 0.4000423 0.3979223 0.3958364 0.3942071
## 3042.9 3040.9 3038.8 3036.8 3034.8 3032.7 3030.7
## 1: 0.3927376 0.3911098 0.389294 0.3873783 0.3854076 0.3833377 0.3813303
## 3028.6 3026.6 3024.6 3022.5 3020.5 3018.4 3016.4
## 1: 0.3798245 0.378882 0.3778149 0.376241 0.374638 0.3733432 0.3721929
## 3014.4 3012.3 3010.3 3008.2 3006.2 3004.2 3002.1
## 1: 0.3708816 0.3694541 0.3680324 0.3665663 0.3651873 0.363994 0.3629195
## 3000.1 2998 2996 2994 2991.9 2989.9 2987.9
## 1: 0.3620983 0.3615842 0.3608212 0.3597927 0.3590308 0.358226 0.3573054
## 2985.8 2983.8 2981.7 2979.7 2977.7 2975.6 2973.6
## 1: 0.3568687 0.3570132 0.3571981 0.3569482 0.3563045 0.3555854 0.3548411
## 2971.5 2969.5 2967.5 2965.4 2963.4 2961.3 2959.3
## 1: 0.3540446 0.3533451 0.3527457 0.3523849 0.3525358 0.3527181 0.352321
## 2957.3 2955.2 2953.2 2951.1 2949.1 2947.1 2945
## 1: 0.3516042 0.3510642 0.3508189 0.3505593 0.3503009 0.3504573 0.3507631
## 2943 2940.9 2938.9 2936.9 2934.8 2932.8 2930.7
## 1: 0.3507062 0.3505201 0.3506619 0.3508518 0.3507602 0.3507479 0.3508274
## 2928.7 2926.7 2924.6 2922.6 2920.5 2918.5 2916.5
## 1: 0.3504285 0.3495554 0.3485362 0.3473839 0.3461746 0.3445974 0.3423133
## 2914.4 2912.4 2910.3 2908.3 2906.3 2904.2 2902.2
## 1: 0.3395411 0.3362026 0.3323449 0.3288594 0.3264198 0.3245966 0.3227441
## 2900.2 2898.1 2896.1 2894 2892 2890 2887.9
## 1: 0.320984 0.3196257 0.3183629 0.3167847 0.3150124 0.3132942 0.3117562
## 2885.9 2883.8 2881.8 2879.8 2877.7 2875.7 2873.6
## 1: 0.3105685 0.3097504 0.3090168 0.3079851 0.3065872 0.3051333 0.3038726
## 2871.6 2869.6 2867.5 2865.5 2863.4 2861.4 2859.4
## 1: 0.3026466 0.3012969 0.3002169 0.2995717 0.2990038 0.2985632 0.2984579
## 2857.3 2855.3 2853.2 2851.2 2849.2 2847.1 2845.1
## 1: 0.2985099 0.2985424 0.298408 0.2976204 0.2955565 0.292193 0.2883257
## 2843 2841 2839 2836.9 2834.9 2832.8 2830.8
## 1: 0.2847506 0.2818656 0.279624 0.2775547 0.275508 0.2737524 0.2724171
## 2828.8 2826.7 2824.7 2822.7 2820.6 2818.6 2816.5
## 1: 0.2711698 0.2695814 0.2678879 0.2665878 0.2655897 0.2645297 0.2634342
## 2814.5 2812.5 2810.4 2808.4 2806.3 2804.3 2802.3
## 1: 0.2623775 0.2612831 0.2602028 0.2591853 0.2582712 0.2573304 0.2562202
## 2800.2 2798.2 2796.1 2794.1 2792.1 2790 2788
## 1: 0.2552605 0.2546754 0.2541961 0.2535369 0.2527328 0.2518808 0.2510207
## 2785.9 2783.9 2781.9 2779.8 2777.8 2775.7 2773.7
## 1: 0.2503209 0.24973 0.2490896 0.2483945 0.2475453 0.2465792 0.2456174
## 2771.7 2769.6 2767.6 2765.5 2763.5 2761.5 2759.4
## 1: 0.244683 0.2438409 0.2429538 0.2419268 0.2410522 0.2404164 0.2399455
## 2757.4 2755.3 2753.3 2751.3 2749.2 2747.2 2745.2
## 1: 0.239663 0.2391533 0.2381958 0.2373295 0.2368063 0.2362972 0.2356566
## 2743.1 2741.1 2739 2737 2735 2732.9 2730.9
## 1: 0.2350737 0.2345497 0.2338663 0.2331409 0.2325692 0.231903 0.2311729
## 2728.8 2726.8 2724.8 2722.7 2720.7 2718.6 2716.6
## 1: 0.2307145 0.2304081 0.2300178 0.2294743 0.2289951 0.2288389 0.2287743
## 2714.6 2712.5 2710.5 2708.4 2706.4 2704.4 2702.3
## 1: 0.2285083 0.228184 0.2280095 0.2278003 0.2274894 0.2272945 0.2270769
## 2700.3 2698.2 2696.2 2694.2 2692.1 2690.1 2688
## 1: 0.2265878 0.22594 0.2253874 0.225072 0.2247745 0.2242955 0.2238819
## 2686 2684 2681.9 2679.9 2677.8 2675.8 2673.8
## 1: 0.2236616 0.223544 0.2233306 0.2227497 0.221904 0.2212504 0.2210051
## 2671.7 2669.7 2667.7 2665.6 2663.6 2661.5 2659.5
## 1: 0.2207698 0.2201602 0.2193687 0.2185495 0.2175338 0.2164703 0.2155813
## 2657.5 2655.4 2653.4 2651.3 2649.3 2647.3 2645.2
## 1: 0.2147695 0.2141363 0.2137252 0.2131507 0.212358 0.2117684 0.2112713
## 2643.2 2641.1 2639.1 2637.1 2635 2633 2630.9
## 1: 0.2105103 0.2096616 0.2089354 0.2084005 0.2079351 0.2073775 0.2069598
## 2628.9 2626.9 2624.8 2622.8 2620.7 2618.7 2616.7
## 1: 0.2067885 0.2065707 0.2061754 0.2057166 0.205264 0.2048489 0.2044144
## 2614.6 2612.6 2610.5 2608.5 2606.5 2604.4 2602.4
## 1: 0.203919 0.2034856 0.2032949 0.2032846 0.2031309 0.2027634 0.2023235
## 2600.3 2598.3 2596.3 2594.2 2592.2 2590.1 2588.1
## 1: 0.2020511 0.2019674 0.2017749 0.2015207 0.2011737 0.2006037 0.2000985
## 2586.1 2584 2582 2580 2577.9 2575.9 2573.8
## 1: 0.1996744 0.199149 0.1986157 0.1979529 0.1971816 0.196717 0.1963912
## 2571.8 2569.8 2567.7 2565.7 2563.6 2561.6 2559.6
## 1: 0.1958149 0.1951383 0.1944825 0.1938472 0.1933301 0.1929015 0.1924474
## 2557.5 2555.5 2553.4 2551.4 2549.4 2547.3 2545.3
## 1: 0.1920758 0.1918961 0.1916155 0.1911568 0.1908246 0.1907399 0.1908108
## 2543.2 2541.2 2539.2 2537.1 2535.1 2533 2531
## 1: 0.1907593 0.1906016 0.190625 0.190644 0.1903998 0.1902221 0.1903922
## 2529 2526.9 2524.9 2522.8 2520.8 2518.8 2516.7
## 1: 0.1906241 0.1907047 0.1907314 0.1909027 0.1912429 0.191473 0.1915401
## 2514.7 2512.6 2510.6 2508.6 2506.5 2504.5 2502.5
## 1: 0.1915556 0.191518 0.1914998 0.1914636 0.1913608 0.191323 0.1912995
## 2500.4 2498.4 2496.3 2494.3 2492.3 2490.2 2488.2
## 1: 0.1912087 0.1911368 0.1909571 0.1905987 0.1903221 0.1901574 0.1899598
## 2486.1 2484.1 2482.1 2480 2478 2475.9 2473.9
## 1: 0.1898361 0.1898071 0.189735 0.189539 0.1891058 0.1885616 0.1881597
## 2471.9 2469.8 2467.8 2465.7 2463.7 2461.7 2459.6
## 1: 0.1878602 0.1876146 0.1874123 0.1871042 0.1867703 0.1867193 0.1868503
## 2457.6 2455.5 2453.5 2451.5 2449.4 2447.4 2445.3
## 1: 0.1868531 0.186872 0.1870877 0.1873379 0.187577 0.1878938 0.1882769
## 2443.3 2441.3 2439.2 2437.2 2435.1 2433.1 2431.1
## 1: 0.1887338 0.1892045 0.1896035 0.1900466 0.1905884 0.1911163 0.1915722
## 2429 2427 2425 2422.9 2420.9 2418.8 2416.8
## 1: 0.1919656 0.1924128 0.1929838 0.1935772 0.1941245 0.194733 0.1954936
## 2414.8 2412.7 2410.7 2408.6 2406.6 2404.6 2402.5
## 1: 0.1961208 0.1964405 0.1968059 0.1974269 0.1980293 0.1983627 0.1985923
## 2400.5 2398.4 2396.4 2394.4 2392.3 2390.3 2388.2
## 1: 0.1989102 0.1993953 0.2001064 0.2008504 0.2016567 0.2026635 0.203835
## 2386.2 2384.2 2382.1 2380.1 2378 2376 2374
## 1: 0.2052747 0.2072179 0.2095475 0.2118544 0.2138398 0.2155401 0.2173137
## 2371.9 2369.9 2367.8 2365.8 2363.8 2361.7 2359.7
## 1: 0.2193464 0.2212174 0.2228134 0.2245507 0.2262253 0.2270229 0.2261788
## 2357.6 2355.6 2353.6 2351.5 2349.5 2347.5 2345.4
## 1: 0.2231189 0.218977 0.2172361 0.220046 0.2243243 0.2256732 0.2245269
## 2343.4 2341.3 2339.3 2337.3 2335.2 2333.2 2331.1
## 1: 0.2245706 0.226635 0.2282614 0.228422 0.2278818 0.2270822 0.2260817
## 2329.1 2327.1 2325 2323 2320.9 2318.9 2316.9
## 1: 0.2251698 0.2242131 0.2226208 0.2203192 0.2181364 0.216905 0.2164398
## 2314.8 2312.8 2310.7 2308.7 2306.7 2304.6 2302.6
## 1: 0.215977 0.2152278 0.2145288 0.2141319 0.2140807 0.2144012 0.2150439
## 2300.5 2298.5 2296.5 2294.4 2292.4 2290.3 2288.3
## 1: 0.2159045 0.2169865 0.2184417 0.2203356 0.2224006 0.2244177 0.2266573
## 2286.3 2284.2 2282.2 2280.1 2278.1 2276.1 2274
## 1: 0.2293695 0.2323925 0.2354934 0.2385634 0.2415636 0.2445503 0.2476283
## 2272 2270 2267.9 2265.9 2263.8 2261.8 2259.8
## 1: 0.2508035 0.2539351 0.2568142 0.2594292 0.2619443 0.2643344 0.266483
## 2257.7 2255.7 2253.6 2251.6 2249.6 2247.5 2245.5
## 1: 0.2684737 0.270452 0.2725147 0.2746207 0.276796 0.2790623 0.2818789
## 2243.4 2241.4 2239.4 2237.3 2235.3 2233.2 2231.2
## 1: 0.285076 0.2878294 0.2894648 0.2898161 0.2890913 0.2877187 0.2861056
## 2229.2 2227.1 2225.1 2223 2221 2219 2216.9
## 1: 0.284319 0.2822145 0.2797021 0.2763741 0.2719711 0.2668023 0.2612127
## 2214.9 2212.8 2210.8 2208.8 2206.7 2204.7 2202.6
## 1: 0.2554203 0.2498267 0.2449351 0.2407101 0.2367809 0.2330648 0.2296744
## 2200.6 2198.6 2196.5 2194.5 2192.4 2190.4 2188.4
## 1: 0.2266406 0.224052 0.2219028 0.2201797 0.2191449 0.218623 0.2182251
## 2186.3 2184.3 2182.3 2180.2 2178.2 2176.1 2174.1
## 1: 0.218071 0.218227 0.2185614 0.2190577 0.2195305 0.2199427 0.2207188
## 2172.1 2170 2168 2165.9 2163.9 2161.9 2159.8
## 1: 0.2219036 0.2231934 0.2246622 0.2263748 0.2282893 0.2305868 0.2332546
## 2157.8 2155.7 2153.7 2151.7 2149.6 2147.6 2145.5
## 1: 0.2361391 0.2393571 0.2428689 0.2464771 0.2502639 0.254244 0.2583639
## 2143.5 2141.5 2139.4 2137.4 2135.3 2133.3 2131.3
## 1: 0.2626402 0.2669046 0.2706926 0.2733262 0.2742656 0.2732744 0.2705629
## 2129.2 2127.2 2125.1 2123.1 2121.1 2119 2117
## 1: 0.2666961 0.2624812 0.2587278 0.2557887 0.253774 0.252658 0.2522013
## 2114.9 2112.9 2110.9 2108.8 2106.8 2104.8 2102.7
## 1: 0.2521722 0.2523921 0.2527611 0.2534698 0.2545506 0.2557837 0.2572536
## 2100.7 2098.6 2096.6 2094.6 2092.5 2090.5 2088.4
## 1: 0.259068 0.2610668 0.2631638 0.2649927 0.2668558 0.268945 0.2711989
## 2086.4 2084.4 2082.3 2080.3 2078.2 2076.2 2074.2
## 1: 0.2737866 0.2767222 0.2798313 0.2830872 0.2863315 0.2894454 0.2928044
## 2072.1 2070.1 2068 2066 2064 2061.9 2059.9
## 1: 0.296687 0.3006549 0.3047351 0.3094227 0.3146083 0.3205504 0.3275099
## 2057.8 2055.8 2053.8 2051.7 2049.7 2047.6 2045.6
## 1: 0.3350146 0.3432627 0.3527284 0.3635199 0.3759581 0.3903468 0.406487
## 2043.6 2041.5 2039.5 2037.4 2035.4 2033.4 2031.3
## 1: 0.4245726 0.4445577 0.4652808 0.4857983 0.5050242 0.5216759 0.5353383
## 2029.3 2027.3 2025.2 2023.2 2021.1 2019.1 2017.1
## 1: 0.5460196 0.5542056 0.5608922 0.5668865 0.5730138 0.5810183 0.5919769
## 2015 2013 2010.9 2008.9 2006.9 2004.8 2002.8
## 1: 0.6057075 0.6215136 0.6371487 0.6509101 0.6628121 0.6722536 0.6789364
## 2000.7 1998.7 1996.7 1994.6 1992.6 1990.5 1988.5
## 1: 0.6837332 0.6870543 0.6886986 0.6896302 0.6898804 0.6885819 0.6880152
## 1986.5 1984.4 1982.4 1980.3 1978.3 1976.3 1974.2
## 1: 0.6889279 0.6897303 0.6902634 0.6903749 0.6900518 0.6894872 0.6881517
## 1972.2 1970.1 1968.1 1966.1 1964 1962 1959.9
## 1: 0.6847953 0.6798356 0.6743259 0.667933 0.6619502 0.6577308 0.6540996
## 1957.9 1955.9 1953.8 1951.8 1949.8 1947.7 1945.7
## 1: 0.6511117 0.6497398 0.6499001 0.6506879 0.6508807 0.6495761 0.6474292
## 1943.6 1941.6 1939.6 1937.5 1935.5 1933.4 1931.4
## 1: 0.6455458 0.6429656 0.6416749 0.6432763 0.6444253 0.64354 0.6421303
## 1929.4 1927.3 1925.3 1923.2 1921.2 1919.2 1917.1
## 1: 0.6408225 0.6390602 0.6378056 0.6378496 0.6404552 0.6495574 0.6627601
## 1915.1 1913 1911 1909 1906.9 1904.9 1902.8
## 1: 0.6771255 0.6948482 0.7148547 0.7355357 0.7565718 0.7774422 0.796982
## 1900.8 1898.8 1896.7 1894.7 1892.6 1890.6 1888.6
## 1: 0.8138902 0.8281921 0.8416411 0.8539357 0.8647389 0.8757226 0.8849502
## 1886.5 1884.5 1882.4 1880.4 1878.4 1876.3 1874.3
## 1: 0.8923687 0.9008589 0.9089894 0.91483 0.9182107 0.9200395 0.9204667
## 1872.3 1870.2 1868.2 1866.1 1864.1 1862.1 1860
## 1: 0.9197532 0.9181081 0.9130774 0.9067181 0.9029787 0.8968185 0.8830624
## 1858 1855.9 1853.9 1851.9 1849.8 1847.8 1845.7
## 1: 0.8630878 0.8397918 0.8144802 0.7877668 0.7604284 0.7347587 0.7135391
## 1843.7 1841.7 1839.6 1837.6 1835.5 1833.5 1831.5
## 1: 0.6938103 0.6764979 0.6681138 0.6652289 0.6613817 0.6581873 0.6583902
## 1829.4 1827.4 1825.3 1823.3 1821.3 1819.2 1817.2
## 1: 0.659372 0.6632024 0.6737301 0.6854708 0.696447 0.7088509 0.7194676
## 1815.1 1813.1 1811.1 1809 1807 1804.9 1802.9
## 1: 0.7265387 0.733813 0.743332 0.7531476 0.7626001 0.7717848 0.7800118
## 1800.9 1798.8 1796.8 1794.7 1792.7 1790.7 1788.6
## 1: 0.7852439 0.7859122 0.7856979 0.789613 0.7944728 0.7944072 0.7950629
## 1786.6 1784.6 1782.5 1780.5 1778.4 1776.4 1774.4
## 1: 0.7996248 0.7996845 0.7933956 0.7847486 0.7737378 0.7614144 0.7487826
## 1772.3 1770.3 1768.2 1766.2 1764.2 1762.1 1760.1
## 1: 0.7308344 0.7099648 0.6950607 0.6838962 0.6742592 0.663413 0.6503311
## 1758 1756 1754 1751.9 1749.9 1747.8 1745.8
## 1: 0.6424942 0.6376837 0.6329696 0.6301775 0.6257612 0.622558 0.6273794
## 1743.8 1741.7 1739.7 1737.6 1735.6 1733.6 1731.5
## 1: 0.6379182 0.6497558 0.6574647 0.6619542 0.6728814 0.6835651 0.6884136
## 1729.5 1727.4 1725.4 1723.4 1721.3 1719.3 1717.2
## 1: 0.7007347 0.718362 0.7327242 0.7400877 0.7430097 0.7485709 0.7548907
## 1715.2 1713.2 1711.1 1709.1 1707.1 1705 1703
## 1: 0.7632685 0.7793766 0.7983832 0.8142949 0.8253139 0.8301442 0.8372598
## 1700.9 1698.9 1696.9 1694.8 1692.8 1690.7 1688.7
## 1: 0.8511749 0.8630756 0.8832048 0.9099836 0.9296537 0.9451532 0.9548337
## 1686.7 1684.6 1682.6 1680.5 1678.5 1676.5 1674.4
## 1: 0.9632362 0.9720988 0.9703767 0.9695725 0.9780273 0.9838293 0.9748406
## 1672.4 1670.3 1668.3 1666.3 1664.2 1662.2 1660.1
## 1: 0.9609842 0.95664 0.9537789 0.9522406 0.9591398 0.9644592 0.9607282
## 1658.1 1656.1 1654 1652 1649.9 1647.9 1645.9
## 1: 0.9558428 0.9592143 0.9627786 0.944855 0.9308831 0.9454197 0.9661474
## 1643.8 1641.8 1639.7 1637.7 1635.7 1633.6 1631.6
## 1: 0.9770033 0.9858872 0.9945096 1.005947 1.02103 1.032875 1.047728
## 1629.6 1627.5 1625.5 1623.4 1621.4 1619.4 1617.3 1615.3
## 1: 1.068045 1.085088 1.10068 1.118557 1.132558 1.148376 1.167747 1.177166
## 1613.2 1611.2 1609.2 1607.1 1605.1 1603 1601 1599
## 1: 1.181439 1.189113 1.193428 1.191191 1.186874 1.182235 1.175511 1.166149
## 1596.9 1594.9 1592.8 1590.8 1588.8 1586.7 1584.7 1582.6
## 1: 1.15459 1.141558 1.129143 1.118826 1.109511 1.099738 1.088334 1.073457
## 1580.6 1578.6 1576.5 1574.5 1572.4 1570.4 1568.4
## 1: 1.056157 1.041774 1.027006 1.007625 0.997574 0.9953833 0.984488
## 1566.3 1564.3 1562.2 1560.2 1558.2 1556.1 1554.1
## 1: 0.9688963 0.9555764 0.9475166 0.9444385 0.9303682 0.9177717 0.9252619
## 1552.1 1550 1548 1545.9 1543.9 1541.9 1539.8
## 1: 0.9398876 0.9490331 0.9508841 0.9487134 0.9452324 0.9488472 0.9660062
## 1537.8 1535.7 1533.7 1531.7 1529.6 1527.6 1525.5
## 1: 0.9849195 1.009903 1.039598 1.058371 1.068892 1.074303 1.068979
## 1523.5 1521.5 1519.4 1517.4 1515.3 1513.3 1511.3 1509.2
## 1: 1.061176 1.054583 1.047749 1.048933 1.054541 1.055031 1.049165 1.045009
## 1507.2 1505.1 1503.1 1501.1 1499 1497 1494.9 1492.9
## 1: 1.048459 1.050195 1.054166 1.06538 1.078351 1.087872 1.09124 1.092707
## 1490.9 1488.8 1486.8 1484.7 1482.7 1480.7 1478.6 1476.6
## 1: 1.094714 1.093907 1.095388 1.102632 1.109686 1.110165 1.103938 1.096193
## 1474.5 1472.5 1470.5 1468.4 1466.4 1464.4 1462.3 1460.3
## 1: 1.092941 1.094769 1.096534 1.101865 1.111025 1.112091 1.104619 1.101636
## 1458.2 1456.2 1454.2 1452.1 1450.1 1448 1446 1444
## 1: 1.10404 1.102548 1.104718 1.116437 1.130162 1.139601 1.14616 1.153346
## 1441.9 1439.9 1437.8 1435.8 1433.8 1431.7 1429.7 1427.6
## 1: 1.159197 1.163249 1.169926 1.176684 1.185152 1.200418 1.213874 1.219774
## 1425.6 1423.6 1421.5 1419.5 1417.4 1415.4 1413.4 1411.3
## 1: 1.224605 1.230257 1.238636 1.250732 1.258729 1.264017 1.271988 1.280354
## 1409.3 1407.2 1405.2 1403.2 1401.1 1399.1 1397 1395
## 1: 1.287074 1.294225 1.301958 1.307837 1.314378 1.321572 1.327622 1.334741
## 1393 1390.9 1388.9 1386.9 1384.8 1382.8 1380.7 1378.7
## 1: 1.3419 1.35018 1.360281 1.36574 1.367126 1.37245 1.381116 1.386504
## 1376.7 1374.6 1372.6 1370.5 1368.5 1366.5 1364.4 1362.4
## 1: 1.389725 1.395255 1.401417 1.407382 1.413147 1.416379 1.418046 1.417489
## 1360.3 1358.3 1356.3 1354.2 1352.2 1350.1 1348.1 1346.1
## 1: 1.414929 1.414946 1.416894 1.417007 1.415711 1.415545 1.416645 1.416662
## 1344 1342 1339.9 1337.9 1335.9 1333.8 1331.8 1329.7
## 1: 1.412989 1.40474 1.39212 1.379583 1.374229 1.371929 1.363388 1.34961
## 1327.7 1325.7 1323.6 1321.6 1319.5 1317.5 1315.5 1313.4
## 1: 1.336855 1.32644 1.316342 1.303723 1.286369 1.266922 1.249876 1.233412
## 1311.4 1309.4 1307.3 1305.3 1303.2 1301.2 1299.2 1297.1
## 1: 1.213433 1.189988 1.164596 1.139891 1.117976 1.097631 1.077008 1.055666
## 1295.1 1293 1291 1289 1286.9 1284.9 1282.8
## 1: 1.03449 1.014309 0.9949605 0.9765551 0.9601166 0.946182 0.9328504
## 1280.8 1278.8 1276.7 1274.7 1272.6 1270.6 1268.6
## 1: 0.9176705 0.9000382 0.8798357 0.856875 0.8318049 0.8055416 0.7789696
## 1266.5 1264.5 1262.4 1260.4 1258.4 1256.3 1254.3
## 1: 0.7522391 0.7248882 0.6974965 0.6708843 0.6453679 0.6212834 0.5991463
## 1252.2 1250.2 1248.2 1246.1 1244.1 1242 1240
## 1: 0.5795731 0.5623887 0.546556 0.5313795 0.5164368 0.5014066 0.4862332
## 1238 1235.9 1233.9 1231.9 1229.8 1227.8 1225.7
## 1: 0.4711551 0.4561473 0.4409237 0.4258466 0.4117343 0.3993773 0.3896341
## 1223.7 1221.7 1219.6 1217.6 1215.5 1213.5 1211.5
## 1: 0.3832918 0.3803936 0.3800659 0.3814077 0.3840582 0.3878914 0.3925252
## 1209.4 1207.4 1205.3 1203.3 1201.3 1199.2 1197.2
## 1: 0.3973109 0.4016806 0.4055205 0.4088893 0.4117463 0.4138082 0.4152618
## 1195.1 1193.1 1191.1 1189 1187 1184.9 1182.9
## 1: 0.41641 0.4174617 0.4182681 0.4186524 0.4185354 0.4183592 0.4186199
## 1180.9 1178.8 1176.8 1174.7 1172.7 1170.7 1168.6
## 1: 0.4193295 0.4207148 0.4230926 0.4265077 0.4314648 0.4390258 0.45081
## 1166.6 1164.5 1162.5 1160.5 1158.4 1156.4 1154.4
## 1: 0.4698372 0.4996755 0.5386854 0.5721505 0.5782802 0.5539836 0.5193987
## 1152.3 1150.3 1148.2 1146.2 1144.2 1142.1 1140.1
## 1: 0.4920336 0.4752426 0.4653306 0.4591783 0.4556306 0.4537032 0.4527488
## 1138 1136 1134 1131.9 1129.9 1127.8 1125.8
## 1: 0.45264 0.4530876 0.4541757 0.4564499 0.4604871 0.4667877 0.4760741
## 1123.8 1121.7 1119.7 1117.6 1115.6 1113.6 1111.5
## 1: 0.4893965 0.5067351 0.5268102 0.5472615 0.5639021 0.5730795 0.5737542
## 1109.5 1107.4 1105.4 1103.4 1101.3 1099.3 1097.2
## 1: 0.5677071 0.5594865 0.5523421 0.545719 0.5388507 0.531889 0.524775
## 1095.2 1093.2 1091.1 1089.1 1087 1085 1083
## 1: 0.518263 0.512896 0.5080931 0.5035716 0.4997366 0.496511 0.4937072
## 1080.9 1078.9 1076.8 1074.8 1072.8 1070.7 1068.7
## 1: 0.4921822 0.4927377 0.4956594 0.5018623 0.5128586 0.5295364 0.5517834
## 1066.7 1064.6 1062.6 1060.5 1058.5 1056.5 1054.4
## 1: 0.5791399 0.6106418 0.6435356 0.674998 0.704585 0.7314813 0.7549881
## 1052.4 1050.3 1048.3 1046.3 1044.2 1042.2 1040.1
## 1: 0.7768853 0.7975787 0.8165885 0.8352177 0.8528181 0.8682247 0.8836612
## 1038.1 1036.1 1034 1032 1029.9 1027.9 1025.9
## 1: 0.8995727 0.913731 0.9270241 0.9419158 0.9573241 0.9695439 0.9764957
## 1023.8 1021.8 1019.7 1017.7 1015.7 1013.6 1011.6
## 1: 0.9781508 0.9768183 0.9773781 0.9815739 0.9870954 0.9928296 0.9993315
## 1009.5 1007.5 1005.5 1003.4 1001.4 999.3 997.3 995.3
## 1: 1.006669 1.0128 1.015397 1.014144 1.00975 1.003282 0.9946108 0.9839067
## 993.2 991.2 989.2 987.1 985.1 983 981
## 1: 0.9735417 0.9645339 0.956132 0.9487029 0.9416921 0.9332432 0.9251598
## 979 976.9 974.9 972.8 970.8 968.8 966.7
## 1: 0.9203745 0.9169893 0.9125625 0.9085623 0.9066138 0.9061237 0.9058103
## 964.7 962.6 960.6 958.6 956.5 954.5 952.4
## 1: 0.9050562 0.9047009 0.9066653 0.9108105 0.9148113 0.9188726 0.9253743
## 950.4 948.4 946.3 944.3 942.2 940.2 938.2
## 1: 0.9348465 0.9461966 0.958491 0.9712009 0.9823509 0.9887967 0.9911999
## 936.1 934.1 932 930 928 925.9 923.9
## 1: 0.9923388 0.9926874 0.9926212 0.9945093 1.000194 1.008093 1.017442
## 921.8 919.8 917.8 915.7 913.7 911.7 909.6 907.6
## 1: 1.029262 1.041144 1.049601 1.054311 1.055449 1.049562 1.033203 1.009329
## 905.5 903.5 901.5 899.4 897.4 895.3 893.3
## 1: 0.9850855 0.9638402 0.9455262 0.931088 0.9195706 0.9093636 0.9007655
## 891.3 889.2 887.2 885.1 883.1 881.1 879
## 1: 0.8929474 0.8861811 0.8826476 0.8827348 0.8847384 0.8853771 0.8839515
## 877 874.9 872.9 870.9 868.8 866.8 864.7
## 1: 0.8832534 0.8838876 0.8843753 0.884126 0.8840216 0.8848061 0.8858573
## 862.7 860.7 858.6 856.6 854.5 852.5 850.5
## 1: 0.8865796 0.8877847 0.8903769 0.8942684 0.8999804 0.9076024 0.9166541
## 848.4 846.4 844.3 842.3 840.3 838.2 836.2
## 1: 0.9267167 0.9368833 0.9476102 0.9606766 0.9775124 0.996714 1.016719
## 834.2 832.1 830.1 828 826 824 821.9 819.9
## 1: 1.039647 1.06624 1.0959 1.130151 1.169797 1.216309 1.270681 1.32758
## 817.8 815.8 813.8 811.7 809.7 807.6 805.6 803.6
## 1: 1.382659 1.430273 1.445481 1.395426 1.286608 1.165328 1.067809 1.006209
## 801.5 799.5 797.4 795.4 793.4 791.3 789.3
## 1: 0.9770509 0.9705174 0.9812149 1.004687 1.027478 1.032775 1.013031
## 787.2 785.2 783.2 781.1 779.1 777 775
## 1: 0.9769564 0.9404109 0.9135262 0.9012579 0.9041522 0.9197652 0.9432277
## 773 770.9 768.9 766.8 764.8 762.8 760.7
## 1: 0.9653238 0.9799578 0.9878464 0.9923843 0.9947126 0.9927589 0.9871795
## 758.7 756.7 754.6 752.6 750.5 748.5 746.5
## 1: 0.9811397 0.9751622 0.9684627 0.9625272 0.9576369 0.9523183 0.9458433
## 744.4 742.4 740.3 738.3 736.3 734.2 732.2
## 1: 0.9388286 0.9330544 0.9298475 0.9290744 0.9274654 0.9229878 0.9185377
## 730.1 728.1 726.1 724 722 719.9 717.9
## 1: 0.9174708 0.9203739 0.926225 0.9331405 0.9393432 0.9478413 0.9626306
## 715.9 713.8 711.8 709.7 707.7 705.7 703.6
## 1: 0.9832187 1.006982 1.035382 1.071967 1.114598 1.159656 1.210158
## 701.6 699.5 697.5 695.5 693.4 691.4 689.3 687.3
## 1: 1.263396 1.296431 1.285549 1.240254 1.192466 1.157585 1.131266 1.108463
## 685.3 683.2 681.2 679.1 677.1 675.1 673 671
## 1: 1.08635 1.063957 1.04276 1.024641 1.011362 1.002306 0.9939887 0.9817234
## 669 666.9 664.9 662.8 660.8 658.8 656.7
## 1: 0.9667233 0.961104 0.9668172 0.9707398 0.9687711 0.9661812 0.9673088
## 654.7 652.6 650.6 648.6 646.5 644.5 642.4
## 1: 0.971487 0.9748294 0.9759796 0.9778861 0.9823143 0.9851651 0.9842871
## 640.4 638.4 636.3 634.3 632.2 630.2 628.2
## 1: 0.9837391 0.9840354 0.9833273 0.9835184 0.9854859 0.9879117 0.9901843
## 626.1 624.1 622 620 618 615.9 613.9 611.8
## 1: 0.993646 1.001137 1.013614 1.024857 1.03083 1.035325 1.041453 1.047529
## 609.8 607.8 605.7 603.7 601.6 599.6 597.6 595.5
## 1: 1.058421 1.077376 1.09301 1.103226 1.118228 1.132412 1.136551 1.135012
## 593.5 591.5 589.4 587.4 585.3 583.3 581.3 579.2
## 1: 1.140959 1.16393 1.187397 1.202764 1.222412 1.233156 1.241099 1.264126
## 577.2 575.1 573.1 571.1 569 567 564.9 562.9
## 1: 1.286093 1.306753 1.332745 1.345832 1.355993 1.386634 1.425907 1.413305
## 560.9 558.8 556.8 554.7 552.7 550.7 548.6 546.6
## 1: 1.338575 1.273166 1.244596 1.22533 1.193218 1.153975 1.118852 1.0916
## 544.5 542.5 540.5 538.4 536.4 534.3 532.3 530.3
## 1: 1.064162 1.035039 1.02096 1.011657 1.006508 1.032715 1.081272 1.109735
## 528.2 526.2 524.1 522.1 520.1 518 516
## 1: 1.105115 1.058516 1.028691 1.040851 1.03179 0.9974678 0.9752454
## 514 511.9 509.9 507.8 505.8 503.8 501.7
## 1: 0.937062 0.8714066 0.8047704 0.7785948 0.7818117 0.7179397 0.6106296
## 499.7
## 1: 0.5528126
The first column of the first row has still the value 0.1116138.
# Check if dimnames attribute is present
str(attributes(spc_dt))## List of 4
## $ names : chr [1:1716] "3997.4" "3995.4" "3993.3" "3991.3" ...
## $ row.names : int 1
## $ class : chr [1:2] "data.table" "data.frame"
## $ .internal.selfref:<externalptr>
We can e.g. also select the first column by its name, which is commonly known in R as name subsetting
spc_dt[, "3997.4"] # Select first column with wavenumber variable "3997.4"## 3997.4
## 1: 0.1116138
spc_dt[, "3997.4"] == spc_dt[, 1] # both are equivalent## 3997.4
## [1,] TRUE
Applying the same function to all elements of a list: Lists are data structures that allow to store complex, hierarchical objects. Lists are fundamental units when applying functions on each elements using apply family functions. Apply family functions are a specific type of functionals that take functions and other objects as input and return lists or atomic vectors. Note that lists are also vectors. Functionals are an elegant way to solve common data manipulation tasks. A often used functional is lapply(). The functional lapply(X, FUN, ...) applies a function FUN to each of the corresponding elements of X and returns the result as a list of the same length as its input X. The argument ... can be other arguments passed to the function. Let us explore the behavior of lapply() on a simple example. A list shall contain three different the numeric vectors named "a", "b", and "c".
x <- list(
"a" = 1:10,
"b" = c(0.5, 2.3, 5),
"c" = seq(0.1, 1, 0.1)
)
x## $a
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $b
## [1] 0.5 2.3 5.0
##
## $c
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
We can simply calculate the mean value for all the elements (vectors) in the list x by using lapply():
lapply(x, mean) # First argument is X, second is FUN;## $a
## [1] 5.5
##
## $b
## [1] 2.6
##
## $c
## [1] 0.55
# you can also supply arguments explicitly with lapply(X = x, FUN = mean)As you can see, the mean value is computed for the elements 'a, 'b', and 'c' and returned as list.
We can also remove the hierarchy from the list and returning it as named numeric vector using unlist(). unlist() concatenates all elements of all components into a single vector:
mean_v <- unlist(lapply(x, mean))
str(mean_v)## Named num [1:3] 5.5 2.6 0.55
## - attr(*, "names")= chr [1:3] "a" "b" "c"
sessionInfo()## R version 3.4.4 (2018-03-15)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: KDE neon User Edition 5.13
##
## Matrix products: default
## BLAS: /usr/lib/libblas/libblas.so.3.6.0
## LAPACK: /usr/lib/lapack/liblapack.so.3.6.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=de_CH.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=de_CH.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=de_CH.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=de_CH.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] simplerspec_0.1.0 foreach_1.4.4 forcats_0.3.0
## [4] stringr_1.3.1 dplyr_0.7.6 purrr_0.2.5
## [7] readr_1.1.1 tidyr_0.8.1 tibble_1.4.2
## [10] ggplot2_3.0.0 tidyverse_1.2.1
##
## loaded via a namespace (and not attached):
## [1] tidyselect_0.2.4 reshape2_1.4.3 haven_1.1.1
## [4] lattice_0.20-35 colorspace_1.3-2 htmltools_0.3.6
## [7] yaml_2.1.19 rlang_0.2.1 pillar_1.2.2
## [10] foreign_0.8-70 glue_1.2.0 withr_2.1.2
## [13] modelr_0.1.2 readxl_1.1.0 bindrcpp_0.2.2
## [16] bindr_0.1.1 plyr_1.8.4 munsell_0.4.3
## [19] gtable_0.2.0 cellranger_1.1.0 rvest_0.3.2
## [22] codetools_0.2-15 psych_1.8.3.3 evaluate_0.10.1
## [25] knitr_1.20 parallel_3.4.4 broom_0.4.4
## [28] Rcpp_0.12.17 scales_0.5.0 backports_1.1.2
## [31] jsonlite_1.5 mnormt_1.5-5 hms_0.4.2
## [34] digest_0.6.15 stringi_1.2.2 grid_3.4.4
## [37] rprojroot_1.3-2 cli_1.0.0 tools_3.4.4
## [40] magrittr_1.5 lazyeval_0.2.1 crayon_1.3.4
## [43] pkgconfig_2.0.1 data.table_1.11.4 xml2_1.2.0
## [46] lubridate_1.7.4 assertthat_0.2.0 rmarkdown_1.9
## [49] httr_1.3.1 rstudioapi_0.7 iterators_1.0.9
## [52] R6_2.2.2 nlme_3.1-137 compiler_3.4.4