In the following, we use the array [x,y] to represent the complex number x + iy, but the following functions also accept a number wherever a complex number is acceptable. It should be look like: Column-1 Column-2 Column-3 Column-4 Column-5 value-1 value-2 value-3 value-4 value-5. Paste Special Transpose | Transpose Function. The transpose of matrix A is written A T. Pandas is a Python library that allows users to parse, clean, and visually represent data quickly and efficiently. Ill try to dynamically figure out the. spinning_plate's answer is conceptually easier to follow for someone new to Python, though not as efficient as it could be. The Python concept of importing is not heavily used in MATLAB, and most of MATLAB’s functions are readily available to the user at the top level. Reshape using Stack() and unstack() function in Pandas python When more than one column header is present we can stack the specific column header by specified the level. In MATLAB®, every function must be in a file of the same name, and you can't define local functions in an ordinary script file or at the command-prompt (inlines are not real functions but macros, like in C). To run in matlab, I wrote the primal in AMPL, saved the MPS file, loaded it into matlab, took the transpose, then assigned it to dual. A solution that’s been working well for me (and is fully implemented in Python) is to use SymPy to set up the basic transform matrices, from each joint to the next, and then use it’s derivative function to calculate the Jacobian. Let’s see how to Transpose the data from rows to columns and from columns to rows pandas. No duplicate members. Method 2- Use Transpose Function Say you have 5 rows and 4 columns, that you want to transpose. Python is a strongly-typed and dynamically-typed language. To practice all test questions on Python, here is complete set of 1000+ Multiple Choice Questions and Answers. Numba-compiled numerical algorithms in Python can approach the speeds of C or FORTRAN. __class__ is int or some class derived from int. Use the 'Paste Special Transpose' option to switch rows to columns or columns to rows in Excel. Python | Numpy numpy. To run in matlab, I wrote the primal in AMPL, saved the MPS file, loaded it into matlab, took the transpose, then assigned it to dual. This is an Google’s research project where you can execute your code on GPUs, TPUs etc. I've written the core functions for a basic 2048 game. transpose_tiled_even. float64 precision. Hermitian matrices are a useful generalization of symmetric matrices for complex matrices A matrix m can be tested to see if it is symmetric using the Wolfram Language code: SymmetricQ[m_List?MatrixQ] := (m === Transpose[m])Written. 99e-23 in Python. unstack() function in pandas converts the data into unstacked format. Pandas series is a One-dimensional ndarray with axis labels. The description here applies to the default and "data. 05 is now available for download. The element at ith row and jth column in X will be placed at jth row and ith column in X'. The transpose of a matrix makes each row into a column. One or more valid python statements that make up the function. 48 videos Play all Data Manipulation and Processing with Python Noureddin Sadawi Program to Transpose a Matrix in C (HINDI) - Duration: 19:25. The type of the resulting array is deduced from the type of the elements in the sequences. Curly braces or the set() function can be used to create. First, let's begin with sine function where we will learn to plot its graph. Python-pres. else: return b. This post will cover several topics. 'Gnumeric' is a module that exists only within Gnumeric, and which defines the Gnumeric Python API. * COUNTs all the rows in the target table whether or not they include NULLs. I created the function due to the need of capturing different number instances from a large CSV file. ndarry transpose of a matrix can be. But given the question title ("Transposing a NumPy array") I suspect many visitors will come here looking for a more generic solution and I wanted to warn them that it is not applicable to 2D arrays. Python for VBA users – 5; Using built in numpy functions. Otherwise, it would be a very time consuming task. Let’s understand it by an example what if looks like after the transpose. Data is 10000x3072 numpy array of uint8s. python sum of digits in a string sum of digits python recursive sum of the digits of a given number in python digit_sum python python program to find sum of n numbers python program to find sum of digits using for loop write a python script to find sum of each digit in the. Transpose the dataframe in pandas - Python: T is the function used to transpose the dataframe in pandas python. Python-Like enumerate() In C++17 November 24, 2018 · Coding · Comments Python has a handy built-in function called enumerate() , which lets you iterate over an object (e. I would like to use Array[] or a similar function that gives out a list of vector-like functions evaluated at different numbers. 2 on the same machine where Python was run. The Excel transpose method has an undocumented limit on the number of cells it can transpose (depends on the Excel version). tensor and transpose (Python recipe) by bearophile - Two functions useful when you don't use a numerical library. For memory-efficient iterators, you can omit the outer list and tuple calls for the respective solutions. IMPORTANT: Determine the rows and columns of your data. Use TRANSPOSE to shift the vertical and horizontal orientation of an array or range on a worksheet. I want to be able to solve the dual. Python-pres. Function naming follows the same rules of writing identifiers in Python. It differs from the NumPy package in the user interface, which is more oriented toward linear algebra and for interactive use. Reading and Writing Images The Python Imaging Library supports a wide variety of image file formats. pandas Flexible and powerful data analysis / manipulation library for Python, providing labeled data structures similar to R data. sum(a) returns the sum of all elements of a, independent of the numer of dimensions of a. Matrix addition function load file Matrix multiplication Matrix transpose Matrix identity Matrix Inverse Inverse Matrix with Marquardt method Matrix operation with malloc Matrix transpose with malloc Fast Fourier Transform (FFT) Format SEGY Header Dumper Python for Geophysicist Python Installation Plot XY Python Plot Surface 2D Python Plot XYZ. Using Google products, like Google Docs, at work or school? Try powerful tips, tutorials, and templates. "Your interpretation of physical objects has everything to do with the historical trajectory of your brain – and little to do with the objects themselves. concatenate). index(‘p’) you would get zero as output (first index). melt() Function in python pandas depicted with an example. 12) from the reshape module in Pandas. As a convenience for parameters U, X0: Numbers (scalars) are converted to constant arrays with the correct shape. Ask Question alternative passing mostly static variables w/ 1 dynamic variable to an external function (COM) instead of a for loop in Python. WorksheetPages ('Book1'). I would like to see if there is a more efficient way of doing this since I feel the way I did might not be the most efficient one. They are optional. So if X is a 3x2 matrix, X' will be a 2x3 matrix. The only guaranteed way to ensure that a free variable in python function scope (it's not a closure) does not change is to pass it explicitly as a default value. Fixing the rotated image "cut off" problem with OpenCV and Python. Then in another for loop the value of ‘i’ variable is initialized to zero and checks the condition that the value of ‘j’ variable is less than the order of row defined in ‘m’ variable. We will use the Python programming language for all assignments in this course. So, this PEP deliberately does not try and innovate Python's type syntax. For example, the following is a 2X3 matrix (meaning the height of the matrix is 2 and the width is 3): To be transposed the the jth item in the ith index should become the ith item in the jth index. If we were to give it another name as part of exposing it in the api, I'd prefer conv_2d_transpose or some such and having documentation that some sources mistakenly refer to that op as deconvolution. Re: Vlookup with Transpose not sure about your your data format, based on your description it looks like HLOOKUP is the way to go, but if this doesn't solve the issue post back with sample data before and after the transpose and the expected results. This is very similar to melt in the R reshape library. Get the absolute value of column in pandas python; Transpose the dataframe in pandas Python; Get the data type of column in pandas python; Check and count Missing values in pandas python; Convert column to categorical in pandas python; Round off the values in column of pandas python; Ceil and floor of the dataframe in pandas python – Round up and Truncate. lapply(ll, function(x) is. In this post I show how you can get started with Tensorflow in both Python and R Tensorflow in Python. Memory efficient alternative passing mostly static variables w/ 1 dynamic variable to an external function (COM) instead of a for loop in Python 6 Sparse matrix compressed sparse row (CSR) in Python 2. Unpivoting Data With Python and pandas There are a few ways of achieving the desired result in Python but my current favorite is to use the “melt” function (in pandas 0. step_response(sys, T=None, X0=0. Jackknife estimate of parameters¶ This shows the leave-one-out calculation idiom for Python. Python’s SciPy Module. a_is_sparse: If True, a is treated as a sparse matrix. Pandas Cheat Sheet — Python for Data Science Pandas is arguably the most important Python package for data science. Gerhard Häring I guess any single-liner will be obfuscated Python and not necessarily any more efficient. pdf), Text File (. x matrix or ask your own question. NumPy (pronounced / ˈ n ʌ m p aɪ / (NUM-py) or sometimes / ˈ n ʌ m p i / (NUM-pee)) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. Do you have any quick way to solve it? Here the Transpose Range function in Kutools for Excel can handle all above jobs easily. Categorical function is used to convert integer or character column to categorical in pandas python. frame(c(A, B)), by appending. Click the cell where you want the transposed cells to begin. Not only does it give you lots of methods and functions that make working with data easier, but it has been optimized for speed which gives you a significant advantage compared with working with numeric data using Python’s. transpose function. ListenData offers free analytics and data science tutorials covering topics such as SAS, R, Python, Advanced Excel, VBA, SQL, Predictive Modeling. Transpose of a matrix is the interchanging of rows and columns. NumPy arrays are used to store lists of numerical data and to represent vectors, matrices, and even tensors. A complete matplotlib python histogram Many things can be added to a histogram such as a fit line, labels and so on. com SciPy DataCamp Learn Python for Data Science Interactively Interacting With NumPy Also see NumPy The SciPy library is one of the core packages for scientific computing that provides mathematical. cython python python3 python2 numpy remap remapping array-manipulations renumbering transpose in-place in-place-transposition looping masking biomedical-image-processing. It's common when first learning NumPy to have trouble remembering all the functions and methods that you need,. Please note that for those who prefer, this list is mirrored to the Usenet newsgroup comp. transpose(). I had to create a function that would combine multiple list elements of the same size into a single one. rotate_bound to solve the issue (although back then I had not created the imutils Python package — it was simply a utility function in a helper file). Return Statement in Python. Pillow is a fork of the. The primary reason for supporting this API is to reduce the learning curve for an average Python user, who is more likely to know Numpy library, rather than the DML language. pdf), Text File (. The cost function here is the same as in the case of Polynomial Regression [1]. Array Creation. In the Python code we assume that you have already run import numpy as np. x, the xrange() function has been renamed to range(). tuple, list, or numpy arrays. py #-----import stdio import sys import stdarray # Accept integer command-line argument n. From the first output of proc print, we see that the data now is in long format except that we don’t have a numeric variable indicating year; instead; we have a character variable that has information on year in it. The TRANSPOSE function must be entered as an array formula in a range that has the same number of rows and columns, respectively, as the source range has columns and rows. Using list comprehension in functions Now, let's see how we can use list comprehension in functions. This document lists the linear algebra routines of the n-dimensional array package:n-dimensional array package:. This problem is straight forward with python. import excelpy. There has been some desire for something like this, so here goes. transpose() Transpose. Python Program to find transpose of a matrix Transpose of a matrix is obtained by changing rows to columns and columns to rows. Join Dennis Taylor for an in-depth discussion in this video Calculate loan payments and investments with PMT and FV functions, part of Excel Tips Weekly Lynda. Like, in this case, I want to transpose the matrix2. You can not delete a part of the result. But given the question title ("Transposing a NumPy array") I suspect many visitors will come here looking for a more generic solution and I wanted to warn them that it is not applicable to 2D arrays. sum(a) returns the sum of all elements of a, independent of the numer of dimensions of a. This works fine as long as the elements in each column have the same (or similar) lengths; if not, the output can get pretty messy. So if X is a 3x2 matrix, X' will be a 2x3 matrix. The TRANSPOSE procedure can often eliminate the need to write a lengthy DATA step to achieve the same result. Mask A boolean object used for selecting data from another object. CasADi Python cheatsheet dense sparse SX sym SX. But None has to be the fill value. The function’s parameters list need to be the same as the object’s attributes list. Symbol API; Random Distribution Generator Symbol API; Linear Algebra Symbol API; Sparse Symbol API; Contrib Symbol API; RNN Cell. Let's take a matrix X, having the following elements:. groovy equivalent of python zip function?. Securing Web Applications before Deployment. seq must be an object which has a __reversed__() method or supports the sequence protocol (the __len__() method and the __getitem__() method with integer arguments starting at 0). You might also want to check out ipython, which is just a different interface to the python toplevel. For example, if A(3,2) is 1+2i and B = A. The whole worksheet can be transposed, or you can opt to transpose only part of the worksheet. sym("x",n,m) SX. Python also includes a data type for sets. TransformedDistribution, tfb. It implements basic matrix operators, matrix functions as well as converters to common Python types (for example: Numpy arrays, PySpark DataFrame and Pandas DataFrame). Pandas for structured data operations and manipulations. Let's take a matrix X, having the following elements:. The parameters of the function will be automatically filled from the attributes of the object passed in the endpoint call. So, these parameters, theta_0, theta_1, theta_2, …, theta_n have to assume such values for which the cost function (or simply cost) reaches to its minimum value possible. Reshape long to wide in pandas python with pivot function Reshaping a data from long to wide in python pandas is done with pivot() function. Transpose a matrix means we’re turning its columns into its rows. Click Worksheet: Transpose and open the wtranspose dialog box, which utilizes the wtranspose x-function. While Python is a robust general-purpose programming language, its libraries targeted towards numerical computation will win out any day when it comes to large batch operations on arrays. Distribution, a tfb. Poor-man’s vector operations: the map () built-in function: >>> map (lambda x : 3*x, [1, 2, 3]) [3, 6, 9] lambda is for an anonymous function, x the input argument, and 3*x the function and the return argument. Pandas is a Python library that allows users to parse, clean, and visually represent data quickly and efficiently. in is an educational website for programming subjects like C, C++, Java etc. Note that for most machine learning problems, is very high dimensional, so we don't be able to plot. Let's see how to Convert column to categorical column. Here we will see 9 important and […] Filed Under: Linear Algebra with NumPy , numpy eye Tagged With: Linear Algebra with NumPy , numpy eye , numpy matrix inverse. NumPy and SciPy were created to do numerical and scientific computing in the most natural way with Python, not to be MATLAB® clones. 93 "Or you can provide it in kwargs as model=. Accelerate Python Functions. com Ph: 998 570 6789 Whatsapp: 7799 83 6789 Pet Project Functions Purpose of a function Defining a function Calling a function Function parameter passing Formal arguments. transpose - Function. Note that, during the operation number of rows and columns are swapped;. in particular, as a reference in probability theory we Mathematics For Engineering Basic Algebra mathematics for engineering basic algebra tutorial 4 – areas and volumes this is the one of a series of basic. transpose function | transpose function excel | transpose function | transpose function in excel | transpose function vba | transpose function r | transpose fun Toggle navigation Keyosa. It reflect the DataFrame over its main diagonal by writing rows as columns and vice-versa. vectorize() function. Returns: composition: A tfd. ' returns the nonconjugate transpose of A, that is, interchanges the row and column index for each element. Array Creation. Hello again, The following function does not seem to be available in Python: vnl_matrix< double > Pinv; Pinv =. Array Formulas and Functions The worksheet formulas that we described in Excel Spreadsheets return a single value that is assigned to the cell that contains the formula. Transpose a Matrix Multiply two matrices Using nested lists as a matrix works for simple computational tasks, however, there is a better way of working with matrices in Python using NumPy package. Python | datetime. Curly braces or the set() function can be used to create. The correct shape is inferred from arguments sys and T. When an array is no longer needed in the program, it can be destroyed by using the del Python command. Transpose the dataframe in pandas - Python: T is the function used to transpose the dataframe in pandas python. This can be accomplished by means of Excel’s TRANSPOSE array function using the following steps: Note that the output range (step 1) must be of the right size. Years later I’m still learning new things about it!. , the result is a 1-row matrix. I'm trying to create a matrix transpose function in Python. Paste Special Transpose. transpose(). Transpose of a matrix is formed in two steps. It will at times be useful to load data into vanilla NumPy arrays using np. Paste Special Transpose | Transpose Function. A new matrix is obtained the following way: each [i, j] element of the new matrix gets the value of the [j, i] element of the original one. In order to get the transpose of the matrix first, we need to unzip the list using * operator then zip it. matplotlib. NumPy arrays are designed to handle large data sets efficiently and with a minimum of fuss. The associated pixel and mask values and coordinate system are transposed. Set objects also support mathematical operations like union, intersection, difference, and symmetric difference. Get the absolute value of column in pandas python: abs is the function used to get the absolute value of the column in pandas python. If you are new to Python, you may be confused by some of the pythonic ways of accessing data, such as negative indexing and array slicing. Linear Algebra Operations¶. I think the easiest answer is that MATLAB is not free. Python is a dynamic language (did I already said that?) and as such, already implements, or makes it easy to implement, a number of popular design patterns with a few lines of code. Transpose of a matrix is formed in two steps. Neither Python itself nor the standard library use function annotations in any way; this section just shows the syntax. This matrix does not have to be a square matrix. The final theta value will then be used to plot the decision boundary on the training data, resulting in a figure similar to the figure below. adjoint_b: If True, b is conjugated and transposed before multiplication. Pivot() function in pandas is one of the efficient function to transform the data from long to wide format. Transpose Matrix | Transpose a matrix in Single line in Python - Transpose of a matrix is a task we all can perform very easily in python (Using a nested loop). The list arguments may be any kind of sequence, and the result is always a list. Dimension also changes to the opposite. …In the range of B3. ceil(), math. From the python documentation on np. Transpose (). Transpose Matrix | Transpose a matrix in Single line in Python - Transpose of a matrix is a task we all can perform very easily in python (Using a nested loop). When rows and columns of a matrix are interchanged, the matrix is said to be transposed. input: documento idade sexo exame componente resultado especialidade_atendimento x 58 m clearance de creatinina - dce altura 1. and more accurate than the version provided in the Scientific Python package in Scientific. Here is a matrix and its transpose: The superscript "T" means "transpose". Introduction. I am trying to create a matrix transpose function for python but I can't seem to make it work. timedelta() function Transpose a matrix in Single line in Python Transpose of a matrix is a task we all can perform very easily in python (Using a nested loop). Overview: TRANSPOSE Procedure. I don't know the case with other programming languages. Here I will make use of Pandas. Matrix addition function load file Matrix multiplication Matrix transpose Matrix identity Matrix Inverse Inverse Matrix with Marquardt method Matrix operation with malloc Matrix transpose with malloc Fast Fourier Transform (FFT) Format SEGY Header Dumper Python for Geophysicist Python Installation Plot XY Python Plot Surface 2D Python Plot XYZ. Reshape wide to long in pandas python with melt() function Reshaping a data from wide to long in pandas python is done with melt() function. As time goes on, you'll learn to appreciate NumPy more and more. Any groupby operation involves one of the following operations on the original object. m'') in which the function is stored. By now, you will have already learned that NumPy, one of the fundamental packages for scientific computing, forms at least for a part the fundament of other important packages that you might use used for data manipulation and machine learning with Python. A simple example The following function calculates the sum of the diagonal elements of a two-dimensional array, verifying that the array is in fact two-dimensional and of type PyArray_DOUBLE. Note that for most machine learning problems, is very high dimensional, so we don't be able to plot. Extract year from given date. The zip() function in Python programming is a built-in standard function that takes multiple iterables or containers as parameters. ' returns the nonconjugate transpose of A, that is, interchanges the row and column index for each element. Rotation matrices satisfy A’A = 1, and consequently det(A) = 1. transpose() Transpose. You can easily switch your column and row layout in an Excel spreadsheet by using the Paste Special - Transpose feature. Python histogram. ifc according to our previous script you will see that the wall is still at 0,0,0 which is wrong. Interview Top Interview Questions Easy Collection #. transpose() function return. Keras backends What is a "backend"? Keras is a model-level library, providing high-level building blocks for developing deep learning models. For more information, including a complete list of supported POLSAR sensors and data products, follow the link to SARINGEST under Related functions at the end of this topic. 3 | March 12, 2002 | Fredrik Lundh, Matthew Ellis Introduction The Python Imaging Library adds image processing capabilities. arg_scope). __neg__() that is closely related to its own inverse. Step 1: Copy the data. So Python 3. The description here applies to the default and "data. ) For a 2-D array, this is the usual matrix transpose. We will use the Python programming language for all assignments in this course. Excel also allows you to define a formula that assigns values to a range of cells at the same time. If you would run x. The Java program is successfully compiled and run on a Windows system. NumPy (pronounced / ˈ n ʌ m p aɪ / (NUM-py) or sometimes / ˈ n ʌ m p i / (NUM-pee)) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. For example, the following is a 2X3 matrix (meaning the height of the matrix is 2 and the width is 3): To be transposed the the jth item in the ith index should become the ith item in the jth index. NumPy is widely used to handle multidimensional arrays, unlike Python’s array class which can handle only unidimensional array. (To change between column and row vectors, first cast the 1-D array into a matrix object. The first one creates a tensor, hopefully in the. Hello again, The following function does not seem to be available in Python: vnl_matrix< double > Pinv; Pinv =. It takes a function and an iterable as arguments. 0, input=None, output=None, transpose=False)¶ Step response of a linear system. Array duplicates: If the array contains duplicates, the index() method will only return the first element. The zip() function is used to map the same indexes of more than one iterable. genfromtxt. Categorical function is used to convert integer or character column to categorical in pandas python. Basic Python programs. 2 z01 x 58 m clearance de creatinina - dce creatinina no sangue 1. The transpose of a matrix makes each row into a column. NumPy code is Python code, so it has no such restrictions. $ python for. Matrix Transpose. Create an n-by-n array and # write it to standard output. ' does not affect the sign of the imaginary parts. ListenData offers free analytics and data science tutorials covering topics such as SAS, R, Python, Advanced Excel, VBA, SQL, Predictive Modeling. Your task now is to construct a Python function called transpose which expects one argument: a two-dimensional table representing a matrix. NumPy arrays are used to store lists of numerical data and to represent vectors, matrices, and even tensors. python programacion. Searching Sorted Lists¶. 3 | March 12, 2002 | Fredrik Lundh, Matthew Ellis Introduction The Python Imaging Library adds image processing capabilities. frame" methods. Mastering Python Lists. It does so using a number of relevant examples from current problems, including data analytics and. concatenate). Ashwini's answer is much more concise and much quicker, but. I have a very basic question which relates to Python, numpy and multiplication of matrices in the setting of logistic regression. NumPy arrays are used to store lists of numerical data and to represent vectors, matrices, and even tensors. As the documentation indicates, if the first argument is None, the identity function is used as the function through which the arguments are mapped. Reflect the DataFrame over its main diagonal by writing rows as columns and vice-versa. If we take the transpose of the transpose matrix, the matrix obtained is equal to the original matrix. Depending on the formula, the return value of INDEX may be used as a reference or as a value. There are various special functions available in numpy such as sine, cosine, tan, log etc. Do you have any quick way to solve it? Here the Transpose Range function in Kutools for Excel can handle all above jobs easily. In this article, you will learn how to transpose numpy array in python using transpose() function. Here I will make use of Pandas. The output of this program is the same as above. com e 3 Table of Contents Python Introduction 13. Turned backward in position, direction, or order: the reverse side of the poster. This happens even if the number divides evenly. Introduction. See this. Layers (0) Col = wks. Considering when to reverse and when to transpose is the hardest part of this easy-to-implement solution. The TRANSPOSE procedure creates an output data set by restructuring the values in a SAS data set, transposing selected variables into observations. How and when do I use for loops under Python programming language? A for loop is a Python statement which repeats a group of statements a specified number of times. Expression made up of a single constant, variable, scalar function, or column name and can also be the pieces of a SQL query that compare values against other values. To transposes a matrix on your own in Python is actually pretty easy. Distribution, a tfb. Sebastian's answer, if you have a list of lists with different lengths, check out this great post from ActiveState. Each pyplot function makes some change to a figure: e. transpose (self, *args, **kwargs) [source] ¶ Transpose index and columns. Numpy function array creates an array given the values of the elements. The associated pixel and mask values and coordinate system are transposed. deepcopy(model. The relevant packages are Ada. For example, the following is a 2X3 matrix (meaning the height of the matrix is 2 and the width is 3):. Producing well-formatted output in a script can be a pain, especially if you want to output a large number of variables per record. Python for VBA users – 5; Using built in numpy functions. A supremely-optimized, well-maintained scientific computing package for Python. Learn from a team of expert teachers in the comfort of your browser with video lessons and fun coding challenges and projects. pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language. x's range function is xrange from Python 2. Reading and Writing Images The Python Imaging Library supports a wide variety of image file formats. the input and output are separate arrays in memory. Note that contrary to usual python slices, both the start and the stop are included A boolean array of the same length as the axis being sliced, e. The labels need not be unique but must be a hashable type. In Python, data is almost universally represented as NumPy arrays. transpose(*axes)¶. There is red, aquamarine, indigo.

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