The Metal Performance Shaders framework contains a collection of highly optimized compute and graphics shaders that are designed to integrate easily and efficiently into your Metal app. 686 mg/g at 23 °C). You may assume that A's column number is equal to B's row number. Function M-files. A reader, Ismael V. The entry point to programming Spark with the Dataset and DataFrame API. Domain decomposition methods are widely used to solve in parallel. The value of DefaultFigurePosition must be a four element vector with the x and y coordinates for the figure, followed by its width and height. kl is the first subdiagonal containing a nonzero band, ku is the last superdiagonal containing one, and m is the first dimension of the matrix AB. class pyspark. Arg1 Object Object Object. jack_miniFMsynth reacts on pitchbender and modulation wheel events. The matrix is sparse, representing a weighted adjacency matrix , and only the weights shall be subject to. To permanently change the song, select Save. Szyld1 Temple University {szyld|loisel}@temple. Although one could argue which language is "better" or clearer overall, the SPL routine is understood very easily by those familiar with C/C++. /O1 sets a combination of optimizations that generate minimum size code. Fixed a bug that freepiano uses C5 as middle C. Changelog, Rules & FAQ, updates: @vimgolf, RSS. How to cite this article: Lécuyer T, Teston E, Ramirez-Garcia G, Maldiney T, Viana B, Seguin J, Mignet N, Scherman D, Richard C. Transpose means changing rows of 2D array into columns and columns into rows. 4/53 for 32 by 32, 64 by 64 and 61 by 67 matrices - prash628/Optimized-Cache-Efficient-Matrix-Transpose. For supervised learning, models are optimized by finding optimal coefficients that minimize cost function. Start-up and warm-up times are negligible, compile times are in the microsecond to millisecond range and the typical performance of compiled LuaJIT programs is close to the one of C/C++. One of the most widely used alternatives to prevent this is the ReLU function. Because the TRANSPOSE function is only used in array formulas, and that's how you finish an array formula. MATLAB Library function mapping Over 300+ MATLAB functions are optimized for CUDA code generation. How to transpose a matrix in c, Transpose matrix program. Use the getLatency function to find the latency of a particular configuration. Transpose a matrix. Finding the transpose of a matrix in C is a popular tutorial under “array”. A reader, Ismael V. Heapsort is a comparison-based sorting algorithm to create a sorted array (or list), and is part of the selection sort family. The columns match the index of the Series returned by the applied function. The /O options control various optimizations that help you create code for maximum speed or minimum size. Script 2 displays a T-SQL code that can be used to transpose rows into columns using the Cursor function. Matrices and Linear Algebra The Wolfram Language automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly optimized algorithms. However, there are a few simple tricks that can make a big difference to the speed of your code. In essence, we just have simplified the cost function in order to use geometry for further steps. 0 B In contrast to digital IIR filter design, the classical design of analog (conic hull), denoted by conv (C ) (cone (C )), is the smallest convex IIR filters looks rather complete, so there is not much further devel- set (cone) in n that contains C. It basically gives the idea of matrix inputting, manipulating and outputting using the standard input/output functions of the C language. Depending on the options used with mkoctfile, the compiled code can be called within Octave or can be used as a stand-alone application. This page aims to provide an overview and some details on how to perform arithmetic between matrices, vectors and scalars with Eigen. At runtime, the autograder will evaluate each registered transpose function and print the results. C program to multiply two matrices using function. Siddharth (view profile) Step 2: A transpose of resultant of step 1 is taken, which. An alternative is to employ the pinv function available in the pracma package. By considering the smallest, medium, and biggest values as the center of the input pattern, each unit in the input pattern has a triangular Gaussian membership function as its inner function, given by Eqs. A slightly different version of this article appeared in the January 1986 issue of Computer Language magazine; this article is reprinted with permission. Nathan Kutz y Abstract. transpose (boolean, optional, default=0) – Use transpose of input matrix. Fast er c ode via stat ic t ypin g an d Usi ng C ytho n wi th N umP y in Cython documentation. 8670477],[3. smoothstep(min, max, x) For values of x between min and max, returns a smoothly varying value that ranges from 0 at x. el can edit html documents that embed server blocks (PHP / JSP / Twig / Django / erb / selmer) and client parts (JavaScript / Css). A POLYNOMIAL-BASED NONLINEAR LEAST SQUARES OPTIMIZED PRECONDITIONER FOR CONTINUOUS AND DISCONTINUOUS ELEMENT-BASED DISCRETIZATIONS OF THE EULER EQUATIONS L. Create the translation and rotation vectors from the simulated state. * trans - A simple baseline transpose function, not optimized for the cache. CULA Dense provides accelerated implementations of the most popular and essential routines for dense linear algebra in a prepackaged library. A 1-d sigma should contain values of standard deviations of errors in ydata. The user will enter the order of a matrix and then its elements and similarly inputs the second matrix. However, there are a few simple tricks that can make a big difference to the speed of your code. It takes a function that is used to combine the overlapping values. Using many original methods, the Wolfram Language can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. Learn more about python, numpy, ndarray MATLAB. In the later case, rownames become variable (column) names. The mkoctfile function compiles source code written in C, C++, or Fortran. How to get the value from URL parameter? How to get the value from URL parameter? This is a very common tip in web development. The main component of a Merkle-Damg ard hash function his a compression function C: f0;1gp f 0;1gm!f0;1gp. This program takes a matrix of order r*c from the user and computes the transpose of the matrix. We introduce a method for constructing a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. This program takes a matrix of order r*c from the user and computes the transpose of the matrix. For further details, please see our FAQs. They do not change the image content but deform the pixel grid and map this deformed grid to the destination image. Note: If you have a current version of Office 365, then you can simply enter the formula in the top-left-cell of the output range, then press ENTER to confirm the formula as a dynamic array formula. At this time, Keras has three backend implementations available:. LeetCode – Sparse Matrix Multiplication (Java) Given two sparse matrices A and B, return the result of AB. transpose (boolean, optional, default=0) – Use transpose of input matrix. It is obtained by interchanging rows and columns of a matrix. By default, a CRF file stores each multidimensional slice in a separate folder and each slice is chunked into tiles. These options are marked ’T’ on the output of ffmpeg-h filter=. [Numpy-discussion] numarray interface and performance issues (for dot product and transpose) [Numpy-discussion] numarray interface and performance issues (for dot. You can use the Capo popup to define a fret for a capo. Because the TRANSPOSE function is only used in array formulas, and that's how you finish an array formula. LuaJIT includes the FFI library which allows to call C function directly. from C to A, but 0 paths of length three from A to J," and the \3" entry below that corresponds to \there is 1 path of length one from C to B, and 3 paths of length three from B to J. Includes simple test programs, as well. The displayed view shows the UAV translating in the Y-direction and losing. Fast er c ode via stat ic t ypin g an d Usi ng C ytho n wi th N umP y in Cython documentation. Pyth on I s No t C: Tak e Tw o. Convert python numpy array to double. For each element it will create a variable in the current symbol table. Anonymous function should be used very sparingly, and should have relatively small bodies. html#ArocenaM98 journals/jodl/AbiteboulCCMMS97 conf. icc (ifort) comes with optimized math libraries •libimf (scalar) and libsvml (vector) •Faster than GNU libm •Driver links libimf automatically, ahead of libm •More functionality (replace math. Use the t() function to transpose a matrix or a data frame. Instead of passing a function pointer as an argument to a function, pass a function-object (or, if using the C++11 standard, a lambda expression). 03/09/2017; 23 minutes to read +4; In this article. You will only need three loops. Or do it the other way around and read in columns while writing linearly. If A contains complex elements, then A. # ===== import numpy as np import cntk as C from. Here is the hypothesis for Linear Regression model. Machine-specific optimized BLAS libraries are available for a variety of computer architectures. Due to the version of. I am sure it can be optimized further, and will look at that in the morning. As I knew Haskell probably had this in its standard library and I'm lazy, I hoogled “transpose” and followed the link to its source code, then translated it to F#:. The extract() function imports variables into the local symbol table from an array. It is a special case of insertBy, which allows the programmer to supply their own comparison function. To compute the inverse Z-transform, use iztrans. In other words, transpose of A[][] is obtained by changing A[i][j] to A[j][i]. the function copies a horizontal range of cells into a vertical range and vice versa). ' returns the nonconjugate transpose of A, that is, interchanges the row and column index for each element. Typically, a convolutional layer is combined with an activation function and max pooling. Keras is a model-level library, providing high-level building blocks for developing deep learning models. Of course, one of the registered functions must be. This optimization is tricky. GIRALDO Abstract. If the first argument contains a symbolic function, then the second argument must be a scalar. Setting the scene. An efficient procedure for recovering spectral reflectance using an object’s tristimulus values under multi-illuminants is proposed by adapting with the characteristics of the testing sample to obtain the transformation matrix of pseudoinverse. This reduces resources used by the function, but negatively impacts performance. correlate function is several times faster than our implementation in C. Each variable in T becomes a column of cells in C. This is the case when bead sort is implemented without a mechanism to assist in finding empty spaces below the beads, such as in software implementations. "Helping to build a cathedral," said the third. Premature optimization is the root of all evil. Changelog, Rules & FAQ, updates: @vimgolf, RSS. Transposing is used in final stage of every loop (they also optimized by multi-thread, but tasks can be really much). See the complete profile on LinkedIn and discover Diane(Dan. NET i'm using, i can't use Tuple and I can't use a Dictionnary because my keys would actually be a string, which is impossible. Because the TRANSPOSE function is only used in array formulas, and that's how you finish an array formula. 65947664],[3. Both mean and var returns a scalar by treating the input as a vector. I need to optimize the transpose of 8x4 and 4x8 float matrices with AVX. MATMUL can do this for a variety of matrix sizes, and for different arithmetics (real, complex, double precision, integer, even logical!). The lowest value obtained showed that the window size applied was optimized. Note that a direct implementation following Figures 1 and 2 shall read and write the 3D image object three times. I have a matrix transpose function that takes arrays with a possibly different number of rows and columns. A function M-file, however, is the "meat and potatoes" of Matlab, allowing you to turn a script into a multi-purpose, reusable, honest-to-goodness program. where U_i are r_i×c matrices of singular vectors, Σ are c×c matrices singular values, and V is a c×c matrix of singular vectors. CUDA kernels syntax is Julia syntax for arrays (real multi-dim arrays). This program takes a matrix of order r*c from the user and computes the transpose of the matrix. vector dot and matrix multiplication) are the basic to linear algebra and are also widely used in other fields such as deep learning. C Program to Find Transpose of a Matrix This program takes a matrix of order r*c from the user and computes the transpose of that matrix. the factor by which you speedup the function. 686 mg/g at 23 °C). Machine-specific optimized BLAS libraries are available for a variety of computer architectures. 4 for this tutorial. RDocumentation R Enterprise Training. All of this is made much simpler using Dynamic Array Functions. Next story C program to calculate the area of a cube using function call. If you profile the function, you'll find a lot of data cache miss. Modelling with Xpress Documentation. We place the nonlinear constraints into a function handle. Adjoint-Based Sensitivity Analysis for Computational Fluid Dynamics Dimitri J. would cringe at a function definition with thousands of parameters. The code above sets the default image to be placed at the top of the monitor, with the width of the monitor and the same height previously set as default. Dear R-list, I am in the process of translating a long function written in Matlab into R (mainly because I am a big of fan of R, and folks will not have to pay to. But , the values in matrix A do not appear where they would be expected to appear in terms of (row,column) as applied to the layout of the DATA statement. at a time between your helper functions and your top level transpose function. Function-objects. Examples:. It is obtained by interchanging rows and columns of a matrix. FUN is a handle to a function that takes a two-dimensional input argument. There are two primary types of values in Accelerate: Scalars and Arrays. Update on december 16, 2015. A short history of Linear Programming: In 1762, Lagrange solved tractable optimization problems with simple equality constraints. Implementing Rubik's Cube: An Exercise in Hybrid Programming by Jim Weigang. Cache efficient matrix transpose function with a performance score of 51. , r = [det(C y) N]/[det(C y) E] row vector composed of N. Using accelerate required a different way of thinking. Travel-friendly and affordable, the FP-50 brings you top-class piano performance along with many other great features to enhance your playing enjoyment. MATLAB Library function mapping Over 300+ MATLAB functions are optimized for CUDA code generation. table2array horizontally concatenates the variables in T to create A. Multiply two Matrices by Passing Matrix to Function. Create a new Function instance which just aliases the specified ‘x’ Function/Variable such that the ‘Output’ of the new ‘Function’ is same as the ‘Output’ of the specified ‘x’ Function/Variable, and has the newly specified name. Transpose Matrix in C. One of the most widely used alternatives to prevent this is the ReLU function. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case O(n log n) runtime. FP-50: Digital Piano - Authentic Piano Performance to Go. Like a script file, you write function M-files in the Matlab editor. NET, and the Optimized for Visual Studio logo. lib and/or 54xdspf. A SparkSession can be used create DataFrame, register DataFrame as tables, execute SQL over tables, cache tables, and read parquet files. the function copies a horizontal range of cells into a vertical range and vice versa). Winds Key Transpose; Winds Key Transpose helps to find the corresponding musical key for your wind instrument when you are looking at a score written in another key. Learn more about transpose, row, column There is a function called transpose. Matrices and Linear Algebra The Wolfram Language automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly optimized algorithms. So for a large enough matrix such that it's larger than the cache size, then if we transpose a 16x16 block (since sizeof(int) == 4, thus 16 ints fit in a cache line, assuming the matrix is aligned on a cacheline bounday) we need to load 32 (16 from the source matrix. Includes simple test programs, as well. SongBook lets you transpose a song into a different key by automatically adjusting all chords. In this case, the optimized function is chisq = sum((r / sigma) ** 2). That is, A*B is C = mtimes(A,B) This function fully supports distributed arrays. Modelling with Xpress Documentation. The extern "C" is a linkage specification and is a flag that everything within the enclosing block (brace-surrounded) uses C linkage, not C++ linkage. Using many original methods, the Wolfram Language can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. This is the case when bead sort is implemented without a mechanism to assist in finding empty spaces below the beads, such as in software implementations. ctranspose(a) returns the complex conjugate transpose of fi object a. The gradients of the constraints should be column vectors; they must be placed in the objective function as a matrix, with each column of the matrix representing the gradient of one constraint function. CS267 Assignment 1: Optimize Matrix Multiplication Due Date: Tuesday February 14, 2012 at 11:59PM Problem statement. Travel-friendly and affordable, the FP-50 brings you top-class piano performance along with many other great features to enhance your playing enjoyment. Re: Why transposing fails using TRANSPOSE(), OFFSET(), INDIRECT()? Many thanks for your help Marcelo and idea of avoid to use TRANSPOSE() function, I got the formula that gives the correct result, the only thing is, the final formula is a little bit large. # example using built-in dataset. Right click, and then click Copy. Visually explore and analyze data—on-premises and in the cloud—all in one view. You need to delete the entire array of values that the TRANSPOSE function returns. [email protected] Must Read: C Program To Calculate Sum of Lower Triangle Elements Output. using some generic C code and some SSE2 optimized code. Simply select the number of sharps or flats, the original instrument's key (for example, in-C), and. The code we wish to optimize is a transpose of a matrix of single precision values that operates out-of-place, i. 2 Finite impulse response (FIR) filter design methods. /O1 sets a combination of optimizations that generate minimum size code. Memory is the biggest limiting factor to the widespread use of FPGAs for high-level image processing, which require complete frame(s) to be stored in situ. c function for an example of how this works. These optimized BLAS libraries are provided by the computer vendor or by an independent software vendor (ISV). If A contains complex elements, then A. Program to perform transpose of a matrix in C++. The first algorithm hard-coded the current market caps for the duration of the algorithm (back to 2008). To transpose the matrix I use the naive approach of iterating through std::vector, calculating for each entry its position in a matrix transpose. Note that a direct implementation following Figures 1 and 2 shall read and write the 3D image object three times. Of course, one of the registered functions must be. +1 for the suggestion to avoid the work of transposing by implementing matrix manipulation functions that transpose at point of use. To get C behavior from the function, transpose the input matrix before calling the function, and then transpose the function output. Or do it the other way around and read in columns while writing linearly. The storage size of the numpy array is close to a C array. Layers Reference with BrainScript. ' returns the nonconjugate transpose of A, that is, interchanges the row and column index for each element. Includes simple test programs, as well. You can also specify how many pieces to split the string into. Examples might be simplified to improve reading and basic understanding. 0 B In contrast to digital IIR filter design, the classical design of analog (conic hull), denoted by conv (C ) (cone (C )), is the smallest convex IIR filters looks rather complete, so there is not much further devel- set (cone) in n that contains C. When importing an image sequence, -i also supports expanding shell-like wildcard patterns (globbing) internally, by selecting the image2-specific -pattern_type glob option. hydrogel obtained from the isotherm model was 1. The code above sets the default image to be placed at the top of the monitor, with the width of the monitor and the same height previously set as default. BORGES , AND F. Nathan Kutz y Abstract. Optimized script display, easier to find which param is channel. A reader, Ismael V. Downsample (every 300th element) and transpose the simOut elements, and convert the Euler angles to quaternions. One of the most widely used alternatives to prevent this is the ReLU function. Regex Tester isn't optimized for mobile devices yet. 0, OpenCV also includes SSE2-optimized code. See LICENSE. The autograder searches for this string to determine which transpose function to evaluate for credit. Matrix multiplication is not universally commutative for nonscalar inputs. Embedded software often runs on processors with limited computation power, thus optimizing the code becomes a necessity. c must compile without. The purpose of this problem is to write optimized_matrix_trans_mult_vec() which is a faster version of the provided baseline_matrix_trans_mult_vec() to perform a matrix transpose multiplied by a vector. I use Agner Fog's vector class library. The transposition is only temporary. Start from a training session at home and be the king of the stage. Using this alpha and num_iters values, the optimized theta is [1. The insert function takes an element and a list and inserts the element into the list at the first position where it is less than or equal to the next element. You may assume that A's column number is equal to B's row number. Real Vim ninjas count every keystroke - do you? Pick a challenge, fire up Vim, and show us what you got. , r = [det(C y) N]/[det(C y) E] row vector composed of N. JS function alternatives and useful snippets of code. procedure then only need to read and write the 3D image object twice. This is the transpose of the form generated by jacobian, so we take the transpose below. An efficient procedure for recovering spectral reflectance using an object’s tristimulus values under multi-illuminants is proposed by adapting with the characteristics of the testing sample to obtain the transformation matrix of pseudoinverse. W3Schools is optimized for learning, testing, and training. ; Previous story C Program to find the largest element in an array using function call. 4/53 for 32 by 32, 64 by 64 and 61 by 67 matrices - prash628/Optimized-Cache-Efficient-Matrix-Transpose. Programming Rules for Part B Include your name and loginID in the header comment for trans. Learn more about python, numpy, ndarray MATLAB. h for C) •Optimized paths for Intel® AVX2 and Intel® AVX-512 (detected at run-time) Don’t link to libm explicitly! -lm. Numb a vs Cyt hon: How to Choo s e. Authentic Piano Performance to Go. If the applied function returns any other type, the final output is a Series. It can be used as a worksheet function (WS) in Excel. Dear R-list, I am in the process of translating a long function written in Matlab into R (mainly because I am a big of fan of R, and folks will not have to pay to. It's then possible to provide a transpose view without needing to move all the elements, which may be useful in some circumstances (in others, you'll want to actually perform the transpose, to keep rows contiguous in cache). " This is the basic structure of matrix multiplication. Update on december 16, 2015. Select the range A1:C1. Using accelerate required a different way of thinking. Start from a training session at home and be the king of the stage. Om du fortsätter ger du ditt medgivande att använda cookies. a about after all also am an and another any are as at be because been before being between both but by came can come copyright corp corporation could did do does. JS function alternatives and useful snippets of code. So that gives us our overall optimization objective function for the support vector machine. View Diane(Dan) Yang’s profile on LinkedIn, the world's largest professional community. Functions are used to perform certain actions, and they are important for reusing code: Define the code once, and use it many times. The function will convert a horizontal range into a vertical range and vice versa. Tomo-Hiko WatanabeandShinyaMaeyama Department of Physics, Nagoya University, Japan Datacommunication optimized onpeta-scalecomputer Data transpose is. /O1 sets a combination of optimizations that generate minimum size code. Specifically, I will optimize a matrix transpose to show how to use shared memory to reorder strided global memory accesses into coalesced accesses. Download Transpose matrix program class file. Comment and share: How to reverse and transpose Excel data with this powerful but simple solution By Susan Harkins Susan Sales Harkins is an IT consultant, specializing in desktop solutions. 4/53 for 32 by 32, 64 by 64 and 61 by 67 matrices - prash628/Optimized-Cache-Efficient-Matrix-Transpose. The Numa Compact 2 is a big step forward in terms of sound quality, digital post processing effects and full MIDI controller features. To speed up such operations, use non-standard optimized function, possibly written by yourself. Commercial development of pattern matching against other data types is starting to be a common function integrated within the total information system. ; Previous story C Program to find the largest element in an array using function call. Using many original methods, the Wolfram Language can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. If the portion of the regular expression is "greedy", it. Getting Started Examples for C/C++ Function Import: Collection of simple examples for a quick introduction to features and capabilities of importing C/C++ functions as custom Model Composer blocks. Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. A slightly different version of this article appeared in the January 1986 issue of Computer Language magazine; this article is reprinted with permission. The latency is the number of cycles between the first valid input and the first valid output, assuming that the input is contiguous. sinh(x) Hyperbolic sine of x. In Part B you will write a matrix transpose function that is optimized for cache performance. The function will convert a horizontal range into a vertical range and vice versa. lib and/or 54xdspf. Sanjay Gupta 2,436 views. It's then possible to provide a transpose view without needing to move all the elements, which may be useful in some circumstances (in others, you'll want to actually perform the transpose, to keep rows contiguous in cache). Proc summary will create summary statistics for specified varaibles within each combination of class variables (or specified subset of them). The primary function of accelerate is to automatically generate optimized code. # example using built-in dataset. Paste Special Transpose | Transpose Function. The result of this study demonstrated, for WVU-OA dataset for 15 degrees off-angle iris of right and left eyes, the window size of [5 5] and [7 7] respectively are optimum to maximize the median filter function. It is an array function, so you need to use Control-Shift-Enter and not just Enter. In the later case, rownames become variable (column) names. Transpose of a matrix in C language: This C program prints transpose of a matrix. The first algorithm hard-coded the current market caps for the duration of the algorithm (back to 2008). It will flip the direction of a given range or array. Description. To transpose any matrix in C++ Programming language, you have to first ask to the user to enter the matrix and replace row by column and column by row to transpose that matrix, then display the transpose of the matrix on the screen as shown here in the following C++ program. at a time between your helper functions and your top level transpose function. Transform data into stunning visuals and share them with colleagues on any device. All of them arrives to a similar cost function value, but only the optimized strategy present a more stable behaviour around the minimum. The displayed view shows the UAV translating in the Y-direction and losing. ' returns the nonconjugate transpose of A, that is, interchanges the row and column index for each element. 151 videos Play all C Programming Tutorials (HINDI/URDU) easytuts4you MATHS-XII-3-06 Transpose of matrix(2016) by Swati Mishra, Pradeep Kshetrapal channel - Duration: 56:12. Like a script file, you write function M-files in the Matlab editor. Learn more about transpose, row, column There is a function called transpose. Since FPGAs have limited on-chip memory capabilities, efficient use of such resources is essential to meet performance, size and power. TablEdit's "Transpose…" feature not only allows you to transpose chords but also to transpose individual notes or an entire song if desired. The ginv function calculates a pseudoinverse using the singular value decomposition provided by the svd function in the base R package. Title says it all. Szyld1 Temple University {szyld|loisel}@temple. The main component of a Merkle-Damg ard hash function his a compression function C: f0;1gp f 0;1gm!f0;1gp. This function accepts fi objects as inputs. probability density function (PDF) of random variable(s) q c: CPT tip resistance data. NET, and the Optimized for Visual Studio logo. One example is using OpenBLAS to replace the default BLAS implementation (further details). md file in the project root # for full license information. There are two primary types of values in Accelerate: Scalars and Arrays. The function will convert a horizontal range into a vertical range and vice versa. -Peter Schultz. func (*HOGSVD) Len ¶ Uses.