octave assign matrix row

Octave Programming Tutorial/Vectors and matrices

• 1 Creating vectors and matrices
• 2.1 Element operations
• 4.1.1 Other matrices
• 4.2 Changing matrices
• 5 Linear algebra

Creating vectors and matrices [ edit | edit source ]

Here is how we specify a row vector in Octave:

• the vector is enclosed in square brackets;
• each entry is separated by an optional comma. x = [1 3 2] results in the same row vector.

To specify a column vector, we simply replace the commas with semicolons:

From this you can see that we use a comma to go to the next column of a vector (or matrix) and a semicolon to go to the next row. So, to specify a matrix, type in the rows (separating each entry with a comma) and use a semicolon to go to the next row.

Operators [ edit | edit source ]

You can use the standard operators to

• subtract ( - ), and
• multiply ( * )

matrices, vectors and scalars with one another. Note that the matrices need to have matching dimensions (inner dimensions in the case of multiplication) for these operators to work.

• The transpose operator is the single quote: ' . To continue from the example in the previous section,

(Note: this is actually the complex conjugate transpose operator, but for real matrices this is the same as the transpose. To compute the transpose of a complex matrix, use the dot transpose ( .' ) operator.)

• The power operator ( ^ ) can also be used to compute real powers of square matrices.

Element operations [ edit | edit source ]

When you have two matrices of the same size, you can perform element by element operations on them. For example, the following divides each element of A by the corresponding element in B :

Note that you use the dot divide ( ./ ) operator to perform element by element division. There are similar operators for multiplication ( .* ) and exponentiation ( .^ ).

Let's introduce a scalar for future use.

The dot divide operators can also be used together with scalars in the following manner.

returns a matrix, C where each entry is defined by

i.e. a is divided by each entry in B . Similarly

return a matrix with

Indexing [ edit | edit source ]

You can work with parts of matrices and vectors by indexing into them. You use a vector of integers to tell Octave which elements of a vector or matrix to use. For example, we create a vector

Now, to see the second element of x , type

You can also view a list of elements as follows.

This last command displays the 1st, 3rd and 4th elements of the vector x .

To select rows and columns from a matrix, we use the same principle. Let's define a matrix

and select the 1st and 3rd rows and 2nd and 3rd columns:

The colon operator ( : ) can be used to select all rows or columns from a matrix. So, to select all the elements from the 2nd row, type

You can also use : like this to select all Matrix elements:

Ranges [ edit | edit source ]

We can also select a range of rows or columns from a matrix. We specify a range with

You can actually type ranges at the Octave prompt to see what the results are. For example,

The first number displayed was start , the second was start + step , the third, start + (2 * step) . And the last number was less than or equal to stop .

Often, you simply want the step size to be 1. In this case, you can leave out the step parameter and type

Finally, there is a keyword called end that can be used when indexing into a matrix or vector. It refers to the last element in the row or column. For example, to see the last column in a Matrix, you can use

Functions [ edit | edit source ]

The following functions can be used to create and manipulate matrices.

Creating matrices [ edit | edit source ]

• tril(A) returns the lower triangular part of A .
• triu(A) returns the upper triangular part of A .

• diag(x) or diag(A) . For a vector, x , this returns a square matrix with the elements of x on the diagonal and 0s everywhere else. For a matrix, A , this returns a vector containing the diagonal elements of A . For example,
• linspace(a, b, n) returns a vector with n values, such that the first element equals a , the last element equals b and the difference between consecutive elements is constant. The last argument, n , is optional with default value 100.

Other matrices [ edit | edit source ]

There are some more functions for creating special matrices. These are

• hankel ( Hankel matrix ),
• hilb ( Hilbert matrix ),
• invhilb (Inverse of a Hilbert matrix),
• sylvester_matrix ( Sylvester matrix ) - In v3.8.1 there is a warning: sylvester_matrix is obsolete and will be removed from a future version of Octave; please use hadamard(2^k) instead,
• toeplitz ( Toeplitz matrix ),
• vander ( Vandermonde matrix ).

Use help to find out more about how to use these functions.

Changing matrices [ edit | edit source ]

• fliplr(A) returns a copy of matrix A with the order of the columns reversed, for example,
• flipud(A) returns a copy of matrix A with the order of the rows reversed, for example,

• sort(x) returns a copy of the vector x with the elements sorted in increasing order.

Linear algebra [ edit | edit source ]

For a description of more operators and functions that can be used to manipulate vectors and matrices, find eigenvalues, etc., see the Linear algebra section.

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Introduction to Octave: Arrays: Vectors and Matrices

1.1 creating, 1.2 indexing, 1.3 describing, 1.4 iterating over, 1.5 concatenating, 2.1 creating, 2.2 indexing, 2.3 describing, 2.4 iterating over, 2.5 finding, 3.1 scalar mathematics, 3.2 element-wise multiplication, 3.3 dot products, 3.4 inverse.

Vectors are 1-dimensional arrays of numbers (as opposed to scalars which are 0-dimensional and matrices which are 2-dimensional).

Vectors are created by using:

• Square brackets
• Commas or spaces between numbers (or a mixture of both)

When working with vectors the output can get quite large so we will use format compact to reduce the space used:

Vectors can also be created by specifying ranges of numbers:

The linspace() function can be used to create a vector of a defined length between a start and an end point with a consistent gap between successive elements:

Read values in a vector by using round brackets:

Use length() and size() to display details about your vector:

This tells us that our vector is 5 elements in length, with 1 row and 5 columns.

You can iterate over a vector using a for loop:

Add a vector onto the end of another vector using square brackets:

Matrices are much the same as vectors except they have two dimensions.

Just like vectors, matrices are created by using square brackets together with either commas or spaces (or both) except, this time, either semi-colons or line breaks are also used as these indicate the line breaks at the end of rows:

A matrix is also indexed using round brackets, but this time two numbers are needed (corresponding to the row and column of the element you want):

More advanced indexing is also possible, using vectors to define the rows and columns you want:

This has given us the odd-numbered rows (1 and 3) and the even-numbered (2 and 4) columns.

A colon : represents ‘all’ rows or columns:

This has given us the odd-numbered rows (1 and 3) and all columns.

The length() , size() , rows() and columns() functions all work for describing a matrix:

You can iterate over a matrix using two for loops:

To find a particular value in a matrix, use == to find which elements are equal to what you are looking for:

Then, use find() to get the indices of these locations (index numbers start at the top-left and increase going down the columns first, then along the rows):

So the number 3 is the second, third and sixth element of this matrix, counting from the top-left downwards and then to the right.

If you search for a two-element vector in a two-column matrix, Octave will search each column separately:

The first column was searched for the number 3 and it was found at indices 2 and 3. The second column was searched for the number 8 and it was found at index 8.

Alternatively, you can search only a subset of the matrix:

All rows and the first column of the matrix was searched for the number 3, and it was found at indices 2 and 3.

3 Array Operations

Addition, subtraction, multiplication and division of an array by a scalar simply applies the operation to all the elements in the array:

If you want to perform an operation between every element in one array and the corresponding elements in a second array, you can add a full stop before the operation:

This causes each element in A to be multiplied by the corresponding element in B . This is not the same as matrix multiplication (dot products and/or cross products). This element-wise mode of operation also applies to division ( ./ ) and exponentiation ( .^ ).

Given an \(r \times n\) matrix A and an \(n \times c\) matrix B the dot product will produce an \(r \times c\) matrix:

A \(3 \times 2\) matrix times a \(2 \times 3\) matrix produces a \(3 \times 3\) matrix.

The inverse of A is inv(A) or A^-1 :

Use this to solve for unknown variables in a system on linear equations: Ax = b

Using Octave

First, follow the installation instructions for:

• GNU/Linux and other Unix systems
• Microsoft Windows

or consult the GNU Octave manual to install GNU Octave on your system. Then, start the GNU Octave by clicking the icon in the programs menu or launch the interactive prompt by typing octave in a terminal. See the manual page on running Octave .

• 1 Variable Assignment
• 3 Command evaluation
• 4 Elementary math
• 6 Linear Algebra
• 7 Accessing Elements
• 8 Control flow with loops
• 9 Vectorization
• 10 Plotting
• 13 Getting Help
• 14 Octave packages
• 15 Octave User Codes

Variable Assignment [ edit ]

Assign values to variables with = (Note: assignment is pass-by-value ). Read more about variables .

Comments [ edit ]

# or % start a comment line, that continues to the end of the line. Read more about comments .

Command evaluation [ edit ]

The output of every command is printed to the console unless terminated with a semicolon ; . The disp command can be used to print output anywhere. Use exit or quit to quit the console. Read more about command evaluation .

Elementary math [ edit ]

Many mathematical operators are available in addition to the standard arithmetic. Operations are floating-point. Read more about elementary math .

Matrices [ edit ]

Arrays in Octave are called matrices. One-dimensional matrices are referred to as vectors. Use a space or a comma , to separate elements in a row and semicolon ; to start a new row. Read more about matrices .

Linear Algebra [ edit ]

Many common linear algebra operations are simple to program using Octave’s matrix syntax. Read more about linear algebra .

Accessing Elements [ edit ]

Octave is 1-indexed. Matrix elements are accessed as matrix(rowNum, columnNum) . Read more about accessing elements .

Control flow with loops [ edit ]

Octave supports for and while loops, as well as other control flow structures. Read more about control flow .

Vectorization [ edit ]

For-loops can often be replaced or simplified using vector syntax. The operators * , / , and ^ all support element-wise operations writing a dot . before the operators. Many other functions operate element-wise by default ( sin , + , - , etc.). Read more about vectorization .

Plotting [ edit ]

The function plot can be called with vector arguments to create 2D line and scatter plots. Read more about plotting .

Strings [ edit ]

Strings are simply arrays of characters. Strings can be composed using C-style formatting with sprintf or fprintf . Read more about strings .

If-else [ edit ]

Conditional statements can be used to create branching logic in your code. Read more in the manual .

Getting Help [ edit ]

The help and doc commands can be invoked at the Octave prompt to print documentation for any function.

Octave packages [ edit ]

Community-developed packages can be added from the Octave Packages website to extend the functionality of Octave’s core library. (Matlab users: Packages act similarly to Matlab’s toolboxes.) The pkg command is used to manage these packages. For example, to use the image processing library visit its page on Octave Packages, copy the install command and run it in octave

Read more about packages .

Octave User Codes [ edit ]

There are also User Codes available for GNU Octave which are not part of the core program or any of the packages.

See Category User Codes .

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How to load and modify matrices and vectors in Octave?

• How to Convert matrix to a list of column vectors in R ?
• How to inverse a vector in MATLAB?
• How to find the transpose of a tensor in PyTorch?
• How to Permute the Rows and Columns in a Matrix on MATLAB?
• Turn a Matrix into a Row Vector in MATLAB
• Program for addition of two matrices
• How to solve Equality of Matrices?
• How to create matrix and vector from CSV file in R ?
• How to find length of matrix in R
• How to Initialize 3D Vector in C++ STL?
• C++ Program For Addition of Two Matrices
• Java Program to Multiply two Matrices of any size
• How to read a Matrix from user in Java?
• How to Find Indices and Values of Nonzero Elements in MATLAB?
• Addition of Two Matrices in PHP
• How to Select Random Rows from a Matrix in MATLAB?
• How to Convert Sparse Matrix to Dense Matrix in R?
• How to Set the Diagonal Elements of a Matrix to 1 in R?
• Reshaping array as a vector in Julia - vec() Method

In this article, we will see how to load and play with the data inside matrices and vectors in Octave. Here are some basic commands and function to regarding with matrices and vector in Octave : 1. The dimensions of the matrix : We can find the dimensions of a matrix or vector using the size() function. 

2. Accessing the elements of the matrix : The elements of a matrix can be accessed by passing the location of the element in parentheses. In Octave, the indexing starts from 1. 

3. Longest Dimension : length() function returns the size of the longest dimension of the matrix/vector. 

4. Loading Data : First of all let us see how to identify the directories in Octave : 

Now before loading the data, we need to change our present working directory to the location where our data is stored. We can do this with the cd command and then load it as follows : 

We can use who command for knowing the variables in our current Octave scope or whos for more a detailed description. 

We can also select some of the rows from a loaded file, for example in our case 25 records data is present in Feature and target, we can create some other variable to store the trimmed data rows as shown below : 

5. Modifying Data : Let us now see how to modify the data of matrices and vectors. 

We can also append the new columns and rows in an existing matrix : 

We can also concatenate 2 different matrices : 

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Scalar, Vector, and Matrix

A scalar is just a fancy word for a number; it is used to distinguish numbers from vectors or matrices.

Rows and Columns

You create a row matrix consisting of the numbers 4 5 6 7 by entering the numbers inside []-brackets and separating the numbers by a comma or a blank.

You create a column matrix consisting of the numbers 0.1 0.2 0.3 by entering the numbers inside []-brackets and separating the numbers by a semicolon.

Row and column matrices are sometimes called vectors.

You can combine row matrices or column matrices

The first number in a vector has index 1. You can get the number at a specified index.

You can use the same notation that creates numbers in for-statements for creating vectors.

You can use the same notation for extracting a vector from a vector.

You can turn a row into a column or the other way around by doing a transpose using the operator '.

Arithmetic with matrices and scalars

You can use the arithmetic operators + , - , * and / on a matrix and a scalar. The operation is applied to each element of the matrix.

Functions of matrices

You can apply functions on matrices, the function is then applied to each element of the matrix.

General matrices

A general matrix consists of n rows and m columns.

Try these commands:

Try the commands ones(3), zeros(4), eye(5) !

Element by Element

You can perform element by element operations on two matrices having the same dimension, i.e. having the same number of rows and columns respectively. When performing an element by element operation the result is a new matrix having the same dimension as the two operands.

When doing an element by element addition, the element on place (row, col) in the resulting matrix will be the sum of the two elements at (row, col) in the operand matrices.

The regular arithmetic operators will become element-by-element operators if you place a dot in front of them.

.+ .- .* ./ .^

When applying a function on a matrix the function is applied to each element of the matrix

Using element by element operations you can combine comparisons and arithmetic.

Regular linear algebra

In regular mathematics, matrix addition and subtraction are defined to be element by element operations. Since using the Octave operators without any dot means "regular" usage, there is no difference between + and .+ , or between - and .- . When it comes to multiplication, division and to-the-power-of, there is a difference between "regular" usage and the element-by-element usage; hence do not use these operators without a dot in front of them (unless you actually know linear algebra).

further info:

GNU Octave, 8.3 Arithmetic Operators by delorie software

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License

www.malinc.se

Multivariate Statistical Techniques Matrix Operations in Octave

Multiplication by a scalar, matrix addition & subtraction, matrix multiplication, transpose of a matrix, common vectors, unit vector, common matrices, unit matrix, diagonal matrix, identity matrix, symmetric matrix, inverse of a matrix, inverse & determinant of a matrix, number of rows & columns, computing column & row sums, computing column & row means, horizontal concatenation, vertical concatenation (appending).

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Assigning a vector to multiple rows of a matrix

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Combining the tactility of analog hardware with the convenience of virtual instrument flexibility, PolyBrute Connect replicates the entire front panel as a standalone Mac/PC app and a plugin for all major DAWs.

Craft sound

Explore the depths of PolyBrute’s advanced features with a like-for-like virtual interface.

Control in real-time

Every parameter change, either on synth or software, is mirrored by the other.

Manage your patches

Organize your favorite sounds with an intuitive drag-and-drop interface, and easily import new presets & sound banks.

Preview sounds from the store

Discover new sonic territories with the Sound Store and preview sound banks directly on PolyBrute.

Distinction in design

PolyBrute 12 represents a leap forward in analog synthesis, while remaining firmly rooted in synth design heritage.

PolyBrute enters a new era with its groundbreaking FullTouch® MPE keyboard combined with the same controls, buttons, and expressive components that are a delight to use. Crafted with the finest materials, including walnut wood and a striking aluminum exterior - PolyBrute 12 is designed to meet the demands of professional musicians as well as appeal to the enthusiasts. Its not just for looks either, the vents at the back provide passive cooling so PolyBrute can operate in complete silence.

Main Features

Analog morphing synthesizer.

• 12 voices of Polyphony
• Mono, Unison, Poly voicing
• Single, Split, Layer modes

61-keys with FullTouch® MPE Technology keyboard

Pitch bend, mod wheel, ribbon controllers, morphée touch and pressure sensitive 3d controller, osc and noise mixer with filter routing, 12db/oct steiner parker filter.

• Continuous LP>Notch>HP>BP morphing
• Cutoff, Resonance, Brute Factor

24dB/Oct Ladder Filter with Distortion

Three envelopes.

• Looping capability

Three stereo digital effects

• Modulation FX : Chorus, Phaser, Flanger, Ring Modulation
• Delay : 9 algorithms including BBD, Digital delay
• Reverb : 9 algorithms including Hall, Plate, Spring, Shimmer
• Distortions : Subtle Tape, Classic Distortion, Soft Clip, Worn Out Tape, Germanium, BitCrusher, DownSampler

Arpeggiator, Matrix Arpeggiator, Sequencer

Stereo audio output, 2 expression and 1 sustain pedal inputs, two analog vco's.

• Triangle + Metalizer
• Square + Pulse Width

Noise Generator

• Continuous tone from rumble noise to white noise
• LFO1 and LFO2 with waveform selection
• LFO3 with waveform shaping using Shape and Symmetry
• Rate control & Tempo Sync
• Various retrig options

480 presets and 768 preset slots

12x32 modulation matrix.

• Notes, Accent, Slide per step
• 3 tracks of automation

MIDI and USB i/o + analog clock i/o

Platform specifications.

• Win 10+ (64bit)
• 4 cores CPU, 3.4 GHz (4.0 GHz Turbo-boost)
• 3GB free hard disk space
• OpenGL 2.0 compatible GPU
• ARM processors not supported on Windows

Required configuration

• Works in Standalone, VST, AAX, Audio Unit.

• 4 cores CPU, 3.4 GHz (4.0 GHz Turbo-boost) or M1 CPU

Work with ASC

• An elegant and simple solution to help you install, activate, and update your Arturia software instruments.

What’s in the box

Box content.

• PolyBrute 12 Unit
• User Manual
• Registration Card

Instrument dimensions

• Size : 38.3 x 17.1 x 6.1 inches (972 x 435 x 156mm)
• Weight : 50.7lbs (23kg)

Next: Increment Ops , Previous: Boolean Expressions , Up: Expressions   [ Contents ][ Index ]

8.6 Assignment Expressions

An assignment is an expression that stores a new value into a variable. For example, the following expression assigns the value 1 to the variable z :

After this expression is executed, the variable z has the value 1. Whatever old value z had before the assignment is forgotten. The ‘ = ’ sign is called an assignment operator .

Assignments can store string values also. For example, the following expression would store the value "this food is good" in the variable message :

(This also illustrates concatenation of strings.)

Most operators (addition, concatenation, and so on) have no effect except to compute a value. If you ignore the value, you might as well not use the operator. An assignment operator is different. It does produce a value, but even if you ignore the value, the assignment still makes itself felt through the alteration of the variable. We call this a side effect .

The left-hand operand of an assignment need not be a variable (see Variables ). It can also be an element of a matrix (see Index Expressions ) or a list of return values (see Calling Functions ). These are all called lvalues , which means they can appear on the left-hand side of an assignment operator. The right-hand operand may be any expression. It produces the new value which the assignment stores in the specified variable, matrix element, or list of return values.

It is important to note that variables do not have permanent types. The type of a variable is simply the type of whatever value it happens to hold at the moment. In the following program fragment, the variable foo has a numeric value at first, and a string value later on:

When the second assignment gives foo a string value, the fact that it previously had a numeric value is forgotten.

Assignment of a scalar to an indexed matrix sets all of the elements that are referenced by the indices to the scalar value. For example, if a is a matrix with at least two columns,

sets all the elements in the second column of a to 5.

Assigning an empty matrix ‘ [] ’ works in most cases to allow you to delete rows or columns of matrices and vectors. See Empty Matrices . For example, given a 4 by 5 matrix A , the assignment

deletes the third row of A , and the assignment

deletes the first, third, and fifth columns.

An assignment is an expression, so it has a value. Thus, z = 1 as an expression has the value 1. One consequence of this is that you can write multiple assignments together:

stores the value 0 in all three variables. It does this because the value of z = 0 , which is 0, is stored into y , and then the value of y = z = 0 , which is 0, is stored into x .

This is also true of assignments to lists of values, so the following is a valid expression

that is exactly equivalent to

In expressions like this, the number of values in each part of the expression need not match. For example, the expression

is equivalent to

The number of values on the left side of the expression can, however, not exceed the number of values on the right side. For example, the following will produce an error.

The symbol ~ may be used as a placeholder in the list of lvalues, indicating that the corresponding return value should be ignored and not stored anywhere:

This is cleaner and more memory efficient than using a dummy variable. The nargout value for the right-hand side expression is not affected. If the assignment is used as an expression, the return value is a comma-separated list with the ignored values dropped.

A very common programming pattern is to increment an existing variable with a given value, like this

This can be written in a clearer and more condensed form using the += operator

Similar operators also exist for subtraction ( -= ), multiplication ( *= ), and division ( /= ). An expression of the form

is evaluated as

where op can be either + , - , * , or / , as long as expr2 is a simple expression with no side effects. If expr2 also contains an assignment operator, then this expression is evaluated as

where temp is a placeholder temporary value storing the computed result of evaluating expr2 . So, the expression

You can use an assignment anywhere an expression is called for. For example, it is valid to write x != (y = 1) to set y to 1 and then test whether x equals 1. But this style tends to make programs hard to read. Except in a one-shot program, you should rewrite it to get rid of such nesting of assignments. This is never very hard.