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Scilab Help >> Elementary Functions > Matrix generation > linspace

# linspace

generates linearly spaced numbers between 2 reached bounds

### Syntax

```row = linspace(x1, x2)
row = linspace(x1, x2, n)
Matrix = linspace(Col1, Col2)
Matrix = linspace(Col1, Col2, n)```

### Arguments

x1, x2

Real or complex scalars, or encoded integer scalars: Bounds between which values must be generated.

Col1, Col2

Column vectors of real or complex numbers, or of encoded integers, of same heights.

n

integer number of requested values or columns. Default value: 100

row

row vector of `n` numbers.

Matrix

Matrix with `n` columns of numbers.

### Description

`linspace(x1, x2)` generates a row vector of `n` equally spaced values ranging exactly from `x1` to `x2`.

 The syntax `y1:y2` or `y1:step:y2` like `1:0.1:%pi` does the same but fixes the starting bound `y1` and the step. The `y2` is used as stopping bound to not be overstepped. The last value actually generated may not reach it. `y2` is then not included in the result. Instead of fixing the step to a given value, `linspace` fixes the final bound `x2` to be exactly reached, and computes the step accordingly.

If `x1` or `x2` are complex numbers, then `linspace(x1,x2)` interpolates separately the real and the imaginary parts of `x1` and `x2`.

If some column vectors `Col1` and `Col2` are provided, `linspace` works in a row-wise way: the resulting `Matrix` has the same number of rows, and `n` columns. We get `Matrix(i,:) = linspace(Col1(i), Col2(i), n)`.

 When specified bounds are encoded integers, the actual step may vary by one unit along the generated series.

### Examples

```linspace(1, %pi, 0)         // n = 0
linspace(1, 2, 10)          // x2 > x1 : increasing values
linspace(2, 1, 10)          // x2 < x1 : decreasing values
linspace(1+%i, 2-2*%i, 5)     // with complex numbers
linspace([1:4]', [5:8]', 10)  // with input columns```
```--> linspace(1, %pi, 0)    // n = 0
ans  =
[]

--> linspace(1, 2, 10)    // x2 > x1 : increasing values
ans  =
1.   1.111   1.222   1.333   1.444   1.556   1.667   1.778   1.889   2.

--> linspace(2, 1, 10)    // x2 < x1 : decreasing values
ans  =
2.   1.889   1.778   1.667   1.556   1.444   1.333   1.222   1.111   1.

--> linspace(1+%i, 2-2*%i, 5)      // with complex numbers
ans  =
1. +i     1.25 +0.25i   1.5 -0.5i   1.75 -1.25i   2. -2.i

--> linspace([1:4]', [5:8]', 10)   // with input columns
ans  =
1.   1.444   1.889   2.333   2.778   3.222   3.667   4.111   4.556   5.
2.   2.444   2.889   3.333   3.778   4.222   4.667   5.111   5.556   6.
3.   3.444   3.889   4.333   4.778   5.222   5.667   6.111   6.556   7.
4.   4.444   4.889   5.333   5.778   6.222   6.667   7.111   7.556   8.
```

With encoded integers: The step may vary by one unit along the series:

```x = linspace(int8([5;127]), int8([127;5]), 10)
x(:,1:\$-1) - x(:,2:\$)```
```--> x = linspace(int8([5;127]), int8([127;5]), 10)
ans  =
5   18   32  45  59  72  86  99  113  127
127  114  100  87  73  60  46  33   19    5

--> x(:,1:\$-1) - x(:,2:\$)
ans  =
-13 -14 -13 -14 -13 -14 -13 -14 -14
13  14  13  14  13  14  13  14  14
```