# SVD: Singular Value Decomposition In Rwave: Time-Frequency Analysis of 1-D Signals

## Description

Computes singular value decomposition of a matrix.

## Usage

 `1` ```SVD(a) ```

## Arguments

 `a` input matrix.

## Details

R interface for Numerical Recipes singular value decomposition routine.

## Value

a structure containing the 3 matrices of the singular value decomposition of the input.

## References

See discussions in the text of “Time-Frequency Analysis”.

## Examples

 ```1 2 3 4``` ``` hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") } X <- hilbert(6) z = SVD(X) z ```

### Example output

```\$d
[,1]
[1,] 1.618900e+00
[2,] 2.423609e-01
[3,] 1.632152e-02
[4,] 6.157484e-04
[5,] 1.257076e-05
[6,] 1.082799e-07

\$u
[,1]       [,2]       [,3]        [,4]        [,5]         [,6]
[1,] -0.7487192  0.6145448 -0.2403254  0.06222659 -0.01114432  0.001248194
[2,] -0.4407175 -0.2110825  0.6976514 -0.49083921  0.17973276 -0.035606643
[3,] -0.3206969 -0.3658936  0.2313894  0.53547692 -0.60421221  0.240679080
[4,] -0.2543114 -0.3947068 -0.1328632  0.41703769  0.44357472 -0.625460387
[5,] -0.2115308 -0.3881904 -0.3627149 -0.04703402  0.44153664  0.689807199
[6,] -0.1814430 -0.3706959 -0.5027629 -0.54068156 -0.45911482 -0.271605453

\$v
[,1]       [,2]       [,3]        [,4]        [,5]         [,6]
[1,] -0.7487192  0.6145448 -0.2403254  0.06222659 -0.01114432  0.001248194
[2,] -0.4407175 -0.2110825  0.6976514 -0.49083921  0.17973276 -0.035606643
[3,] -0.3206969 -0.3658936  0.2313894  0.53547692 -0.60421221  0.240679080
[4,] -0.2543114 -0.3947068 -0.1328632  0.41703769  0.44357472 -0.625460387
[5,] -0.2115308 -0.3881904 -0.3627149 -0.04703402  0.44153664  0.689807199
[6,] -0.1814430 -0.3706959 -0.5027629 -0.54068156 -0.45911482 -0.271605453
```

Rwave documentation built on May 2, 2019, 9:15 a.m.