# Calculate Weighted Norm of series

### Description

Function calculates the W-norm for input objects or for objects stored in input ssa obect.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## S3 method for class '1d.ssa'
wnorm(x, ...)
## S3 method for class 'nd.ssa'
wnorm(x, ...)
## S3 method for class 'toeplitz.ssa'
wnorm(x, ...)
## S3 method for class 'mssa'
wnorm(x, ...)
## Default S3 method:
wnorm(x, L = (N + 1) %/% 2, ...)
## S3 method for class 'complex'
wnorm(x, L = (N + 1) %/% 2, ...)
``` |

### Arguments

`x` |
the input object. This might be ssa object for |

`L` |
window length. |

`...` |
arguments to be passed to methods. |

### Details

`L`

-weighted norm of series is Frobenius norm of its
`L`

-trajectory matrix. So, if `x`

is vector (series), the
result of `wnorm(x, L)`

is equal to ```
sqrt(sum(hankel(x,
L)^2)
```

, but in fact is calculated much more efficiently. For 1d SSA and
Toeplitz SSA `wnorm(x)`

calculates weighted norm for stored
original input series and stored window length.

`L`

-weighted norm of 2d array is Frobenius norm of its ```
L[1]
* L[2]
```

-trajectory hankel-block-hankel matrix. For 2d SSA this method
calculates weighted norm for stored original input array and stored
2d-window lengths.

### References

Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): *Analysis of
Time Series Structure: SSA and related techniques.* Chapman and
Hall/CRC. ISBN 1584881941

### See Also

`ssa-input`

,
`hankel`

,
`wcor`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
wnorm(co2, 20)
# Construct ssa-object for 'co2' with default parameters but don't decompose
ss <- ssa(co2, force.decompose = FALSE)
wnorm(ss)
# Artificial image for 2D SSA
mx <- outer(1:50, 1:50,
function(i, j) sin(2*pi * i/17) * cos(2*pi * j/7) + exp(i/25 - j/20)) +
rnorm(50^2, sd = 0.1)
# Construct ssa-object for 'mx' with default parameters but don't decompose
s <- ssa(mx, kind = "2d-ssa", force.decompose = FALSE)
wnorm(s)
``` |

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