Programmer Guide/Command Reference/EVAL/optmm: Difference between revisions
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Smooth multiplier matrix using a two dimensional convolution. | Smooth the multiplier matrix using a two dimensional convolution. | ||
;Usage:<code>optmm(<var>mflag</var>, <var>a</var>, <var>w</var>)</code> | ;Usage:<code>optmm(<var>mflag</var>, <var>a</var>, <var>w</var>)</code> | ||
:;<var>mflag</var>:selects the method used to modify the multiplier matrix; currently only the method ''mflag''='''0''' is implemented | :;<var>mflag</var>:selects the method used to modify the multiplier matrix; currently only the method ''mflag''='''0''' is implemented | ||
:;<var>a</var>:The multiplier matrix. Each row ''a''[i] contains one linear filter spectrum to be applied to a signal. | :;<var>a</var>:The multiplier matrix. Each row ''a''[i] contains one linear filter spectrum to be applied to a signal. | ||
:;<var> | :;<var>w</var>:The smoothing matrix, containg a two dimensional a smoothing function. | ||
;Description: | ;Description: | ||
:*<code>nrow(''w'') = 2M+1</code> and <code>nrow(''a'') >> M</code> | |||
:*<code>ncol(''w'') = 2N+1</code> and <code>ncol(''w'') = ncol(''a'')</code> | |||
:*The matrix ''w'' contains the weighting function, with the maximum at ''w''[M,N] and which should be symetrical in both dimensions. | |||
;Result: The | ::<code>''w''[M-i,N-j]=''w''[M-i,N+j]=''w''[M+i,N-j]=''w''[M+i,N+j]; with: i=1..M, j=1..N</code> | ||
:*The smoothed output is computed as follows: | |||
::<math>r[i]=\sum_{j=-M}^M \sum_{k=-N}^N a[i+j,N+k].w[M+j,N+k]</math> | |||
::with: <code>i=0..nrow(''a'')-1</code>; <code>''a''[i+j]=0</code> if <code>i+j<0</code> or <code>i+j>=nrow(''a'')</code> | |||
;Result: The vector ''r'' with the length <code>nrow(''a'')</code>, containing the smoothed filter spectrum. | |||
;See also: [[../hcomb|hcomb]], [[../cvphase|cvphase]], [[Programmer_Guide/BScript#MulAc|script application '''MulAc''']] | ;See also: [[../hcomb|hcomb]], [[../cvphase|cvphase]], [[Programmer_Guide/BScript#MulAc|script application '''MulAc''']] | ||
[[../#Functions|<function list>]] | [[../#Functions|<function list>]] | ||
Latest revision as of 11:28, 21 April 2011
Smooth the multiplier matrix using a two dimensional convolution.
- Usage
optmm(mflag, a, w)- mflag
- selects the method used to modify the multiplier matrix; currently only the method mflag=0 is implemented
- a
- The multiplier matrix. Each row a[i] contains one linear filter spectrum to be applied to a signal.
- w
- The smoothing matrix, containg a two dimensional a smoothing function.
- Description
-
nrow(w) = 2M+1andnrow(a) >> Mncol(w) = 2N+1andncol(w) = ncol(a)- The matrix w contains the weighting function, with the maximum at w[M,N] and which should be symetrical in both dimensions.
w[M-i,N-j]=w[M-i,N+j]=w[M+i,N-j]=w[M+i,N+j]; with: i=1..M, j=1..N
- The smoothed output is computed as follows:
- with:
i=0..nrow(a)-1;a[i+j]=0ifi+j<0ori+j>=nrow(a)
![{\displaystyle r[i]=\sum _{j=-M}^{M}\sum _{k=-N}^{N}a[i+j,N+k].w[M+j,N+k]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36f48c25bc2d1689feb87554d158b6c261b9bdcc)
- Result
- The vector r with the length
nrow(a), containing the smoothed filter spectrum. - See also
- hcomb, cvphase, script application MulAc
