Gram: Difference between revisions
Jump to navigation
Jump to search
imported>Jeremy (Importing text file) |
imported>Bob No edit summary |
||
| Line 1: | Line 1: | ||
===Purpose=== | ===Purpose=== | ||
Generalized rank | Generalized rank annihilation method. | ||
===Synopsis=== | ===Synopsis=== | ||
| Line 10: | Line 9: | ||
===Description=== | ===Description=== | ||
GRAM determines the joint invariant subspaces common to the two input matrices a and b, the ratio of their magnitudes ssq, and the response in both modes/orders ord1 and ord2. GRAM assumes that the input matrices a and b are bilinear, ''i.e.'' are the summation over outer products. | GRAM determines the joint invariant subspaces common to the two input matrices <tt>a</tt> and <tt>b</tt>, the ratio of their magnitudes <tt>ssq</tt>, and the response in both modes/orders <tt>ord1</tt> and <tt>ord2</tt>. GRAM assumes that the input matrices <tt>a</tt> and <tt>b</tt> are bilinear, ''i.e.'' are the summation over outer products. | ||
Inputs are the two response matrices <tt>a</tt> and <tt>b</tt>, and the number of factors to calculate or tolerance on the ratio of smallest to largest singular value <tt>tol</tt>. Optional inputs ''scl1'' and ''scl2'' are scales to plot against when producing plots of the response in each mode/order. Optional input ''out'' suppresses plotting and printing of results to the command window when set to 0 {default ''out'' = 1}. | |||
Outputs are the pure component responses in each mode <tt>ord1</tt> and <tt>ord2</tt>, the table of eigenvalues and their ratios <tt>ssq</tt>, and the eigenvalues for each matrix <tt>aeigs</tt> and <tt>beigs</tt>. | |||
====Inputs==== | |||
* '''a''' = first input matrix. | |||
* '''b''' = second input matrix. | |||
* '''tol''' = number of factors to calculate or tolerance on the ratio of the samllest to largest singular value. | |||
====Optional Inputs==== | |||
* '''scl1''' and '''scl2'''= scales to plot against. | |||
* '''out''' = input to suppress plotting and printing of results when set to 0 (default value = 1). | |||
====Outputs==== | |||
* '''ord1''' and '''ord2''' = pure component responses in each mode. | |||
* '''ssq''' = table of eigenvalues and their ratios. | |||
* '''aeigs''' = eigenvalues for <tt>a</tt>. | |||
* '''beigs''' = eigenvalues for <tt>b</tt>. | |||
===See Also=== | ===See Also=== | ||
[[mpca]], [[parafac]], [[parafac2]], [[tld]] | [[mpca]], [[parafac]], [[parafac2]], [[tld]] | ||
Latest revision as of 18:18, 9 October 2008
Purpose
Generalized rank annihilation method.
Synopsis
- [ord1,ord2,ssq,aeigs,beigs] = gram(a,b,tol,scl1,scl2,out)
Description
GRAM determines the joint invariant subspaces common to the two input matrices a and b, the ratio of their magnitudes ssq, and the response in both modes/orders ord1 and ord2. GRAM assumes that the input matrices a and b are bilinear, i.e. are the summation over outer products.
Inputs are the two response matrices a and b, and the number of factors to calculate or tolerance on the ratio of smallest to largest singular value tol. Optional inputs scl1 and scl2 are scales to plot against when producing plots of the response in each mode/order. Optional input out suppresses plotting and printing of results to the command window when set to 0 {default out = 1}.
Outputs are the pure component responses in each mode ord1 and ord2, the table of eigenvalues and their ratios ssq, and the eigenvalues for each matrix aeigs and beigs.
Inputs
- a = first input matrix.
- b = second input matrix.
- tol = number of factors to calculate or tolerance on the ratio of the samllest to largest singular value.
Optional Inputs
- scl1 and scl2= scales to plot against.
- out = input to suppress plotting and printing of results when set to 0 (default value = 1).
Outputs
- ord1 and ord2 = pure component responses in each mode.
- ssq = table of eigenvalues and their ratios.
- aeigs = eigenvalues for a.
- beigs = eigenvalues for b.