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## fe_coor

Purpose

Coordinate transformation matrices for Component Mode Synthesis problems.

Syntax

```[t] = fe_coor(cp)
[t,nc] = fe_coor(cp,opt)
```

Description

The different uses of fe_coor are selected by the use of options given in the argument opt which contains [type method] (with the default values [1 3]).

type=1(default) the output t is a basis for the kernel of the constraints cp
 range([T]N× (N−NC))=ker([c]NS × N)

NCNS is the number of independent constraints.

type=2the output argument t gives a basis of vectors linked to unit outputs followed by a basis for the kernel
 T = [[TU]N × NS [TK]N × (N−NS)]  with    [c]NS × N[T]=[[\ I \ ] [0]NS × (N−NS)]

If NC<NS such a matrix cannot be constructed and an error occurs.

methodthe kernel can be computed using: 1 a singular value decomposition svd (default) or 3 a lu decomposition. The lu has lowest computational cost. The svd is most robust to numerical conditioning problems.

Usage

fe_coor is used to solve problems of the general form

 [Ms2+Cs+K]{q(s)}=[b] {u(s)} {y(s)}= [c] {q(s)}
with   [cint]{q(s)}=0

which are often found in CMS problems (see section 6.2.6 and [40]).

To eliminate the constraint, one determines a basis T for the kernel of [cint] and projects the model

 [TTMTs2+TTCTs+TTKT]{qR(s)}=[TTb] {u(s)} {y(s)}= [cT] {qR(s)}