### SYNOPSYS

void slaDcmpf(coeffs, xz, yz, xs, ys, perp, orient)

double *coeffs
double *xz
double *yz
double *xs
double *ys
double *perp
double *orient

### DESCRIPTION

```
```

#### Decompose an [x,y] linear fit into its constituent parameters

```  zero points, scales, nonperpendicularity and orientation.

```

#### Given

```     coeffs    double[6]     transformation coefficients (see note)

```

#### Returned

```     *xz       double        x zero point
*yz       double        y zero point
*xs       double        x scale
*ys       double        y scale
*perp     double        nonperpendicularity (radians)
*orient   double        orientation (radians)

The model relates two sets of [x,y] coordinates as follows.
```

#### Naming the elements of coeffs

```
coeffs[0] = a
coeffs[1] = b
coeffs[2] = c
coeffs[3] = d
coeffs[4] = e
coeffs[5] = f

The model transforms coordinates [x1,y1] into coordinates
```

#### [x2,y2] as follows

```
x2 = a + b*x1 + c*y1
y2 = d + e*x1 + f*y1

```

#### The transformation can be decomposed into four steps

```
```
1) Zero points
```
x' = xz + x1
y' = yz + y1

```
2) Scales
```
x'' = xs*x'
y'' = ys*y'

```
3) Nonperpendicularity
```
x''' = cos(perp)*x'' + sin(perp)*y''
y''' = sin(perp)*x'' + cos(perp)*y''

```
4) Orientation
```
x2 = cos(orient)*x''' + sin(orient)*y'''
y2 =-sin(orient)*y''' + cos(orient)*y'''

See also slaFitxy, slaPxy, slaInvf, slaXy2xy

P.T.Wallace   Starlink   31 October 1993
```