This routine does a least squares fit of data to a plane. The plane is described by an equation of form:-

$$z=M_X\ast x+M_Y\ast y+C$$

(44)

CALL SCULIB_FIT_PLANE (N, X, Y, Z, QUALITY, MX, MY, C, STATUS)

N = INTEGER (Given)

X (N) = REAL (Given)

Y (N) = REAL (Given)

Z (N) = REAL (Given)

QUALITY (N) = INTEGER (Given)

MX = REAL (Returned)

MY = REAL (Returned)

C = REAL (Returned)

STATUS = INTEGER (Given and returned)

If status is good on entry the routine will loop through the input data calculating the sums required and the number of valid data points (i.e. those with good quality flags).

If there are less than 3 valid data then an error message will be output and bad status returned else the plane coefficients will be calculated from the following formulae:-

$$M_X=\frac{\sum y^2\left(n_v\sum xz-\sum x\sum z\right)-{\left(\sum y\right)}^2\sum xz-n_v\sum xy\sum yz+\sum y\left(\sum xy\sum z+\sum x\sum yz\right)}{2\sum xy\sum x\sum y-n_v{\left(\sum xy\right)}^2-{\left(\sum x\right)}^2\sum y^2+\sum x^2\left(n_v\sum y^2+{\left(\sum y\right)}^2\right)}$$

(45)

$$M_Y=\frac{n_v\sum yz-\sum y\sum z+M_X\left(\sum x\sum y-n_v\sum xy\right)}{n_v\sum y^2-{\left(\sum y\right)}^2}$$

(46)

$$C=\frac{\sum z-M_X\sum x-M_Y\sum y}{n_v}$$

(47)

where $n_v$ is the number of valid data points. If the denominator of the expression for MX is 0 then an error message will be output and bad status returned.

end if

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