hyper.basic {hyper.fit}

Functions to calculate various basic properties important for line fitting

Description

rotdata2d: Function to generate a 2xN matrix with rotated columns x and y.

rotdata3d: Function to generate a 3xN matrix with rotated columns x,y and z.

makerotmat2d: Function to generate a 2x2 rotation matrix.

makerotmat3d: Function to generate a 3x3 rotation matrix.

rotcovmat: Function to generate a rotated covariance matrix, either 2x2 or 3x3.

ranrotcovmat2d: Function to generate a randomly rotated 2x2 covariance matrix.

ranrotcovmat3d: Function to generate a randomly rotated 3x3 covariance matrix.

makecovarray2d: Function to generate a 2x2xN covariance array.

makecovarray3d: Function to generate a 3x3xN covariance array.

makecovmat2d: Function to generate a 2x2 covariance matrix.

makecovmat3d: Function to generate a 3x3 covariance matrix.

projX: Projection of position (or possibly velocity) elements along a vector (any number of dimensions, but matrices must conform).

projcovmat: Projection of a covariance matrix along a vector (any number of dimensions, but matrices must conform).

projcovarray: Projection of a covariance array (dim x dim x N) along a vector (any number of dimensions, but matrices must conform).

arrayvecmult: Matrix multiply array elements by a vector. To behave sensibly the second dimension of the AxBxC (i.e. B) array should be the same length as the multiplication vector.

Usage

rotdata2d(x, y, theta)

rotdata3d(x, y, z, theta, dim = 'z')

makerotmat2d(theta)

makerotmat3d(theta, dim = 'z')

rotcovmat(covmat, theta, dim = 'x')

ranrotcovmat2d(covmat)

ranrotcovmat3d(covmat)

makecovarray2d(sx, sy, corxy)

makecovarray3d(sx, sy, sz, corxy, corxz, coryz)

makecovmat2d(sx, sy, corxy)

makecovmat3d(sx, sy, sz, corxy, corxz, coryz)

projX(X, projvec)

projcovmat(covmat, projvec)

projcovarray(covarray, projvec)

arrayvecmult(array, vec)

Arguments

x

Vector of x data. Should be the same length as y.

y

Vector of y data. Should be the same length as x.

z

Vector of z data. Should be the same length as x/y.

X

A position matrix with the N (number of data points) rows by d (number of dimensions) columns.

sx

Vector of x errors. Should be the same length as sy.

sy

Vector of y errors. Should be the same length as sx.

sz

Vector of z errors. Should be the same length as sx/sy.

corxy

Vector of correlation values between sx and sy values. Should be the same length as sx.

corxz

Vector of correlation values between sx and sz values. Should be the same length as sx/sy/sz/corxy/coryz.

coryz

Vector of correlation values between sy and sz values. Should be the same length as sx/sy/sz/corxy/corxz.

covmat

A dxd (d=dimensions, i.e. 2x2 for 2d or 3x3 for 3d). The makecovmat2d and makecovmat3d are convenience functions that make populating 2x2 and 3x3 matrices easier for a novice user.

covarray

A dxdxN array containing the full covariance (d=dimensions, N=number of dxd matrices in the array stack). The makecovarray2d and makecovarray3d are convenience functions that make populating 2x2xN and 3x3xN arrays easier for a novice user.

theta

Angle in degrees for rotation. x -> y = +ve rotation, x -> z = +ve rotation, y -> z = +ve rotation.

dim

In 3D this specifies the axis around which the rotation takes place. If dim='x' rotation is in the yz plane and y -> z = +ve rotation. If dim='y' rotation is in the xz plane and x -> z = +ve rotation. If dim='z' rotation is in the xy plane and x -> y = +ve rotation.

projvec

The vector defining the desired projection. This does not need to be of length 1, but the user should be aware that unless it is of length 1 then the solution will not be normalised correctly for the unit vector case (if this is desired the input should be projvec=exprojvec/(sqrt(sum(exprojvec^2))), where exprojvec is the desired direction of projection).

array

A AxBxC array.

vec

A vector of length B (same length as the second array dimension of array argument).

Value

rotdata2d: A 2xN matrix with rotated columns x and y.

rotdata3d: A 3xN matrix with rotated columns x,y and z.

makerotmat2d: A 2x2 rotation matrix.

makerotmat3d: A 3x3 rotation matrix.

rotcovmat: A rotated covariance matrix, either 2x2 or 3x3.

ranrotcovmat2d: A randomly rotated 2x2 covariance matrix.

ranrotcovmat3d: A randomly rotated 3x3 covariance matrix.

makecovarray2d: A 2x2 covariance matrix.

makecovarray3d: A 3x3 covariance matrix.

makecovmat2d: A 2x2xN covariance array.

makecovmat3d: A 3x3xN covariance array.

projX: Projection of X along vector (length N).

projcovmat: Projection of covariance matrix along vector (length 1).

projcovarray: Projection of covariance array along vector (length N).

arrayvecmult: Matrix multiplication of array stack slices by vector (size dxN).

Author(s)

Aaron Robotham and Danail Obreschkow

References

Robotham, A.S.G., & Obreschkow, D., PASA, in press

See Also

hyper.basic, hyper.convert, hyper.fit-data, hyper.fit, hyper.plot, hyper.sigcor, hyper.summary

Examples

extheta=30    #Experiment with changing this
exdim='z'     #Experiment with chaging to 'x' or 'y'
exvecx=1:10   #Experiment with changin this
exvecy=1:10   #Experiment with changin this
exvecz=1:10   #Experiment with changin this

print(cbind(exvecx, exvecy))
print(rotdata2d(exvecx, exvecy, extheta))
print(rotdata3d(exvecx, exvecy, exvecz, extheta, exdim))
print(makerotmat2d(extheta))
print(makerotmat3d(extheta, dim=exdim))

exsx=1        #Experiment with changing this
exsy=2        #Experiment with changing this
exsz=3        #Experiment with changing this
excorxy=0.8   #Experiment with changing this between -1 and 1
excorxz=-0.3  #Experiment with changing this between -1 and 1
excoryz=0.5   #Experiment with changing this between -1 and 1

print(makecovmat2d(exsx, exsy, excorxy))
print(makecovmat3d(exsx, exsy, exsz, excorxy, excorxz, excoryz))
print(makecovarray2d(exsx*1:4, exsy*1:4, excorxy))
print(makecovarray3d(exsx*1:4, exsy*1:4, exsz*1:4, excorxy, excorxz, excoryz))

excovmat2d=makecovmat2d(exsx, exsy, excorxy)
excovmat3d=makecovmat3d(exsx, exsy, exsz, excorxy, excorxz, excoryz)
excovarray2d=makecovarray2d(exsx*1:4, exsy*1:4, excorxy)
excovarray3d=makecovarray3d(exsx*1:4, exsy*1:4, exsz*1:4, excorxy, excorxz, excoryz)

print(rotcovmat(excovmat2d, extheta))
print(rotcovmat(excovmat3d, extheta, exdim))
print(ranrotcovmat2d(excovmat2d))
print(ranrotcovmat3d(excovmat3d))

exprojvec2d=c(1, 2)
exprojvec2d=exprojvec2d/sqrt(sum(exprojvec2d^2))
exprojvec3d=c(1, 2, 3)
exprojvec3d=exprojvec3d/sqrt(sum(exprojvec3d^2))

print(projX(cbind(exvecx, exvecy), exprojvec2d))
print(projX(cbind(exvecx, exvecy, exvecz), exprojvec3d))
print(projcovmat(excovmat2d, exprojvec2d))
print(projcovmat(excovmat3d, exprojvec3d))
print(projcovarray(excovarray2d, exprojvec2d))
print(projcovarray(excovarray3d, exprojvec3d))

#Notice that the first outputs of the 2d/3d projcovarray example correspond to the outputs
#of the 2d/3d projcovmat examples.

#First for comparison:

print(t(matrix(1:9,3) %*% 1:3))
print(t(matrix(10:18,3) %*% 1:3))
print(t(matrix(19:27,3) %*% 1:3))

#And now an array example of the above operations:

print(arrayvecmult(array(1:27,c(3,3,3)),1:3))

#And an example where all array dimensions are different:

print(matrix(1:6,2) %*% 1:3)
print(matrix(7:12,2) %*% 1:3)
print(matrix(13:18,2) %*% 1:3)
print(matrix(19:24,2) %*% 1:3)
print(arrayvecmult(array(1:24,c(2,3,4)),1:3))

#Note that the following is not allowed:

try(arrayvecmult(array(1:24,c(3,2,4)),1:3))