complex arithemtic

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Because the current version of the STx EVAL command do not support a complex data type, a package of functions is used to implement arithmetic and special handling for complex numbers.

Note:

  • A numerical object containing N x M complex numbers (N>=1, M>=1), consists of 2N rows and M columns, because each complex number uses two cells of a row.
  • If a numerical object containing N x M complex numbers, is converted element-wise to real numbers, the resulting object consists of N rows and M columns.

complex -> complex
argument xc any complex type
result rc same complex type as xc
rc=cr2p(xc)
Convert xc from cartesian (real, imaginary) to polar (length, phase) format.
rc=cp2r(xc)
Convert xc from polar (length, phase) to cartesian (real, imaginary) format.
rc=conj(xc)
Conjugate xc; xc must be in cartesian format.

complex -> real
argument xc any complex type
result r same real type as xc
r=cr2len(xc)
Compute length of xc; xc is stored in cartesian format.
r=cr2phi(xc)
Compute phase of xc; xc is stored in cartesian format.
r=cget(xc,0)
Get real part or length of xc (depends on format of xc).
r=cget(xc,1)
Get imaginary part or phase of xc (depends on format of xc).

real -> complex
argument x any real type
argument y same type as x
result rc same complex type as x
rc=cset(x,y)
Combine elements of x (real part or length) and y (imaginary part or phase) to complex numbers.

multiplication (element-wise)
argument xc any complex type (re,im)
argument yc same type as 'xc'
argument n a real or complex number (re,im)
result rc same complex type as xc
rc=cmul(xc,n)
rc=cmul(n,xc)
Multiply each element of xc with the real or complex number n.
rci,j = xci,j * n
rc=cmul(xc,yc)
Multiply xc and yc element by element.
rci,j = xci,j * yci,j

special functions
rcmatrix=cmulv(xcvector,ycvector)
Compute the tensor (or dyadic) product of the two complex vectors xc and yc:
rci,j = xci * ycj
rcvector=cmulv(xcvector,ycmatrix)
Compute the product of the complex vector xc (N elements) and the complex matrix yc (N rows, M columns).
rcj = sumi=0..N-1 (xci * yci,j) , j=0..M-1
rcvector=cmulv(xcmatrix,ycvector)
Compute the product of the complex matrix xc (N rows, M columns) and the complex vector yc (M elements).
rci = sumj=0..M-1 (xci,j * ycj) , i=0..N-1
rcmatrix=cmulv(xcmatrix,ycmatrix)
Compute the product of the complex NxM matrix xc and the complex MxL matrix yc. The result is the complex NxL matrix rc.
rci,k = sumj=0..M-1 (xci,j * ycj,i) , i=0..N-1 and k=0..L-1

special functions
rc=cdot(xc,yc)
the result rc (complex number) is the dot product of the complex vectors xc and yc (both with N elements).
rc = sumi=0..N-1 (xci * yci) , i=0..N-1
rc=ctrn(xc)
the result rc is transposed matrix of the complex matrix xc
rci,j = sumj=0..M-1 (xci,j * ycj,i) , i=0..N-1 and k=0..L-1


See also
fft, dft, complex numbers

<function list>

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