Programmer Guide/Command Reference/EVAL/complex arithmetic

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{{DISPLAYTITLE:complex arithmetic

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.

The package consists of the functions:

cr2p, cr2len, cr2phi, cp2r, cget, cset, conj, ctrn, cdot, cmul, cmulv

Note:

  • A complex number or complex scalar is a numerical object v with 2 rows and 1 column (a vector):
v[0] = re (cartesian: real part) or len (polar: length)
v[1] = im (cartesian: imaginary part) or phi (polar: phase)
  • A complex vector with N elements is a numerical object v with 2N rows and 1 column (a vector):
v[2i] = rei or reireal part (re) or length (len, polar)
v[1] = imaginary part (im, cartesian) or phase (phi, polar)
  • In general 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
xc ... any complex type
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
xc ... any complex type
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
x ... any real type
y ... same type as x
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)
xc ... any complex type (re,im)
yc ... same complex type as 'xc'
n ... 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
rcscalar=cdot(xcvector,ycvector)
Compute the dot product (inner product) of the two complex vectors xc and yc (both with N elements).
rc = sumi=0..N-1 (xci * yci) , i=0..N-1
rcmatrix=ctrn(xcmatrix)
Transposed the complex matrix xc.
rci,j = xcj,i
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


See also
complex numbers, vvset, vvget, vv, fft, dft,

<function list>

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