Programmer Guide/Command Reference/EVAL/complex arithmetic: Difference between revisions
From STX Wiki
< Programmer Guide | Command Reference | EVAL
Jump to navigationJump to search
No edit summary |
|||
| Line 8: | Line 8: | ||
====complex numerical objects==== | ====complex numerical objects==== | ||
:* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector): | :* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector): | ||
::{|class="keinrahmen" | |||
|- | |- | ||
|''v''[0] = || ''re'' (cartesian: real part) or ''len'' (polar: length) | |''v''[0] = || ''re'' (cartesian: real part) or ''len'' (polar: length) | ||
| Line 15: | Line 15: | ||
|} | |} | ||
:* A complex vector with N elements is a numerical object ''v'' with 2N rows and 1 column (a vector): | :* A complex vector with N elements is a numerical object ''v'' with 2N rows and 1 column (a vector): | ||
::{|class="keinrahmen" | |||
|- | |- | ||
|''v''[2*i] = || ''re''<sub>i</sub> or ''len''<sub>i</sub> | |''v''[2*i] = || ''re''<sub>i</sub> or ''len''<sub>i</sub> | ||
| Line 22: | Line 22: | ||
|} | |} | ||
:* A complex matrix with MxN elements is a numerical object ''v'' with 2N rows and M columns (a matrix): | :* A complex matrix with MxN elements is a numerical object ''v'' with 2N rows and M columns (a matrix): | ||
::{|class="keinrahmen" | |||
|- | |- | ||
|''v''[2*i,j] = || ''re''<sub>i,j</sub> or ''len''<sub>i,j</sub> | |''v''[2*i,j] = || ''re''<sub>i,j</sub> or ''len''<sub>i,j</sub> | ||
Revision as of 09:27, 8 April 2011
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 following functions:
Contents
complex numerical objects
- 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[2*i] = rei or leni v[2*i+1] = imi or phii
- A complex matrix with MxN elements is a numerical object v with 2N rows and M columns (a matrix):
v[2*i,j] = rei,j or leni,j v[2*i+1,j] = imi,j or phii,j
- 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, the resulting object consists of N x M real numbers.
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 * nrc=cmul(xc,yc)- Multiply xc and yc element by element.
rci,j = xci,j * yci,j
special functions
rcmatrix=ctrn(xcmatrix)- Transposed the complex matrix xc.
rci,j = xcj,ircscalar=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-1rcmatrix=cmulv(xcvector,ycvector)- Compute the tensor (or dyadic) product of the two complex vectors xc and yc.
rci,j = xci * ycjrcvector=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-1rcvector=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-1rcmatrix=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
