Programmer Guide/Command Reference/EVAL/complex arithmetic: Difference between revisions
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|''v''[2*i+1,j] = || ''im''<sub>i,j</sub> or ''phi''<sub>i,j</sub> | |''v''[2*i+1,j] = || ''im''<sub>i,j</sub> or ''phi''<sub>i,j</sub> | ||
|} | |} | ||
:* In general a numerical object containing '''N x M''' complex numbers (N | :* 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. | :* 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. | ||
Revision as of 19:25, 21 April 2011
Because the current version of the STx EVAL command does 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:
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 * n
rc = 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,i
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 = 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