cplxpair

Sorting complex numbers into conjugate pairs

Usage

cplxpair(A)

• A is an array of real or complex numbers.
• It sorts complex numbers in acesending order of their real parts. Conjugate pairs are grouped such that the one with a negative imaginary part comes before its conjugate.
• Real numbers are sorted in ascending order and appear after all complex numbers in the sorted array.
• NaNs will appear after the real numbers.
• It sorts in the direction of the first non-singleton dimension.
• A number is considered as real if the absolute value of its imaginary part does not exceed eps(1).
• Complex numbers c1 = a1 + b1*i and c2 = a2 + b2*i form a conjugate pair if abs(a1-a2) and abs(abs(b1) - abs(b2)) are both smaller than the default tolerance max(abs(c1), abs(c2)) * eps(1), and b1 and b2 have opposite signs.
• For the complex number a + bi, if a or b is either NaN or Inf, its complex conjugate cannot be paired.
• It returns error if the conjugate of a complex number cannot be paired or not found in A. This happens when, for example, there are odd number of complex numbers.

cplxpair(A, [ ], dim)

• A is as specified in the description above for cplxpair(A).
• [] means an empty array.
• It sorts in the direction of dimension dim.
• dim should be a real positive integer.

cplxpair(A, tol)

• A is as specified in the description above for cplxpair(A).
• tol is a tolerance used in determining real numbers and conjugate pairs.
• tol should be a non-negative scalar smaller than 1.
• A number is considered real if the absolute value of its imaginary part does not exceed tol.
• Complex numbers c1 = a1 + b1*i and c2 = a2 + b2*i form a conjugate pair if abs(a1-a2) and abs(b1-b2) are both smaller than tol, and b1 and b2 have opposite signs.

cplxpair(A, tol, dim)

• A, tol and dim are as specified in the descriptions above for cplxpair(A), cplxpair(A,[],dim) and cplxpair(A,tol).
• It sorts A along the dim-th dimension using the tolerance tol.

Examples

• Sorting a complex vector.

Input

a=[-27.62 - 4.075i
 -0.014 + 0.032i
 -27.62 + 7.557i
 -0.014 - 19.00i
  28.05 - 0.161i
 -27.62 - 7.557i
  28.05 - 4.384i
 -0.014 + 19.00i
  28.05 + 4.384i
  26.37 + 0.000i
 -0.014 - 0.032i
  0.020 + 0.000i
  0.005 + 0.000i
 -27.62 + 4.075i
  28.05 + 0.161i];
cplxpair(a)

Output

ans = 
-27.620 - 4.0750i
-27.620 + 4.0750i
-27.620 - 7.5570i
-27.620 + 7.5570i
-0.0140 - 0.0320i
-0.0140 + 0.0320i
-0.0140 - 19.000i
-0.0140 + 19.000i
 28.050 - 0.1610i
 28.050 + 0.1610i
 28.050 - 4.3840i
 28.050 + 4.3840i
 0.0050 + 0.0000i
 0.0200 + 0.0000i
 26.370 + 0.0000i

• Sorting a complex matrix along the second dimension.

Input

a=[
-0.495 - 0.344i  -49.62 - 0.014i
-4.611 + 0.000i  -3.663 + 0.000i
 0.085 + 0.042i  -47.09 - 0.024i
 0.029 + 20.22i   0.682 - 10.84i
 0.085 - 0.042i  -47.09 + 0.024i
 0.029 + 0.216i   0.682 - 1.132i
-0.495 + 38.07i  -49.62 + 2.114i
 0.085 - 4.951i  -47.09 + 0.022i
-0.495 - 38.07i  -49.62 - 2.114i
 0.085 + 4.951i  -47.09 - 0.022i
 0.522 + 0.000i   1.122 + 0.000i
 0.029 - 0.216i   0.682 + 1.132i
-0.495 + 0.344i  -49.62 + 0.014i
 0.029 - 20.22i   0.682 + 10.84i
-2.575 + 0.000i  -37.70 + 0.000i
]'
cplxpair(a,[],2)

Output

a = 
Columns 1 through 5:
-0.4950 + 0.3440i  -4.6110 + 0.0000i   0.0850 - 0.0420i   0.0290 - 20.220i   0.0850 + 0.0420i
-49.620 + 0.0140i  -3.6630 + 0.0000i  -47.090 + 0.0240i   0.6820 + 10.840i  -47.090 - 0.0240i
Columns 6 through 10:
 0.0290 - 0.2160i  -0.4950 - 38.070i   0.0850 + 4.9510i  -0.4950 + 38.070i   0.0850 - 4.9510i
 0.6820 + 1.1320i  -49.620 - 2.1140i  -47.090 - 0.0220i  -49.620 + 2.1140i  -47.090 + 0.0220i
Columns 11 through 15:
 0.5220 + 0.0000i   0.0290 + 0.2160i  -0.4950 - 0.3440i   0.0290 + 20.220i  -2.5750 + 0.0000i
 1.1220 + 0.0000i   0.6820 - 1.1320i  -49.620 - 0.0140i   0.6820 - 10.840i  -37.700 + 0.0000i

ans = 
Columns 1 through 5:
-0.4950 - 0.3440i  -0.4950 + 0.3440i  -0.4950 - 38.070i  -0.4950 + 38.070i   0.0290 - 0.2160i
-49.620 - 0.0140i  -49.620 + 0.0140i  -49.620 - 2.1140i  -49.620 + 2.1140i  -47.090 - 0.0220i
Columns 6 through 10:
 0.0290 + 0.2160i   0.0290 - 20.220i   0.0290 + 20.220i   0.0850 - 0.0420i   0.0850 + 0.0420i
-47.090 + 0.0220i  -47.090 - 0.0240i  -47.090 + 0.0240i   0.6820 - 1.1320i   0.6820 + 1.1320i
Columns 11 through 15:
 0.0850 - 4.9510i   0.0850 + 4.9510i  -4.6110 + 0.0000i  -2.5750 + 0.0000i   0.5220 + 0.0000i
 0.6820 - 10.840i   0.6820 + 10.840i  -37.700 + 0.0000i  -3.6630 + 0.0000i   1.1220 + 0.0000i

• The matrix a is sorted along the first dimension with tolerance tol = 0.00101. Hence, in the first and second rows of the sorted array, -0.3794973 - 0.4599557i and -0.3784973 + 0.4609557i form a conjugate pair, even though the real parts (and also the imaginary parts) differ by 0.001.

Input

a =[
-0.1092265 - 0.0175371i  -34.228177 + 4.7641329i
-0.0308166 + 0.0000000i  -0.1631809 + 0.0000000i
-0.1102265 + 0.0185371i  -34.229177 - 4.7631329i
 2.4420461 - 0.0238848i   0.1105287 - 0.1661568i
 2.4430461 + 0.0248848i   0.1115287 + 0.1671568i
-0.1102265 - 0.0621998i  -34.229177 - 41.254490i
 47.129957 + 0.0000000i   0.4034812 + 0.0000000i
-3.6544816 + 0.0000000i   0.0116494 + 0.0000000i
 2.4420461 - 1.7635095i   0.1105287 - 0.5415976i
-0.1102265 + 0.0621998i  -34.229177 + 41.254490i
 2.4420461 + 1.7635095i   0.1105287 + 0.5415976i
-0.3794973 - 0.4599557i   4.7495474 + 5.9845691i
-0.3794973 - 4.1173533i   4.7495474 + 0.1136352i
-0.3784973 + 0.4609557i   4.7505474 - 5.9835691i
-0.3794973 + 4.1173533i   4.7495474 - 0.1136352i
]
cplxpair(a,0.00101)

Output

a = 
-0.1092 - 0.0175i  -34.228 + 4.7641i
-0.0308 + 0.0000i  -0.1632 + 0.0000i
-0.1102 + 0.0185i  -34.229 - 4.7631i
 2.4420 - 0.0239i   0.1105 - 0.1662i
 2.4430 + 0.0249i   0.1115 + 0.1672i
-0.1102 - 0.0622i  -34.229 - 41.254i
 47.130 + 0.0000i   0.4035 + 0.0000i
-3.6545 + 0.0000i   0.0116 + 0.0000i
 2.4420 - 1.7635i   0.1105 - 0.5416i
-0.1102 + 0.0622i  -34.229 + 41.254i
 2.4420 + 1.7635i   0.1105 + 0.5416i
-0.3795 - 0.4600i   4.7495 + 5.9846i
-0.3795 - 4.1174i   4.7495 + 0.1136i
-0.3785 + 0.4610i   4.7505 - 5.9836i
-0.3795 + 4.1174i   4.7495 - 0.1136i

ans = 
-0.3795 - 0.4600i  -34.229 - 4.7631i
-0.3785 + 0.4610i  -34.228 + 4.7641i
-0.3795 - 4.1174i  -34.229 - 41.254i
-0.3795 + 4.1174i  -34.229 + 41.254i
-0.1092 - 0.0175i   0.1105 - 0.1662i
-0.1102 + 0.0185i   0.1115 + 0.1672i
-0.1102 - 0.0622i   0.1105 - 0.5416i
-0.1102 + 0.0622i   0.1105 + 0.5416i
 2.4420 - 0.0239i   4.7495 - 0.1136i
 2.4430 + 0.0249i   4.7495 + 0.1136i
 2.4420 - 1.7635i   4.7505 - 5.9836i
 2.4420 + 1.7635i   4.7495 + 5.9846i
-3.6545 + 0.0000i  -0.1632 + 0.0000i
-0.0308 + 0.0000i   0.0116 + 0.0000i
 47.130 + 0.0000i   0.4035 + 0.0000i