10 Complex numbers

10.1 Representation of complex numbers


The complex numbers are represented by structures

typedef  struct  FCOMPLEX {
    float    r,
               i;
}  fcomplex ;

typedef  struct  DCOMPLEX {
    double    r,
                  i;
}  dcomplex ;

typedef  struct  FPOLAIRE {
    float     rm,
                th;
}  fpolaire ;

typedef  struct  DPOLAIRE {
    double     rm,
                  th;
}  dpolaire ;

The first two structures represent complex numbers in the usual way (in simple precision for the first one, in double precision for the second), i.e. the member  r  is the real part and the member  i  is the imaginary part. The last two structures represent complex numbers in polar coordinates (in simple precision for the third, in double precision for the fourth), i.e. the member  rm  is the modulus and the member   th  is the phase.

The library contains many functions that are useful to manipulate complex numbers of the two types.
 
 
 
 

10.2 Functions using complex numbers


float   Cabs (fcomplex);

This function returns the modulus of its argument.


fcomplex   Cadd (fcomplex, fcomplex)

This function returns the sum of its arguments.


fcomplex    Ccos_c (fcomplex);

This function returns the complex cosine of its argument.


fcomplex   Cdiv (fcomplex, fcomplex);

This function returns the quotient of the first argument by the second.


fcomplex   Cexp_c (fcomplex);

This function returns the complex exponential of its argument.


fcomplex   Cinv (fcomplex);

This function returns the inverse of its argument.


fcomplex   Clog_c (fcomplex);

This function returns the complex logarithm of its argument.


fcomplex   Clog_p (fpolaire);

This function returns the complex logarithm of its argument.


fcomplex   Cmul (fcomplex, fcomplex);

This function returns the product of its arguments.


fcomplex   Cnegat (fcomplex);

This function returns the opposite of its argument.


fcomplex   Complex (float, float);

This function returns the complex number whose real and imaginary parts are respectively the first and the second argument.


fcomplex   Conjg (fcomplex);

This function returns the conjugate of its argument.


fpolaire   Conv_ctp (fcomplex);

This function returns its argument in polar coordinates.


fcomplex   Conv_ptc (fpolaire);

This function returns its argument in usual coordinates.


fcomplex   Cpuis (fcomplex, float);

This function returns the power of the first argument to the second.


fcomplex   Csqrt (fcomplex);

This function returns the principal square root of its argument.


fcomplex   Csin_c (fcomplex);

This function returns the complex sine of its argument.


fcomplex   Csub (fcomplex, fcomplex);

This function returns the difference of its arguments (1st - 2nd).


double   dCabs (dcomplex);

This function returns the modulus of its argument.


dcomplex   dCadd (dcomplex, dcomplex);

This function returns the sum of its arguments.


dcomplex   dCcos_c (dcomplex);

This function returns the complex cosine of its argument.


dcomplex   dCdiv (dcomplex, dcomplex);

This function returns the quotient of the first argument by the second.


dcomplex   dCexp_c (dcomplex);

This function returns the complex exponential of its argument.

dcomplex   dClog_c (dcomplex);

This function returns the complex logarithm of its argument.


dcomplex   dClog_p (dpolaire);

This function returns the complex logarithm of its argument.


dcomplex   dCmul (dcomplex, dcomplex);

This function returns the product of its arguments.


dcomplex   dCnegat (dcomplex);

This function returns the opposite of its argument.


dcomplex   dComplex (double, double);

This function returns the complex number whose real and imaginary parts are respectively the first and the second argument.


dcomplex   dConjg (dcomplex);

This function returns the conjugate of its argument.


dpolaire   dConv_ctp (dcomplex);

This function returns its argument in polar coordinates.


dcomplex   dConv_ptc (dpolaire);

This function returns its argument in usual coordinates.


dcomplex   dCpuis (dcomplex, double);

This function returns the power of the first argument to the second.


dcomplex   dCsin_c (dcomplex);

This function returns the complex sine of its argument.


dcomplex   dCsub (dcomplex, dcomplex);

This function returns the difference of its arguments (1st - 2nd).


dpolaire   dPadd (dpolaire, dpolaire);

This function returns the sum of its arguments.


dpolaire   dPconjg (dpolaire);

This function returns the conjugate of its argument.


dpolaire   dPdiv (dpolaire, dpolaire);

This function returns the quotient of its arguments.


dpolaire   dPexp_c (dcomplex);

This function returns the complex exponential of its argument.


dpolaire   dPexp_p (dpolaire);

This function returns the complex exponential of its argument.


dpolaire   dPinv (dpolaire);

This function returns the inverse of its argument.


dpolaire   dPlog_c (dpolaire);

This function returns the complex logarithm of its argument.


dpolaire   dPmul (dpolaire, dpolaire);

This function returns the product of its arguments.


dpolaire   dPolaire (double, double);

This function returns the complex number whose polar coordinates are the arguments.


dpolaire   dPpuis (dpolaire, double);

This function returns the power of the first argument to the second.


dpolaire   dPsqrt (dpolaire);

This function returns the principal square root of its argument.


dpolaire   dPsub (dpolaire, dpolaire);

This function returns the difference of its arguments (1st - 2nd).


dcomplex   dRCdiv (dcomplex, double);

This function returns the quotient of the first argument by the second.


dcomplex   dRCmul (double, dcomplex);

This function returns the product of the two arguments.


dpolaire   dRPdiv (dpolaire, double);

This function returns the quotient of the first argument by the second.


dpolaire   dRPmul (double, dpolaire);

This function returns the product of the two arguments.


fpolaire   Padd (fpolaire, fpolaire);

This function returns the sum of its arguments.


fpolaire   Pconjg (fpolaire);

This function returns the conjugate of its argument.


fpolaire   Pdiv (fpolaire, fpolaire);

This function returns the quotient of the first argument by the second.


fpolaire   Pexp_c (fcomplex);

This function returns the complex exponential of its argument.


fpolaire   Pexp_p (fpolaire);

This function returns the complex exponential of its argument.


fpolaire   Pinv (fpolaire);

This function returns the inverse of its argument.


fpolaire   Plog_c (fpolaire);

This function returns the complex logarithm of its argument.


fpolaire   Pmul (fpolaire, fpolaire);

This function returns the product of its arguments.


fpolaire   Polaire (float, float);

This function returns the complex number whose polar coordinates are the arguments.


fpolaire   Ppuis (fpolaire, float);

This function returns the power of the first argument to the second.


fpolaire   Psqrt (fpolaire);

This function returns the principal square root of its argument.


fpolaire   Psub (fpolaire, fpolaire);

This function returns the difference of its arguments (1st - 2nd).


fcomplex   RCdiv (fcomplex, float);

This function returns the quotient of the first argument by the second.


fcomplex   RCmul (float, fcomplex);

This function returns the product of the two arguments.


fpolaire   Rpdiv (fpolaire, float);

This function returns the quotient of the first argument by the second.


fpolaire   RPmul (float, fpolaire);

This function returns the product of the two arguments.


dcomplex   xdCinv (dcomplex);

This function returns the inverse of its argument.


dcomplex   xdCsqrt (dcomplex);

This function returns the principal square root of its argument.
 
 

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