/* complex.h        define type complex and arithmetic operations */
/*                  also elementary functions and vector,matrix operations */
#ifndef COMPLEX_H_
#define COMPLEX_H_

typedef struct {double re; double im;} complex;

complex cmplx(double  a, double  b); /* create a complex number            */  
double  real (complex a);            /* get real part                      */
double  imag (complex a);            /* get imaginary part                 */
complex cxadd(complex a, complex b); /* add two complex numbers            */
complex cxsub(complex a, complex b); /* subtract b from a, complex         */
complex cxmul(complex a, complex b); /* multiply two complex numbers       */
complex cdmul(double  a, complex b); /* multiply double times complex      */
complex cmuld(complex a, double  b); /* multiply complex times double      */
complex cxdiv(complex a, complex b); /* divide complex by complex          */
complex cdivd(complex a, double  b); /* divide complex by double           */
double  cxabs(complex a);            /* return magnitude of complex munber */
double  cxarg(complex a);            /* return argument of complex number  */
complex cxneg(complex a);            /* negate a complex number            */
complex cxconj(complex a);           /* conjugate a complex number         */
double  sumabs(complex a);           /* abs re + abs im                    */

/* elementary functions */
complex cxsqrt(complex a);           /* square root of a complex number    */
complex cxexp(complex a);            /* e^a exp of a complex number        */
complex cxlog(complex a);            /* log base e of a complex number     */
complex cxsin(complex a);            /* sine of a complex number           */
complex cxcos(complex a);            /* cosine of a complex number         */
complex cxtan(complex a);            /* tangent of a complex number        */
complex cxatan(complex a);           /* arctangent of a complex number     */
complex cxsinh(complex a);           /* sinh of a complex number           */
complex cxcosh(complex a);           /* cosh of a complex number           */
complex cxtanh(complex a);           /* tanh of a complex number           */
complex cxatanh(complex a);          /* atanh of a complex number          */

/* vector, matrix operations */
void cxvadd(int n, complex A[n], complex B[n], complex C[n]); /* C = A + B */
void cxvsub(int n, complex A[n], complex B[n], complex C[n]); /* C = A - B */
void cxvcopy(int n, complex A[n], complex B[n]); /* copy vector A to B     */
double cxvnorm(int n, complex A[n]);       /* vector norm of A             */
void cxvident(int n, int i, complex A[n]); /* identity vector at i         */
void cxvprint(int n, complex A[n]);        /* print complex vector         */
void cxvran(int n, complex A[n]);          /* generate random complex vec  */

void cxmadd(int n, complex A[n][n], complex B[n][n], complex C[n][n]);/*C=A+B*/
void cxmsub(int n, complex A[n][n], complex B[n][n], complex C[n][n]);/*C=A-B*/
void cxmmul(int n, complex A[n][n], complex B[n][n], complex C[n][n]);/*C=A*B*/
void cxmcopy(int n, complex A[n][n], complex B[n][n]); /* copy matrix A to B */
double cxmnorm(int n, complex A[n][n]);     /* matrix norm of A              */
void cxmident(int n, complex A[n][n]);      /* initialize identity matrix    */
void cxmprint(int n, complex A[n][n]);      /* print complex matrix          */
void cxmran(int n, complex A[n][n]);        /* generate random complex matrix*/
void cxmvmul(int n, complex A[n][n], complex B[n], complex C[n]); /* C=A*B   */

void cxsimeq(int n, complex A[n][n], complex Y[n], complex X[n]);
                                            /* solve complex A*X=Y for X   */
complex cxdet(int n, complex A[n][n]);       /* complex determinant of A    */
void cxinv(int n, complex A[n][n], complex AA[n][n]); /* complex AA = A^-1 */

#endif /* COMPLEX_H_ */