/********** Copyright 1990 Regents of the University of California. All rights reserved. Author: 1985 Wayne A. Christopher, U. C. Berkeley CAD Group **********/ /* * Routines to do complex mathematical functions. These routines require * the -lm libraries. We sacrifice a lot of space to be able * to avoid having to do a seperate call for every vector element, * but it pays off in time savings. These routines should never * allow FPE's to happen. * * Complex functions are called as follows: * cx_something(data, type, length, &newlength, &newtype), * and return a char * that is cast to complex or double. */ #include "ngspice/ngspice.h" #include "ngspice/cpdefs.h" #include "ngspice/dvec.h" #include "ngspice/randnumb.h" #include "cmath.h" #include "cmath2.h" static double cx_max_local(void *data, short int type, int length) { double largest = 0.0; if (type == VF_COMPLEX) { ngcomplex_t *cc = (ngcomplex_t *) data; int i; for (i = 0; i < length; i++) if (largest < cmag(cc[i])) largest = cmag(cc[i]); } else { double *dd = (double *) data; int i; for (i = 0; i < length; i++) if (largest < fabs(dd[i])) largest = fabs(dd[i]); } return largest; } /* Normalize the data so that the magnitude of the greatest value is 1. */ void * cx_norm(void *data, short int type, int length, int *newlength, short int *newtype) { double largest = 0.0; largest = cx_max_local(data, type, length); if (largest == 0.0) { fprintf(cp_err, "Error: can't normalize a 0 vector\n"); return (NULL); } *newlength = length; if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = realpart(cc[i]) / largest; imagpart(c[i]) = imagpart(cc[i]) / largest; } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) d[i] = dd[i] / largest; return ((void *) d); } } void * cx_uminus(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = - realpart(cc[i]); imagpart(c[i]) = - imagpart(cc[i]); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) d[i] = - dd[i]; return ((void *) d); } } /* random integers drawn from a uniform distribution * data in: integer numbers, their absolut values are used, * maximum is RAND_MAX (32767) * data out: random integers in interval [0, data[i][ * standard library function rand() is used */ void * cx_rnd(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; checkseed(); if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { int j, k; j = (int)floor(realpart(cc[i])); k = (int)floor(imagpart(cc[i])); realpart(c[i]) = j ? rand() % j : 0; imagpart(c[i]) = k ? rand() % k : 0; } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) { int j; j = (int)floor(dd[i]); d[i] = j ? rand() % j : 0; } return ((void *) d); } } /* random numbers drawn from a uniform distribution * data out: random numbers in interval [-1, 1[ */ void * cx_sunif(void *data, short int type, int length, int *newlength, short int *newtype) { NG_IGNORE(data); *newlength = length; checkseed(); if (type == VF_COMPLEX) { ngcomplex_t *c; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = drand(); imagpart(c[i]) = drand(); } return ((void *) c); } else { double *d; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) { d[i] = drand(); } return ((void *) d); } } /* random numbers drawn from a poisson distribution * data in: lambda * data out: random integers according to poisson distribution, * with lambda given by each vector element */ void * cx_poisson(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; checkseed(); if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = poisson (realpart(cc[i])); imagpart(c[i]) = poisson (imagpart(cc[i])); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) { d[i] = poisson(dd[i]); } return ((void *) d); } } /* random numbers drawn from an exponential distribution * data in: Mean values * data out: exponentially distributed random numbers, * with mean given by each vector element */ void * cx_exponential(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; checkseed(); if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = exprand(realpart(cc[i])); imagpart(c[i]) = exprand(imagpart(cc[i])); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) { d[i] = exprand(dd[i]); } return ((void *) d); } } /* random numbers drawn from a Gaussian distribution mean 0, std dev 1 */ void * cx_sgauss(void *data, short int type, int length, int *newlength, short int *newtype) { NG_IGNORE(data); *newlength = length; checkseed(); if (type == VF_COMPLEX) { ngcomplex_t *c; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = gauss0(); imagpart(c[i]) = gauss0(); } return ((void *) c); } else { double *d; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) { d[i] = gauss1(); } return ((void *) d); } } /* Compute the avg of a vector. * Created by A.M.Roldan 2005-05-21 */ void * cx_avg(void *data, short int type, int length, int *newlength, short int *newtype) { double sum_real = 0.0, sum_imag = 0.0; int i; if (type == VF_REAL) { double *d = alloc_d(length); double *dd = (double *) data; *newtype = VF_REAL; *newlength = length; for (i = 0; i < length; i++) { sum_real += dd[i]; d[i] = sum_real / ((double) i + 1.0); } return ((void *) d); } else { ngcomplex_t *c = alloc_c(length); ngcomplex_t *cc = (ngcomplex_t *) data; *newtype = VF_COMPLEX; *newlength = length; for (i = 0; i < length; i++) { sum_real += realpart(cc[i]); realpart(c[i]) = sum_real / ((double) i + 1.0); sum_imag += imagpart(cc[i]); imagpart(c[i]) = sum_imag / ((double) i + 1.0); } return ((void *) c); } } /* Compute the mean of a vector. */ void *cx_mean(void *data, short int type, int length, int *newlength, short int *newtype) { if (length == 0) { (void) fprintf(cp_err, "mean calculation requires " "at least one element.\n"); return NULL; } *newlength = 1; if (type == VF_REAL) { double *d; double *dd = (double *) data; int i; d = alloc_d(1); *newtype = VF_REAL; for (i = 0; i < length; i++) *d += dd[i]; *d /= length; return ((void *) d); } else { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(1); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(*c) += realpart(cc[i]); imagpart(*c) += imagpart(cc[i]); } realpart(*c) /= length; imagpart(*c) /= length; return ((void *) c); } } /* Compute the standard deviation of all elements of a vector. */ void *cx_stddev(void *data, short int type, int length, int *newlength, short int *newtype) { if (length == 0) { (void) fprintf(cp_err, "standard deviation calculation requires " "at least one element.\n"); return NULL; } *newlength = 1; if (type == VF_REAL) { double *p_mean = (double *) cx_mean(data, type, length, newlength, newtype); double mean = *p_mean; double *d, sum = 0.0; double *dd = (double *) data; d = alloc_d(1); *newtype = VF_REAL; int i; for (i = 0; i < length; i++) { const double tmp = dd[i] - mean; sum += tmp * tmp; } *d = sqrt(sum / ((double) length - 1.0)); txfree(p_mean); return (void *) d; } else { ngcomplex_t * const p_cmean = (ngcomplex_t *) cx_mean(data, type, length, newlength, newtype); const ngcomplex_t cmean = *p_cmean; const double rmean = realpart(cmean); const double imean = imagpart(cmean); double *d, sum = 0.0; ngcomplex_t *cc = (ngcomplex_t *) data; d = alloc_d(1); *newtype = VF_REAL; int i; for (i = 0; i < length; i++) { const double a = realpart(cc[i]) - rmean; const double b = imagpart(cc[i]) - imean; sum += a * a + b * b; } *d = sqrt(sum / ((double) length - 1.0)); txfree(p_cmean); return (void *) d; } } /* end of function cx_stddev */ void * cx_length(void *data, short int type, int length, int *newlength, short int *newtype) { double *d; NG_IGNORE(data); NG_IGNORE(type); *newlength = 1; *newtype = VF_REAL; d = alloc_d(1); *d = length; return ((void *) d); } /* Return a vector from 0 to the magnitude of the argument. Length of the * argument is irrelevent. */ void * cx_vector(void *data, short int type, int length, int *newlength, short int *newtype) { ngcomplex_t *cc = (ngcomplex_t *) data; double *dd = (double *) data; int i, len; double *d; NG_IGNORE(length); if (type == VF_REAL) len = (int)fabs(*dd); else len = (int)cmag(*cc); if (len == 0) len = 1; d = alloc_d(len); *newlength = len; *newtype = VF_REAL; for (i = 0; i < len; i++) d[i] = i; return ((void *) d); } /* Create a vector of the given length composed of all ones. */ void * cx_unitvec(void *data, short int type, int length, int *newlength, short int *newtype) { ngcomplex_t *cc = (ngcomplex_t *) data; double *dd = (double *) data; int i, len; double *d; NG_IGNORE(length); if (type == VF_REAL) len = (int)fabs(*dd); else len = (int)cmag(*cc); if (len == 0) len = 1; d = alloc_d(len); *newlength = len; *newtype = VF_REAL; for (i = 0; i < len; i++) d[i] = 1; return ((void *) d); } /* Calling methods for these functions are: * cx_something(data1, data2, datatype1, datatype2, length) * * The length of the two data vectors is always the same, and is the length * of the result. The result type is complex if one of the args is * complex. */ void * cx_plus(void *data1, void *data2, short int datatype1, short int datatype2, int length) { double *dd1 = (double *) data1; double *dd2 = (double *) data2; double *d; ngcomplex_t *cc1 = (ngcomplex_t *) data1; ngcomplex_t *cc2 = (ngcomplex_t *) data2; ngcomplex_t *c, c1, c2; int i; if ((datatype1 == VF_REAL) && (datatype2 == VF_REAL)) { d = alloc_d(length); for (i = 0; i < length; i++) d[i] = dd1[i] + dd2[i]; return ((void *) d); } else { c = alloc_c(length); for (i = 0; i < length; i++) { if (datatype1 == VF_REAL) { realpart(c1) = dd1[i]; imagpart(c1) = 0.0; } else { c1 = cc1[i]; } if (datatype2 == VF_REAL) { realpart(c2) = dd2[i]; imagpart(c2) = 0.0; } else { c2 = cc2[i]; } realpart(c[i]) = realpart(c1) + realpart(c2); imagpart(c[i]) = imagpart(c1) + imagpart(c2); } return ((void *) c); } } void * cx_minus(void *data1, void *data2, short int datatype1, short int datatype2, int length) { double *dd1 = (double *) data1; double *dd2 = (double *) data2; double *d; ngcomplex_t *cc1 = (ngcomplex_t *) data1; ngcomplex_t *cc2 = (ngcomplex_t *) data2; ngcomplex_t *c, c1, c2; int i; if ((datatype1 == VF_REAL) && (datatype2 == VF_REAL)) { d = alloc_d(length); for (i = 0; i < length; i++) d[i] = dd1[i] - dd2[i]; return ((void *) d); } else { c = alloc_c(length); for (i = 0; i < length; i++) { if (datatype1 == VF_REAL) { realpart(c1) = dd1[i]; imagpart(c1) = 0.0; } else { c1 = cc1[i]; } if (datatype2 == VF_REAL) { realpart(c2) = dd2[i]; imagpart(c2) = 0.0; } else { c2 = cc2[i]; } realpart(c[i]) = realpart(c1) - realpart(c2); imagpart(c[i]) = imagpart(c1) - imagpart(c2); } return ((void *) c); } } void * cx_times(void *data1, void *data2, short int datatype1, short int datatype2, int length) { double *dd1 = (double *) data1; double *dd2 = (double *) data2; double *d; ngcomplex_t *cc1 = (ngcomplex_t *) data1; ngcomplex_t *cc2 = (ngcomplex_t *) data2; ngcomplex_t *c, c1, c2; int i; if ((datatype1 == VF_REAL) && (datatype2 == VF_REAL)) { d = alloc_d(length); for (i = 0; i < length; i++) d[i] = dd1[i] * dd2[i]; return ((void *) d); } else { c = alloc_c(length); for (i = 0; i < length; i++) { if (datatype1 == VF_REAL) { realpart(c1) = dd1[i]; imagpart(c1) = 0.0; } else { c1 = cc1[i]; } if (datatype2 == VF_REAL) { realpart(c2) = dd2[i]; imagpart(c2) = 0.0; } else { c2 = cc2[i]; } realpart(c[i]) = realpart(c1) * realpart(c2) - imagpart(c1) * imagpart(c2); imagpart(c[i]) = imagpart(c1) * realpart(c2) + realpart(c1) * imagpart(c2); } return ((void *) c); } } void *cx_mod(void *data1, void *data2, short int datatype1, short int datatype2, int length) { int xrc = 0; void *rv; double *dd1 = (double *) data1; double *dd2 = (double *) data2; if ((datatype1 == VF_REAL) && (datatype2 == VF_REAL)) { double *d; rv = d = alloc_d(length); int i; for (i = 0; i < length; i++) { const int r1 = (int) floor(fabs(dd1[i])); rcheck(r1 > 0, "mod"); const int r2 = (int)floor(fabs(dd2[i])); rcheck(r2 > 0, "mod"); const int r3 = r1 % r2; d[i] = (double) r3; } } else { ngcomplex_t *c, c1, c2; ngcomplex_t *cc1 = (ngcomplex_t *) data1; ngcomplex_t *cc2 = (ngcomplex_t *) data2; rv = c = alloc_c(length); int i; for (i = 0; i < length; i++) { if (datatype1 == VF_REAL) { realpart(c1) = dd1[i]; imagpart(c1) = 0.0; } else { c1 = cc1[i]; } if (datatype2 == VF_REAL) { realpart(c2) = dd2[i]; imagpart(c2) = 0.0; } else { c2 = cc2[i]; } const int r1 = (int) floor(fabs(realpart(c1))); rcheck(r1 > 0, "mod"); const int r2 = (int) floor(fabs(realpart(c2))); rcheck(r2 > 0, "mod"); const int i1 = (int) floor(fabs(imagpart(c1))); rcheck(i1 > 0, "mod"); const int i2 = (int) floor(fabs(imagpart(c2))); rcheck(i2 > 0, "mod"); const int r3 = r1 % r2; const int i3 = i1 % i2; realpart(c[i]) = (double) r3; imagpart(c[i]) = (double) i3; } } EXITPOINT: if (xrc != 0) { /* Free resources on error */ txfree(rv); rv = NULL; } return rv; } /* end of function cx_mod */ /* Routoure JM : Compute the max of a vector. */ void *cx_max(void *data, short int type, int length, int *newlength, short int *newtype) { if (length == 0) { (void) fprintf(cp_err, "maximum calculation requires " "at least one element.\n"); return NULL; } *newlength = 1; if (type == VF_REAL) { double largest = 0.0; double *d; double *dd = (double *) data; int i; d = alloc_d(1); *newtype = VF_REAL; largest = dd[0]; for (i = 1; i < length; i++) { const double tmp = dd[i]; if (largest < tmp) { largest = tmp; } } *d = largest; return (void *) d; } else { double largest_real = 0.0; double largest_complex = 0.0; ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(1); *newtype = VF_COMPLEX; largest_real = realpart(*cc); largest_complex = imagpart(*cc); for (i = 1; i < length; i++) { const double tmpr = realpart(cc[i]); if (largest_real < tmpr) { largest_real = tmpr; } const double tmpi = imagpart(cc[i]); if (largest_complex < tmpi) { largest_complex = tmpi; } } realpart(*c) = largest_real; imagpart(*c) = largest_complex; return (void *) c; } } /* end of function cx_max */ /* Routoure JM : Compute the min of a vector. */ void *cx_min(void *data, short int type, int length, int *newlength, short int *newtype) { if (length == 0) { (void) fprintf(cp_err, "minimum calculation requires " "at least one element.\n"); return NULL; } *newlength = 1; if (type == VF_REAL) { double smallest; double *d; double *dd = (double *) data; int i; d = alloc_d(1); *newtype = VF_REAL; smallest = dd[0]; for (i = 1; i < length; i++) { const double tmp = dd[i]; if (smallest > tmp) { smallest = tmp; } } *d = smallest; return (void *) d; } else { double smallest_real; double smallest_complex; ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(1); *newtype = VF_COMPLEX; smallest_real = realpart(*cc); smallest_complex = imagpart(*cc); for (i = 1; i < length; i++) { const double tmpr = realpart(cc[i]); if (smallest_real > tmpr) { smallest_real = tmpr; } const double tmpi = imagpart(cc[i]); if (smallest_complex > tmpi) { smallest_complex = tmpi; } } realpart(*c) = smallest_real; imagpart(*c) = smallest_complex; return (void *) c; } } /* end of function cx_min */ /* Routoure JM : Compute the differential of a vector. */ void *cx_d(void *data, short int type, int length, int *newlength, short int *newtype) { if (length == 0) { (void) fprintf(cp_err, "differential calculation requires " "at least one element.\n"); return NULL; } *newlength = length; if (type == VF_REAL) { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; d[0] = dd[1] - dd[0]; d[length-1] = dd[length-1] - dd[length-2]; for (i = 1; i < length - 1; i++) { d[i] = dd[i+1] - dd[i-1]; } return (void *) d; } else { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; realpart(*c) = realpart(cc[1]) - realpart(cc[0]); imagpart(*c) = imagpart(cc[1]) - imagpart(cc[0]); realpart(c[length-1]) = realpart(cc[length-1]) - realpart(cc[length-2]); imagpart(c[length-1]) = imagpart(cc[length-1]) - imagpart(cc[length-2]); for (i = 1; i < length - 1; i++) { realpart(c[i]) = realpart(cc[i+1]) - realpart(cc[i-1]); imagpart(c[i]) = imagpart(cc[i+1]) - imagpart(cc[i-1]); } return (void *) c; } } /* end of function cx_d */ void * cx_floor(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = floor(realpart(cc[i])); imagpart(c[i]) = floor(imagpart(cc[i])); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) d[i] = floor(dd[i]); return ((void *) d); } } void * cx_ceil(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = ceil(realpart(cc[i])); imagpart(c[i]) = ceil(imagpart(cc[i])); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) d[i] = ceil(dd[i]); return ((void *) d); } } void * cx_nint(void *data, short int type, int length, int *newlength, short int *newtype) { *newlength = length; if (type == VF_COMPLEX) { ngcomplex_t *c; ngcomplex_t *cc = (ngcomplex_t *) data; int i; c = alloc_c(length); *newtype = VF_COMPLEX; for (i = 0; i < length; i++) { realpart(c[i]) = nearbyint(realpart(cc[i])); imagpart(c[i]) = nearbyint(imagpart(cc[i])); } return ((void *) c); } else { double *d; double *dd = (double *) data; int i; d = alloc_d(length); *newtype = VF_REAL; for (i = 0; i < length; i++) d[i] = nearbyint(dd[i]); return ((void *) d); } }