spsolver.cpp

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/*
 * spsolver.cpp - S-parameter solver class implementation
 *
 * Copyright (C) 2003-2008 Stefan Jahn <stefan@lkcc.org>
 *
 * This is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2, or (at your option)
 * any later version.
 *
 * This software is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this package; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street - Fifth Floor,
 * Boston, MA 02110-1301, USA.
 *
 * $Id$
 *
 */

#if HAVE_CONFIG_H
# include <config.h>
#endif

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "logging.h"
#include "complex.h"
#include "object.h"
#include "node.h"
#include "circuit.h"
#include "strlist.h"
#include "vector.h"
#include "matvec.h"
#include "dataset.h"
#include "net.h"
#include "analysis.h"
#include "sweep.h"
#include "nodelist.h"
#include "netdefs.h"
#include "characteristic.h"
#include "spsolver.h"
#include "constants.h"
#include "components/component_id.h"
#include "components/tee.h"
#include "components/open.h"
#include "components/itrafo.h"
#include "components/cross.h"
#include "components/ground.h"

/* Evolved optimization flags. */
#define USE_GROUNDS 1   // use extra grounds ?
#define USE_CROSSES 1   // use additional cross connectors ?
#define SORTED_LIST 1   // use sorted node list?

#define TINYS (NR_TINY * 1.235) // 'tiny' value for singularities

namespace qucs {

// Constructor creates an unnamed instance of the spsolver class.
spsolver::spsolver () : analysis () {
  type = ANALYSIS_SPARAMETER;
  swp = NULL;
  saveCVs = 0;
  noise = 0;
  nlist = NULL;
  tees = crosses = opens = grounds = 0;
  gnd = NULL;
}

// Constructor creates a named instance of the spsolver class.
spsolver::spsolver (char * n) : analysis (n) {
  type = ANALYSIS_SPARAMETER;
  swp = NULL;
  saveCVs = 0;
  noise = 0;
  nlist = NULL;
  tees = crosses = opens = grounds = 0;
  gnd = NULL;
}

// Destructor deletes the spsolver class object.
spsolver::~spsolver () {
  delete swp;
  delete nlist;
}

/* The copy constructor creates a new instance of the spsolver class
   based on the given spsolver object. */
spsolver::spsolver (spsolver & n) : analysis (n) {
  tees = n.tees;
  crosses = n.crosses;
  opens = n.opens;
  grounds = n.grounds;
  noise = n.noise;
  saveCVs = n.saveCVs;
  swp = n.swp ? new sweep (*n.swp) : NULL;
  nlist = n.nlist ? new nodelist (*n.nlist) : NULL;
  gnd = n.gnd;
}

/* This function joins two nodes of a single circuit (interconnected
   nodes) and returns the resulting circuit. */
circuit * spsolver::interconnectJoin (node * n1, node * n2) {

  circuit * s = n1->getCircuit ();
  circuit * result = new circuit (s->getSize () - 2);
  nr_complex_t p;

  // allocate S-parameter and noise corellation matrices
  result->initSP (); if (noise) result->initNoiseSP ();

  // interconnected port numbers
  int k = n1->getPort (), l = n2->getPort ();

  // denominator needs to be calculated only once
  nr_complex_t d = (1.0 - s->getS (k, l)) * (1.0 - s->getS (l, k)) -
    s->getS (k, k) * s->getS (l, l);

  // avoid singularity when two full reflective ports are interconnected
  nr_double_t tiny1 = (d == 0) ? 1.0 - TINYS : 1.0;
  nr_double_t tiny2 = tiny1 * tiny1;
  nr_double_t tiny3 = tiny1 * tiny2;
  d = (1.0 - s->getS (k, l) * tiny1) * (1.0 - s->getS (l, k) * tiny1) -
    s->getS (k, k) * s->getS (l, l) * tiny2;

  int j2; // column index for resulting matrix
  int i2; // row index for resulting matrix
  int j1; // column index for S matrix
  int i1; // row index for S matrix

  // handle single S block only
  i2 = j2 = 0;
  for (j1 = 0; j1 < s->getSize (); j1++) {

    // skip connected node
    if (j1 == k || j1 == l) continue;

    // assign node name of resulting circuit
    result->setNode (j2, s->getNode(j1)->getName ());

    // inside S only
    for (i1 = 0; i1 < s->getSize (); i1++) {

      // skip connected node
      if (i1 == k || i1 == l) continue;

      // compute S'ij
      p = s->getS (i1, j1);
      p +=
        (s->getS (k, j1) * s->getS (i1, l) * (1.0 - s->getS (l, k)) * tiny3 +
         s->getS (l, j1) * s->getS (i1, k) * (1.0 - s->getS (k, l)) * tiny3 +
         s->getS (k, j1) * s->getS (l, l) * s->getS (i1, k) * tiny3 +
         s->getS (l, j1) * s->getS (k, k) * s->getS (i1, l) * tiny3) / d;
      result->setS (i2++, j2, p);
    }

    // next column
    j2++; i2 = 0;
  }
  return result;
}

/* This function joins two nodes of two different circuits (connected
   nodes) and returns the resulting circuit. */
circuit * spsolver::connectedJoin (node * n1, node * n2) {

  circuit * s = n1->getCircuit ();
  circuit * t = n2->getCircuit ();
  circuit * result = new circuit (s->getSize () + t->getSize () - 2);
  nr_complex_t p;

  // allocate S-parameter and noise corellation matrices
  result->initSP (); if (noise) result->initNoiseSP ();

  // connected port numbers
  int k = n1->getPort (), l = n2->getPort ();

  // denominator needs to be calculated only once
  nr_complex_t d = 1.0 - s->getS (k, k) * t->getS (l, l);

  // avoid singularity when two full reflective ports are connected
  nr_double_t tiny1 = (d == 0) ? 1.0 - TINYS : 1.0;
  nr_double_t tiny2 = tiny1 * tiny1;
  nr_double_t tiny3 = tiny1 * tiny2;
  d = 1.0 - s->getS (k, k) * t->getS (l, l) * tiny2;

  int j2; // column index for resulting matrix
  int i2; // row index for resulting matrix
  int j1; // column index for S matrix
  int i1; // row index for S matrix

  // handle S block
  i2 = j2 = 0;
  for (j1 = 0; j1 < s->getSize (); j1++) {

    // skip connected node
    if (j1 == k) continue;

    // assign node name of resulting circuit
    result->setNode (j2, s->getNode(j1)->getName());

    // inside S
    for (i1 = 0; i1 < s->getSize (); i1++) {

      // skip connected node
      if (i1 == k) continue;

      // compute S'ij
      p  = s->getS (i1, j1);
      p += s->getS (k, j1) * t->getS (l, l) * s->getS (i1, k) * tiny3 / d;
      result->setS (i2++, j2, p);
    }

    // across S and T
    for (i1 = 0; i1 < t->getSize (); i1++) {

      // skip connected node
      if (i1 == l) continue;

      // compute S'mj
      p = s->getS (k, j1) * t->getS (i1, l) * tiny2 / d;
      result->setS (i2++, j2, p);
    }
    // next column
    j2++; i2 = 0;
  }

  // handle T block
  for (j1 = 0; j1 < t->getSize (); j1++) {

    // skip connected node
    if (j1 == l) continue;

    // assign node name of resulting circuit
    result->setNode (j2, t->getNode(j1)->getName ());

    // across T and S
    for (i1 = 0; i1 < s->getSize (); i1++) {

      // skip connected node
      if (i1 == k) continue;

      // compute S'mj
      p = t->getS (l, j1) * s->getS (i1, k) * tiny2 / d;
      result->setS (i2++, j2, p);
    }

    // inside T
    for (i1 = 0; i1 < t->getSize (); i1++) {

      // skip connected node
      if (i1 == l) continue;

      // compute S'ij
      p  = t->getS (i1, j1);
      p += t->getS (l, j1) * s->getS (k, k) * t->getS (i1, l) * tiny3 / d;
      result->setS (i2++, j2, p);
    }

    // next column
    j2++; i2 = 0;
  }

  return result;
}

/* This function joins the two given nodes of a single circuit
   (interconnected nodes) and modifies the resulting circuit
   appropriately. */
void spsolver::noiseInterconnect (circuit * result, node * n1, node * n2) {

  circuit * c = n1->getCircuit ();
  nr_complex_t p, k1, k2, k3, k4;

  // interconnected port numbers
  int k = n1->getPort (), l = n2->getPort ();

  // denominator needs to be calculated only once
  nr_complex_t t = (1.0 - c->getS (k, l)) * (1.0 - c->getS (l, k)) -
    c->getS (k, k) * c->getS (l, l);

  // avoid singularity when two full reflective ports are interconnected
  nr_double_t tiny1 = (t == 0) ? 1.0 - TINYS : 1.0;
  nr_double_t tiny2 = tiny1 * tiny1;
  t = (1.0 - c->getS (k, l) * tiny1) * (1.0 - c->getS (l, k) * tiny1) -
    c->getS (k, k) * c->getS (l, l) * tiny2;

  int j2; // column index for resulting matrix
  int i2; // row index for resulting matrix
  int j1; // column index for S matrix
  int i1; // row index for S matrix

  // handle single C block only
  i2 = j2 = 0;
  for (j1 = 0; j1 < c->getSize (); j1++) {

    // skip connected node
    if (j1 == k || j1 == l) continue;

    // inside C only
    for (i1 = 0; i1 < c->getSize (); i1++) {

      // skip connected node
      if (i1 == k || i1 == l) continue;

      k1 = (c->getS (i1, l) * (1.0 - c->getS (l, k)) +
            c->getS (l, l) * c->getS (i1, k)) * tiny2 / t;
      k2 = (c->getS (i1, k) * (1.0 - c->getS (k, l)) +
            c->getS (k, k) * c->getS (i1, l)) * tiny2 / t;
      k3 = (c->getS (j1, l) * (1.0 - c->getS (l, k)) +
            c->getS (l, l) * c->getS (j1, k)) * tiny2 / t;
      k4 = (c->getS (j1, k) * (1.0 - c->getS (k, l)) +
            c->getS (k, k) * c->getS (j1, l)) * tiny2 / t;

      p =
        c->getN (i1, j1) + c->getN (k, j1) * k1 + c->getN (l, j1) * k2 +
        conj (k3) * (c->getN (i1, k) + c->getN (k, k) * k1 +
                     c->getN (l, k) * k2) +
        conj (k4) * (c->getN (i1, l) + c->getN (k, l) * k1 +
                     c->getN (l, l) * k2);
      result->setN (i2, j2, p);

      if (i2 >= j2) break; // the other half need not be computed
      result->setN (j2, i2, conj (p));
      i2++;
    }

    // next column
    j2++; i2 = 0;
  }
}


/* The following function joins two nodes of two different circuits
   and saves the noise wave correlation matrix in the resulting
   circuit. */
void spsolver::noiseConnect (circuit * result, node * n1, node * n2) {
  circuit * c = n1->getCircuit ();
  circuit * d = n2->getCircuit ();
  nr_complex_t p;

  // connected port numbers
  int k = n1->getPort (), l = n2->getPort ();

  // denominator needs to be calculated only once
  nr_complex_t t = 1.0 - c->getS (k, k) * d->getS (l, l);

  // avoid singularity when two full reflective ports are connected
  nr_double_t tiny1 = (t == 0) ? 1.0 - TINYS : 1.0;
  nr_double_t tiny2 = tiny1 * tiny1;
  nr_double_t tiny3 = tiny1 * tiny2;
  nr_double_t tiny4 = tiny1 * tiny3;
  t = 1.0 - c->getS (k, k) * d->getS (l, l) * tiny2;

  int j2; // column index for resulting matrix
  int i2; // row index for resulting matrix
  int j1; // column index for S matrix
  int i1; // row index for S matrix

  // handle C block
  i2 = j2 = 0;
  for (j1 = 0; j1 < c->getSize (); j1++) {

    // skip connected node
    if (j1 == k) continue;

    // inside C
    for (i1 = 0; i1 < c->getSize (); i1++) {

      // skip connected node
      if (i1 == k) continue;

      // compute C'ij
      p = c->getN (i1, j1) +
        c->getN (k, j1) * d->getS (l, l) * c->getS (i1, k) * tiny2 / t +
        c->getN (i1, k) * conj (d->getS (l, l) * c->getS (j1, k) * tiny2 / t) +
        (c->getN (k, k) * norm (d->getS (l, l)) + d->getN (l, l)) *
        c->getS (i1, k) * conj (c->getS (j1, k)) * tiny4 / norm (t);

      result->setN (i2, j2, p);
      if (i2 >= j2) break; // the other half need not be computed
      result->setN (j2, i2, conj (p));
      i2++;
    }

    /* The formulas "across C and D" are calculated elsewhere by the
       other half of the matrix (conjugate complex).  Therefore, they
       are missing here. */

    // next column
    j2++; i2 = 0;
  }

  // handle D block
  for (j1 = 0; j1 < d->getSize (); j1++) {

    // skip connected node
    if (j1 == l) continue;

    // across D and C
    for (i1 = 0; i1 < c->getSize (); i1++) {

      // skip connected node
      if (i1 == k) continue;

      // compute C'ij
      p = (c->getN (k, k) * d->getS (l, l) +
           d->getN (l, l) * conj (c->getS (k, k))) *
        c->getS (i1, k) * conj (d->getS (j1, l)) * tiny3 / norm (t) +
        d->getN (l, j1) * c->getS (i1, k) * tiny1 / t +
        c->getN (i1, k) * conj (d->getS (j1, l) * tiny1 / t);
      result->setN (i2, j2, p);
      result->setN (j2, i2, conj (p));
      i2++;
    }

    // inside D
    for (i1 = 0; i1 < d->getSize (); i1++) {

      // skip connected node
      if (i1 == l) continue;

      // compute C'ij
      p = d->getN (i1, j1) +
        (d->getN (l, l) * norm (c->getS (k, k)) + c->getN (k, k)) *
        d->getS (i1, l) * conj (d->getS (j1, l)) * tiny4 / norm (t) +
        d->getN (i1, l) * conj (c->getS (k, k) * d->getS (j1, l) * tiny2 / t) +
        d->getN (l, j1) * c->getS (k, k) * d->getS (i1, l) * tiny2 / t;
      result->setN (i2, j2, p);
      if (i2 >= j2) break; // the other half need not be computed
      result->setN (j2, i2, conj (p));
      i2++;
    }

    // next column
    j2++; i2 = 0;
  }
}

/* Goes through the list of circuit objects and runs its frequency
   dependent calcSP() function. */
void spsolver::calc (nr_double_t freq) {
  circuit * root = subnet->getRoot ();
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    c->calcSP (freq);
    if (noise) c->calcNoiseSP (freq);
  }
}

/* Go through each registered circuit object in the list and find the
   connection which results in a new subnetwork with the smallest
   number of s-parameters to calculate. */
void spsolver::reduce (void) {

#if SORTED_LIST
  node * n1, * n2;
  circuit * result, * cand1, * cand2;

  nlist->sortedNodes (&n1, &n2);
  cand1 = n1->getCircuit ();
  cand2 = n2->getCircuit ();
#else /* !SORTED_LIST */
  node * n1, * n2, * cand;
  circuit * result, * c1, * c2, * cand1, * cand2;
  int ports;
  circuit * root = subnet->getRoot ();

  // initialize local variables
  result = c1 = c2 = cand1 = cand2 = NULL;
  n1 = n2 = cand = NULL;
  ports = 10000; // huge

  // go through the circuit list
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {

    // skip signal ports
    if (c->getPort ()) continue;

    // and each node in the circuit
    for (int i = 0; i < c->getSize (); i++) {

      // find duplicate node
      if ((cand = subnet->findConnectedCircuitNode (c->getNode (i))) != NULL) {

        // save both candidates
        c1 = c; c2 = cand->getCircuit ();
        // connected
        if (c1 != c2) {
          if (c1->getSize () + c2->getSize () - 2 < ports) {
            ports = c1->getSize () + c2->getSize () - 2;
            cand1 = c1; cand2 = c2; n1 = c1->getNode (i); n2 = cand;
          }
        }
        // interconnect
        else {
          if (c1->getSize () - 2 < ports) {
            ports = c1->getSize () - 2;
            cand1 = c1; cand2 = c2; n1 = c1->getNode (i); n2 = cand;
          }
        }
      }
    }
  }
#endif /* !SORTED_LIST */

  // found a connection ?
  if (cand1 != NULL && cand2 != NULL) {
    // connected
    if (cand1 != cand2) {
#if DEBUG && 0
      logprint (LOG_STATUS, "DEBUG: connected node (%s): %s - %s\n",
                n1->getName (), cand1->getName (), cand2->getName ());
#endif /* DEBUG */
      result = connectedJoin (n1, n2);
      if (noise) noiseConnect (result, n1, n2);
      subnet->reducedCircuit (result);
#if SORTED_LIST
      nlist->remove (cand1);
      nlist->remove (cand2);
      nlist->insert (result);
#endif /* SORTED_LIST */
      subnet->removeCircuit (cand1);
      subnet->removeCircuit (cand2);
      subnet->insertCircuit (result);
      result->setOriginal (0);
    }
    // interconnect
    else {
#if DEBUG && 0
      logprint (LOG_STATUS, "DEBUG: interconnected node (%s): %s\n",
                n1->getName (), cand1->getName ());
#endif
      result = interconnectJoin (n1, n2);
      if (noise) noiseInterconnect (result, n1, n2);
      subnet->reducedCircuit (result);
#if SORTED_LIST
      nlist->remove (cand1);
      nlist->insert (result);
#endif /* SORTED_LIST */
      subnet->removeCircuit (cand1);
      subnet->insertCircuit (result);
      result->setOriginal (0);
    }
  }
}

/* Goes through the list of circuit objects and runs initializing
   functions if necessary. */
void spsolver::init (void) {
  circuit * root = subnet->getRoot ();
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    if (c->isNonLinear ()) c->calcOperatingPoints ();
    c->initSP ();
    if (noise) c->initNoiseSP ();
  }
}

/* This is the netlist solver.  It prepares the circuit list for each
   requested frequency and solves it then. */
int spsolver::solve (void) {
  nr_double_t freq;
  int ports;
  runs++;

  // fetch simulation properties
  saveCVs |= !strcmp (getPropertyString ("saveCVs"), "yes") ? SAVE_CVS : 0;
  saveCVs |= !strcmp (getPropertyString ("saveAll"), "yes") ? SAVE_ALL : 0;

  // run additional noise analysis ?
  noise = !strcmp (getPropertyString ("Noise"), "yes") ? 1 : 0;

  // create frequency sweep if necessary
  if (swp == NULL) {
    swp = createSweep ("frequency");
  }

  init ();
  insertConnections ();

#if SORTED_LIST
#if DEBUG
  logprint (LOG_STATUS, "NOTIFY: %s: creating sorted nodelist for "
            "SP analysis\n", getName ());
#endif
  nlist = new nodelist (subnet);
  nlist->sort ();
#endif /* SORTED_LIST */

#if DEBUG
  logprint (LOG_STATUS, "NOTIFY: %s: solving SP netlist\n", getName ());
#endif

  swp->reset ();
  for (int i = 0; i < swp->getSize (); i++) {
    freq = swp->next ();
    if (progress) logprogressbar (i, swp->getSize (), 40);

    ports = subnet->countNodes ();
    subnet->setReduced (0);
    calc (freq);

#if DEBUG && 0
    logprint (LOG_STATUS, "NOTIFY: %s: solving netlist for f = %e\n",
              getName (), (double) freq);
#endif

    while (ports > subnet->getPorts ()) {
      reduce ();
      ports -= 2;
    }

    saveResults (freq);
    subnet->getDroppedCircuits (nlist);
    subnet->deleteUnusedCircuits (nlist);
    if (saveCVs & SAVE_CVS) saveCharacteristics (freq);
  }
  if (progress) logprogressclear (40);
  dropConnections ();
#if SORTED_LIST
  delete nlist; nlist = NULL;
#endif
  return 0;
}

/* The function goes through the list of circuit objects and creates
   tee and cross circuits if necessary.  It looks for nodes in the
   circuit list connected to the given node. */
void spsolver::insertConnectors (node * n) {

  int count = 0;
  node * nodes[4], * _node;
  const char * _name = n->getName ();
  circuit * root = subnet->getRoot ();

#if USE_GROUNDS
  if (!strcmp (_name, "gnd")) return;
#endif /* USE_GROUNDS */

  nodes[0] = n;

  // go through list of circuit objects
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    // and each node in a circuit
    for (int i = 0; i < c->getSize (); i++) {
      _node = c->getNode (i);
      if (!strcmp (_node->getName (), _name)) {
        if (_node != n) {

          // found a connected node
          nodes[++count] = _node;
#if USE_CROSSES
          if (count == 3) {
            // create an additional cross and assign its nodes
            insertCross (nodes, _name);
            count = 1;
          }
#else /* !USE_CROSSES */
          if (count == 2) {
            // create an additional tee and assign its nodes
            insertTee (nodes, _name);
            count = 1;
          }
#endif /* !USE_CROSSES */
        }
      }
    }
  }
#if USE_CROSSES
  /* if using crosses there can be a tee left here */
  if (count == 2) {
    insertTee (nodes, _name);
  }
#endif /* USE_CROSSES */
}

/* The following function creates a tee circuit with the given nodes
   and the node name.  The tee's node names are adjusted to be
   internal nodes. */
void spsolver::insertTee (node ** nodes, const char * name) {
  circuit * result;
  // create a tee and assign its node names
  result = new tee ();
  subnet->insertedCircuit (result);
  result->setNode (0, name);
  subnet->insertedNode (result->getNode (1));
  subnet->insertedNode (result->getNode (2));
  // rename the nodes connected to the tee
  nodes[1]->setName (result->getNode(1)->getName ());
  nodes[2]->setName (result->getNode(2)->getName ());
  // complete the nodes of the tee
  result->getNode(1)->setCircuit (result);
  result->getNode(2)->setCircuit (result);
  result->getNode(1)->setPort (1);
  result->getNode(2)->setPort (2);
  // put the tee into the circuit list and initialize it
  subnet->insertCircuit (result);
  result->initSP (); if (noise) result->initNoiseSP ();
  // put the tee's first node into the node collection
  nodes[1] = result->getNode (0);
  tees++;
}

/* The following function creates a cross circuit with the given nodes
   and the node name.  The cross's node names are adjusted to be
   internal nodes. */
void spsolver::insertCross (node ** nodes, const char * name) {
  circuit * result;
  // create a cross and assign its node names
  result = new cross ();
  subnet->insertedCircuit (result);
  result->setNode (0, name);
  subnet->insertedNode (result->getNode (1));
  subnet->insertedNode (result->getNode (2));
  subnet->insertedNode (result->getNode (3));
  // rename the nodes connected to the cross
  nodes[1]->setName (result->getNode(1)->getName ());
  nodes[2]->setName (result->getNode(2)->getName ());
  nodes[3]->setName (result->getNode(3)->getName ());
  // complete the nodes of the cross
  result->getNode(1)->setCircuit (result);
  result->getNode(2)->setCircuit (result);
  result->getNode(3)->setCircuit (result);
  result->getNode(1)->setPort (1);
  result->getNode(2)->setPort (2);
  result->getNode(3)->setPort (3);
  // put the cross into the circuit list and initialize it
  subnet->insertCircuit (result);
  result->initSP (); if (noise) result->initNoiseSP ();
  // put the cross's first node into the node collection
  nodes[1] = result->getNode (0);
  crosses++;
}

/* This function removes an inserted tee from the netlist and restores
   the original node names. */
void spsolver::dropTee (circuit * c) {
  node * n;
  if (c->getType () == CIR_TEE) {
    const char * name = c->getNode(0)->getName ();
    n = subnet->findConnectedNode (c->getNode (1)); n->setName (name);
    n = subnet->findConnectedNode (c->getNode (2)); n->setName (name);
    c->setOriginal (0);
    subnet->removeCircuit (c);
  }
}

/* This function removes an inserted cross from the netlist and restores
   the original node names. */
void spsolver::dropCross (circuit * c) {
  node * n;
  if (c->getType () == CIR_CROSS) {
    const char * name = c->getNode(0)->getName ();
    n = subnet->findConnectedNode (c->getNode (1)); n->setName (name);
    n = subnet->findConnectedNode (c->getNode (2)); n->setName (name);
    n = subnet->findConnectedNode (c->getNode (3)); n->setName (name);
    c->setOriginal (0);
    subnet->removeCircuit (c);
  }
}

/* The function adds an open to the circuit list if the given node is
   unconnected. */
void spsolver::insertOpen (node * n) {
  if (strcmp (n->getName (), "gnd") &&
      subnet->findConnectedNode (n) == NULL) {
    circuit * result = new open ();
    subnet->insertedCircuit (result);
    result->setNode (0, n->getName ());
    subnet->insertCircuit (result);
    result->initSP (); if (noise) result->initNoiseSP ();
    opens++;
  }
}

// This function removes an inserted open from the netlist.
void spsolver::dropOpen (circuit * c) {
  if (c->getType () == CIR_OPEN) {
    c->setOriginal (0);
    subnet->removeCircuit (c);
  }
}

/* The function adds a ground circuit to the circuit list if the given
   node is a ground connection. */
void spsolver::insertGround (node * n) {
  if (!strcmp (n->getName (), "gnd") && !n->getCircuit()->getPort () &&
      n->getCircuit()->getType () != CIR_GROUND) {
    circuit * result = new ground ();
    subnet->insertedCircuit (result);
    subnet->insertedNode (result->getNode (0));
    result->getNode(0)->setCircuit (result);
    result->getNode(0)->setPort (0);
    n->setName (result->getNode(0)->getName ());
    subnet->insertCircuit (result);
    result->initSP (); if (noise) result->initNoiseSP ();
    grounds++;
  }
}

// This function removes an inserted ground from the netlist.
void spsolver::dropGround (circuit * c) {
  if (c->getType () == CIR_GROUND) {
    node * n = subnet->findConnectedNode (c->getNode (0));
    n->setName ("gnd");
    c->setOriginal (0);
    subnet->removeCircuit (c);
  }
}

/* This function prepares the circuit list by adding Ts and opens to
   the circuit list.  With this adjustments the solver is able to
   solve the circuit. */
void spsolver::insertConnections (void) {

  circuit * root, * c;
#if DEBUG
  logprint (LOG_STATUS, "NOTIFY: %s: preparing circuit for analysis\n",
            getName ());
#endif /* DEBUG */

#if USE_GROUNDS
  // remove original ground circuit from netlist
  root = subnet->getRoot ();
  for (c = root; c != NULL; c = (circuit *) c->getNext ()) {
    if (c->getType () == CIR_GROUND) {
      gnd = c;
      subnet->removeCircuit (c, 0);
      break;
    }
  }
#endif /* USE_GROUNDS */

  // insert opens, tee and crosses where necessary
  tees = crosses = opens = grounds = 0;
  root = subnet->getRoot ();
  for (c = root; c != NULL; c = (circuit *) c->getNext ()) {
    for (int i = 0; i < c->getSize (); i++) {
      insertConnectors (c->getNode (i));
      insertOpen (c->getNode (i));
    }
  }

  // insert S-parameter port transformers
  insertDifferentialPorts ();

#if USE_GROUNDS
  // insert grounds where necessary
  root = subnet->getRoot ();
  for (c = root; c != NULL; c = (circuit *) c->getNext ()) {
    for (int i = 0; i < c->getSize (); i++) {
      insertGround (c->getNode (i));
    }
  }
#endif /* USE_GROUNDS */

#if DEBUG
  logprint (LOG_STATUS, "NOTIFY: %s: inserted %d tees, %d crosses, %d opens "
            "and %d grounds\n",
            getName (), tees, crosses, opens, grounds);
#endif /* DEBUG */
}

/* The function is the counterpart of insertConnections().  It removes
   all additional circuits from the netlist which were necessary to
   run the analysis algorithm. */
void spsolver::dropConnections (void) {
  circuit * next, * cand;
  int inserted;

  // drop all additional inserted circuits in correct order
  do {
    // find last inserted circuit
    inserted = -1;
    cand = NULL;
    for (circuit * c = subnet->getRoot (); c != NULL; c = next) {
      next = (circuit *) c->getNext ();
      if (c->getInserted () > inserted) {
        inserted = c->getInserted ();
        cand = c;
      }
    }
    // if found, then drop that circuit
    if (cand != NULL) {
      switch (cand->getType ()) {
      case CIR_OPEN:
        dropOpen (cand);
        break;
      case CIR_TEE:
        dropTee (cand);
        break;
      case CIR_CROSS:
        dropCross (cand);
        break;
      case CIR_GROUND:
        dropGround (cand);
        break;
      case CIR_ITRAFO:
        dropDifferentialPort (cand);
        break;
      }
    }
  } while (cand != NULL);

#if USE_GROUNDS
  // attach the original ground to the netlist
  subnet->insertCircuit (gnd);
#endif /* USE_GROUNDS */
}

/* This function inserts an ideal transformer before an AC power
   source in order to allow differential S parameter ports.  */
void spsolver::insertDifferentialPorts (void) {
  circuit * root = subnet->getRoot ();
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    if (c->getPort ()) {

      // create an ideal transformer and assign its node names
      circuit * result = new itrafo ();
      subnet->insertedCircuit (result);
      subnet->insertedNode (result->getNode (0));
      result->setNode (1, c->getNode(0)->getName ());
      result->setNode (2, c->getNode(1)->getName ());

      // rename the nodes connected to the trafo
      c->getNode(0)->setName (result->getNode(0)->getName ());
      c->getNode(1)->setName ("PacGround");

      // complete the nodes of the trafo
      result->getNode(0)->setCircuit (result);
      result->getNode(0)->setPort (0);

      // pass the port impedance to the ideal trafo
      result->addProperty ("Z", c->getPropertyDouble ("Z"));

      // put the trafo in the circuit list
      subnet->insertCircuit (result);

      // allocate S-parameter and noise correlation matrices
      result->initSP (); if (noise) result->initNoiseSP ();
    }
  }
}

/* This function removes an ideal transformer which was necessary to
   be placed in front of a s-parameter port in order to allow
   differential s-parameters.  It also restores the original node
   names. */
void spsolver::dropDifferentialPort (circuit * c) {
  circuit * pac;
  node * n;
  if (c->getType () == CIR_ITRAFO) {
    n = subnet->findConnectedNode (c->getNode (0));
    pac = n->getCircuit ();
    pac->getNode(0)->setName (c->getNode(1)->getName ());
    pac->getNode(1)->setName (c->getNode(2)->getName ());
    c->setOriginal (0);
    subnet->removeCircuit (c);
  }
}

/* This function saves the results of a single solve() functionality
   (for the given frequency) into the output dataset. */
void spsolver::saveResults (nr_double_t freq) {

  vector * f;
  node * sig_i, * sig_j;
  char * n;
  int res_i, res_j;
  circuit * root = subnet->getRoot ();

  // temporary noise matrices and input port impedance
  nr_complex_t noise_c[4], noise_s[4];
  nr_double_t z0 = circuit::z0;

  // add current frequency to the dependency of the output dataset
  if ((f = data->findDependency ("frequency")) == NULL) {
    f = new vector ("frequency");
    data->addDependency (f);
  }
  if (runs == 1) f->add (freq);

  // go through the list of remaining circuits
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    // skip signals
    if (!c->getPort ()) {
      // handle each s-parameter
      for (int i = 0; i < c->getSize (); i++) {
        for (int j = 0; j < c->getSize (); j++) {

          // generate the appropriate variable name
          sig_i = subnet->findConnectedNode (c->getNode (i));
          sig_j = subnet->findConnectedNode (c->getNode (j));
          res_i = sig_i->getCircuit()->getPropertyInteger ("Num");
          res_j = sig_j->getCircuit()->getPropertyInteger ("Num");
          n = createSP (res_i, res_j);

          // add variable data item to dataset
          saveVariable (n, c->getS (i, j), f);

          // if noise analysis is requested
          if (noise) {
            int ro, co;
            int ni = getPropertyInteger ("NoiseIP");
            int no = getPropertyInteger ("NoiseOP");
            if ((res_i == ni || res_i == no) && (res_j == ni || res_j == no)) {
              if (ni == res_i) {
                // assign input port impedance
                z0 = sig_i->getCircuit()->getPropertyDouble ("Z");
              }
              ro = (res_i == ni) ? 0 : 1;
              co = (res_j == ni) ? 0 : 1;
              // save results in temporary data items
              noise_c[co + ro * 2] = c->getN (i, j);
              noise_s[co + ro * 2] = c->getS (i, j);
            }
          }
        }
      }
    }
  }

  // finally compute and save noise parameters
  if (noise) {
    saveNoiseResults (noise_s, noise_c, z0, f);
  }
}

/* This function takes the s-parameter matrix and noise wave
   correlation matrix and computes the noise parameters based upon
   these values.  Then it save the results into the dataset. */
void spsolver::saveNoiseResults (nr_complex_t s[4], nr_complex_t c[4],
                                 nr_double_t z0, vector * f) {
  nr_complex_t c22 = c[3], c11 = c[0], c12 = c[1];
  nr_complex_t s11 = s[0], s21 = s[2];
  nr_complex_t n1, n2, F, Sopt, Fmin, Rn;

  // linear noise figure
  F    = real (1.0 + c22 / norm (s21));
  n1   =
    c11 * norm (s21) - 2.0 * real (c12 * s21 * conj (s11)) +
    c22 * norm (s11);
  n2   = 2.0 * (c22 * s11 - c12 * s21) / (c22 + n1);

  // optimal source reflection coefficient
  Sopt = 1.0 - norm (n2);
  if (real (Sopt) < 0.0)
    Sopt = (1.0 + sqrt (Sopt)) / n2;  // avoid a negative radicant
  else
    Sopt = (1.0 - sqrt (Sopt)) / n2;

  // minimum noise figure
  Fmin = real (1.0 + (c22 - n1 * norm (Sopt)) /
               norm (s21) / (1.0 + norm (Sopt)));

  // equivalent noise resistance
  Rn   = real ((c11 - 2.0 * real (c12 * conj ((1.0 + s11) / s21)) +
                c22 * norm ((1.0 + s11) / s21)) / 4.0);
  Rn   = Rn * z0;

  // add variable data items to dataset
  saveVariable ("F", F, f);
  saveVariable ("Sopt", Sopt, f);
  saveVariable ("Fmin", Fmin, f);
  saveVariable ("Rn", Rn, f);
}

// Create an appropriate variable name.
char * spsolver::createSP (int i, int j) {
  return matvec::createMatrixString ("S", i - 1, j - 1);
}

/* Create an appropriate variable name for characteristic values.  The
   caller is responsible to free() the returned string. */
const char * spsolver::createCV (const std::string &c, const std::string &n) {
  return (c+"."+n).c_str();
}

/* Goes through the list of circuit objects and runs its
   saveCharacteristics() function.  Then puts these values into the
   dataset. */
void spsolver::saveCharacteristics (nr_double_t freq) {
  circuit * root = subnet->getRoot ();
  const char * n;
  vector * f = data->findDependency ("frequency");
  for (circuit * c = root; c != NULL; c = (circuit *) c->getNext ()) {
    c->saveCharacteristics (freq);
    if (!c->getSubcircuit ().empty() && !(saveCVs & SAVE_ALL)) continue;
    c->calcCharacteristics (freq);
    for (auto ps: c->getCharacteristics ()) {
      characteristic &p = ps.second;
      n = createCV (c->getName (), p.getName ());
      saveVariable (n, p.getValue (), f);
    }
  }
}

// properties
PROP_REQ [] = {
  { "Type", PROP_STR, { PROP_NO_VAL, "lin" }, PROP_RNG_TYP },
  PROP_NO_PROP };
PROP_OPT [] = {
  { "Noise", PROP_STR, { PROP_NO_VAL, "no" }, PROP_RNG_YESNO },
  { "NoiseIP", PROP_INT, { 1, PROP_NO_STR }, PROP_RNGII (1, MAX_PORTS) },
  { "NoiseOP", PROP_INT, { 2, PROP_NO_STR }, PROP_RNGII (1, MAX_PORTS) },
  { "Start", PROP_REAL, { 1e9, PROP_NO_STR }, PROP_POS_RANGE },
  { "Stop", PROP_REAL, { 10e9, PROP_NO_STR }, PROP_POS_RANGE },
  { "Points", PROP_INT, { 10, PROP_NO_STR }, PROP_MIN_VAL (2) },
  { "Values", PROP_LIST, { 10, PROP_NO_STR }, PROP_POS_RANGE },
  { "saveCVs", PROP_STR, { PROP_NO_VAL, "no" }, PROP_RNG_YESNO },
  { "saveAll", PROP_STR, { PROP_NO_VAL, "no" }, PROP_RNG_YESNO },
  PROP_NO_PROP };
struct define_t spsolver::anadef =
  { "SP", 0, PROP_ACTION, PROP_NO_SUBSTRATE, PROP_LINEAR, PROP_DEF };

} // namespace qucs