Constrained tuning: Difference between revisions

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As a standard optimization problem, numerous algorithms exist to solve for this tuning, such as [[Wikipedia: Sequential quadratic programming|sequential quadratic programming]], to name one.

The following [https://www.python.org Python] code is an excerpt from [[Flora Canou]]'s [https://github.com/FloraCanou/te_temperament_measures/blob/~~c72b7a9ab603f5f46fef8465c3c5355c2caf19bc~~/tuning_optimizer.py tuning optimizer]. Note: it depends on [https://scipy.org/ Scipy].

The following [https://www.python.org Python] code is an excerpt from [[Flora Canou]]'s [https://github.com/FloraCanou/te_temperament_measures/blob/54c9ec58acf0ad5adc7c1d96f2deaf1d2a503702/tuning_optimizer.py tuning optimizer]. Note: it depends on [https://scipy.org/ Scipy].

~~{{Todo|inline=1| update | comment=The code was based on the wrong definition. }}~~

{{Databox| Code |

# This work is licensed under the GNU General Public License version 3.

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SCALAR = 1200 #could be in octave, but for precision reason

def weighted (matrix, subgroup):

def weighted (matrix, subgroup, type = "tenney"):

~~tenney_weighter~~ = np.diag (1/np.log2 (subgroup))

if not type in {"tenney", "frobenius"}:

return matrix @ ~~tenney_weighter~~

type = "tenney"

if type == "tenney":

weighter = np.diag (1/np.log2 (subgroup))

elif type == "frobenius":

weighter = np.eye (len (subgroup))

return matrix @ weighter

def error (gen, map, jip, order = 2):

return linalg.norm (gen @ map - jip, ord = order)

def optimizer_main (map, subgroup = [], order = 2, cons_monzo_list = np.array ([]), stretch_monzo = np.array ([]), show = True):

def optimizer_main (map, subgroup = [], order = 2, weighter = "tenney", cons_monzo_list = np.array ([]), stretch_monzo = np.array ([]), show = True):

if len (subgroup) == 0:

subgroup = PRIME_LIST[:map.shape[1]]

jip = np.log2 (subgroup)*SCALAR

map_w = weighted (map, subgroup)

map_w = weighted (map, subgroup, type = weighter)

jip_w = weighted (jip, subgroup)

jip_w = weighted (jip, subgroup, type = weighter)

if order == 2 and not cons_monzo_list.size: #te with no constraints, simply use lstsq for better performance

res = linalg.lstsq (map_w.T, jip_w)

gen = res[0]

print ("TE tuning without constraints, solved using lstsq. ")

print ("L2 tuning without constraints, solved using lstsq. ")

else:

gen0 = [SCALAR]*map.shape[0] #initial guess

cons = {'type': 'eq', 'fun': lambda gen: (gen @ ~~map_w~~ - ~~jip_w~~) @ cons_monzo_list} if cons_monzo_list.size else ()

cons = {'type': 'eq', 'fun': lambda gen: (gen @ map - jip) @ cons_monzo_list} if cons_monzo_list.size else ()

res = optimize.minimize (error, gen0, args = (map_w, jip_w, order), method = "SLSQP", constraints = cons)

print (res.message)

@@ Line 23: / Line 23: @@
 As a standard optimization problem, numerous algorithms exist to solve for this tuning, such as [[Wikipedia: Sequential quadratic programming|sequential quadratic programming]], to name one.
-The following [https://www.python.org Python] code is an excerpt from [[Flora Canou]]'s [https://github.com/FloraCanou/te_temperament_measures/blob/c72b7a9ab603f5f46fef8465c3c5355c2caf19bc/tuning_optimizer.py tuning optimizer]. Note: it depends on [https://scipy.org/ Scipy].
+The following [https://www.python.org Python] code is an excerpt from [[Flora Canou]]'s [https://github.com/FloraCanou/te_temperament_measures/blob/54c9ec58acf0ad5adc7c1d96f2deaf1d2a503702/tuning_optimizer.py tuning optimizer]. Note: it depends on [https://scipy.org/ Scipy].
-{{Todo|inline=1| update | comment=The code was based on the wrong definition. }}
 {{Databox| Code |
 <syntaxhighlight lang="python">
-# © 2020-2021 Flora Canou | Version 0.5
+# © 2020-2021 Flora Canou | Version 0.8
 # This work is licensed under the GNU General Public License version 3.
@@ Line 39: / Line 37: @@
 SCALAR = 1200 #could be in octave, but for precision reason
-def weighted (matrix, subgroup):
+def weighted (matrix, subgroup, type = "tenney"):
-     tenney_weighter = np.diag (1/np.log2 (subgroup))
+     if not type in {"tenney", "frobenius"}:
-     return matrix @ tenney_weighter
+        type = "tenney"
+    if type == "tenney":
+        weighter = np.diag (1/np.log2 (subgroup))
+    elif type == "frobenius":
+        weighter = np.eye (len (subgroup))
+     return matrix @ weighter
 def error (gen, map, jip, order = 2):
      return linalg.norm (gen @ map - jip, ord = order)
-def optimizer_main (map, subgroup = [], order = 2, cons_monzo_list = np.array ([]), stretch_monzo = np.array ([]), show = True):
+def optimizer_main (map, subgroup = [], order = 2, weighter = "tenney", cons_monzo_list = np.array ([]), stretch_monzo = np.array ([]), show = True):
      if len (subgroup) == 0:
          subgroup = PRIME_LIST[:map.shape[1]]
      jip = np.log2 (subgroup)*SCALAR
-     map_w = weighted (map, subgroup)
+     map_w = weighted (map, subgroup, type = weighter)
-     jip_w = weighted (jip, subgroup)
+     jip_w = weighted (jip, subgroup, type = weighter)
      if order == 2 and not cons_monzo_list.size: #te with no constraints, simply use lstsq for better performance
          res = linalg.lstsq (map_w.T, jip_w)
          gen = res[0]
-         print ("TE tuning without constraints, solved using lstsq. ")
+         print ("L2 tuning without constraints, solved using lstsq. ")
      else:
          gen0 = [SCALAR]*map.shape[0] #initial guess
-         cons = {'type': 'eq', 'fun': lambda gen: (gen @ map_w - jip_w) @ cons_monzo_list} if cons_monzo_list.size else ()
+         cons = {'type': 'eq', 'fun': lambda gen: (gen @ map - jip) @ cons_monzo_list} if cons_monzo_list.size else ()
          res = optimize.minimize (error, gen0, args = (map_w, jip_w, order), method = "SLSQP", constraints = cons)
          print (res.message)