Merge pull request #273 from dynamicslab/parametric_library

Parametric library

examples/17_parameterized_pattern_formation/data/auto/c.cycle_even

@@ -0,0 +1,15 @@
+dat='cycle_even.dat'
+NDIM=   4, IPS =   9, IRS =   0, ILP =   1
+PAR={1:-1,11:50.26548245743669}
+ICP =  [1,11,2,3,4]
+NTST=  256, NCOL=   4, IAD =   1, ISP =   2, ISW = 1, IPLT= 0, NBC= 0, NINT= 0
+NMX=   1000, NPR=   1, MXBF=   0, IID =   2, ITMX=  10, ITNW= 7, NWTN= 3, JAC= 0
+EPSL= 1e-05, EPSU = 1e-05, EPSS = 1e-05
+DS  =  0.001, DSMIN=1e-10, DSMAX=  1e-2, IADS=   1
+NPAR = 15, THL =  {}, THU =  {2:0,3:0,4:0}
+UZR =  {1: [-1,0.1,2.5,5,7.5,10.0]}
+RL0=-5.0
+RL1=10.1
+A1=0.8
+IEQUIB = 0
+IREV = [0,1,0,1]

examples/17_parameterized_pattern_formation/data/auto/c.cycle_odd

@@ -0,0 +1,15 @@
+dat='cycle_odd.dat'
+NDIM=   4, IPS =   9, IRS =   0, ILP =   1
+PAR={1:-1,11:50.26548245743669}
+ICP =  [1,11,2,3,4]
+NTST=  256, NCOL=   4, IAD =   1, ISP =   2, ISW = 1, IPLT= 0, NBC= 0, NINT= 0
+NMX=   1000, NPR=   1, MXBF=   0, IID =   2, ITMX=  10, ITNW= 7, NWTN= 3, JAC= 0
+EPSL= 1e-05, EPSU = 1e-05, EPSS = 1e-05
+DS  =  0.001, DSMIN=1e-10, DSMAX=  1e-2, IADS=   1
+NPAR = 15, THL =  {}, THU =  {2:0,3:0,4:0}
+UZR =  {1: [-1,0.1,2.5,5,7.5,10.0]}
+RL0=-5.0
+RL1=1.0
+A1=0.8
+IEQUIB = 0
+IREV = [1,0,1,0]

examples/17_parameterized_pattern_formation/data/auto/c.periodic_E

@@ -0,0 +1,12 @@
+dat='periodic.dat'
+NDIM=   4, IPS =   4, IRS =   0, ILP =   1
+ICP =  [1,11,2,3,4]
+PAR={1:-1,11:6.283185307179586}
+NTST=  35, NCOL=   4, IAD =   1, ISP =   1, ISW = 1, IPLT= 0, NBC= 4, NINT= 0
+NMX=   1000, NPR=   1, MXBF=   0, IID =   2, ITMX=  10, ITNW= 7, NWTN= 3, JAC= 0
+EPSL= 1e-07, EPSU = 1e-07, EPSS = 1e-05
+DS  =  1e-6, DSMIN=1e-20, DSMAX=  1e-2, IADS=   1
+NPAR = 4, THL =  {}, THU =  {2:0,3:0,4:0}
+UZR =  {1: [-1,0,2.5,5,7.5,10.0]}
+RL0=-2.0
+RL1=10.1

examples/17_parameterized_pattern_formation/data/auto/c.steady_E

@@ -0,0 +1,10 @@
+NDIM=   4, IPS =   1, IRS =   0, ILP =   1
+ICP =  [1,11,2,3,4]
+NTST=  35, NCOL=   4, IAD =   1, ISP =   2, ISW = 1, IPLT= 0, NBC= 0, NINT= 0
+NMX=   1000, NPR=   20, MXBF=   0, IID =   2, ITMX=  10, ITNW= 7, NWTN= 3, JAC= 1
+EPSL= 1e-07, EPSU = 1e-07, EPSS = 1e-05
+DS  =  0.01, DSMIN=0.0001, DSMAX=  0.05, IADS=   1
+NPAR = 15, THL =  {}, THU =  {2:0,3:0,4:0}
+UZR =  {1: [0.0,2.5,5,7.5,10.0]}
+RL0=-0.1
+RL1=10.1

examples/17_parameterized_pattern_formation/data/auto/even.auto

@@ -0,0 +1,21 @@
+import numpy as np
+import os
+
+even=run('snaking_E',c='cycle_even')
+sols=[]
+pars=[]
+for i in range(len(even[0])):
+    u=even(i+1)['U(1)']
+    t=even(i+1)['t']
+    e=even(i+1)['PAR(1)']
+    r=even(i+1)['PAR(2)']
+    b=even(i+1)['PAR(3)']
+    c=even(i+1)['PAR(4)']
+    T=even(i+1)['PAR(11)']
+    norm=even(i+1)['L2-NORM']
+    sols=sols+[np.vstack([t,u]).T]
+    pars=pars+[[e,r,b,c,T,norm]]
+
+np.save('even_sols.npy',sols)
+np.save('even_pars.npy',pars)
+cl()

examples/17_parameterized_pattern_formation/data/auto/odd.auto

@@ -0,0 +1,21 @@
+import numpy as np
+import os
+
+odd=run('snaking_E',c='cycle_odd')
+sols=[]
+pars=[]
+for i in range(len(odd[0])):
+    u=odd(i+1)['U(1)']
+    t=odd(i+1)['t']
+    e=odd(i+1)['PAR(1)']
+    r=odd(i+1)['PAR(2)']
+    b=odd(i+1)['PAR(3)']
+    c=odd(i+1)['PAR(4)']
+    T=odd(i+1)['PAR(11)']
+    norm=odd(i+1)['L2-NORM']
+    sols=sols+[np.vstack([t,u]).T]
+    pars=pars+[[e,r,b,c,T,norm]]
+
+np.save('odd_sols.npy',sols)
+np.save('odd_pars.npy',pars)
+cl()

examples/17_parameterized_pattern_formation/data/auto/periodic.auto

@@ -0,0 +1,21 @@
+import numpy as np
+import os
+
+periodic=run('snaking_E_T',c='periodic_E')
+sols=[]
+pars=[]
+for i in range(len(periodic[0])):
+    u=periodic(i+1)['U(1)']
+    t=periodic(i+1)['t']
+    e=periodic(i+1)['PAR(1)']
+    r=periodic(i+1)['PAR(2)']
+    b=periodic(i+1)['PAR(3)']
+    c=periodic(i+1)['PAR(4)']
+    T=periodic(i+1)['PAR(11)']
+    norm=periodic(i+1)['L2-NORM']
+    sols=sols+[np.vstack([t,u]).T]
+    pars=pars+[[e,r,b,c,T,norm]]
+
+np.save('periodic_sols.npy',sols)
+np.save('periodic_pars.npy',pars)
+cl()

examples/17_parameterized_pattern_formation/data/auto/snaking_E.f90

@@ -0,0 +1,160 @@
+!----------------------------------------------------------------------
+!----------------------------------------------------------------------
+!   cir :    Homoclinic Bifurcation in an Electronic Circuit
+!                (the same equations as in demo tor)
+!----------------------------------------------------------------------
+!----------------------------------------------------------------------
+
+      SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP)
+!     ---------- ----
+
+      IMPLICIT NONE
+      INTEGER, INTENT(IN) :: NDIM, ICP(*), IJAC
+      DOUBLE PRECISION, INTENT(IN) :: U(NDIM), PAR(*)
+      DOUBLE PRECISION, INTENT(OUT) :: F(NDIM)
+      DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDIM,NDIM), DFDP(NDIM,*)
+
+      DOUBLE PRECISION E
+      DOUBLE PRECISION P
+      DOUBLE PRECISION R
+      DOUBLE PRECISION B
+      DOUBLE PRECISION C
+      DOUBLE PRECISION DRDE
+      DOUBLE PRECISION DBDE
+      DOUBLE PRECISION DCDE
+
+       E=PAR(1)
+       P=2
+       R=-6.9142484373744839e-01-7.3260087859986806e-02*E-2.7462906764622484e-03*E*E
+       B=1.7910887544563148e+00-3.0554994266613233e-01*E-2.4878961651300643e-02*E*E
+       C=7.5841639153560658e-01+5.5761858956235276e-02*E+5.1480291789433611e-03*E*E
+       DRDE=-7.3260087859986806e-02-2.7462906764622484e-03*E*2
+       DBDE=-3.0554994266613233e-01-2.4878961651300643e-02*E*2
+       DCDE=5.5761858956235276e-02+5.1480291789433611e-03*E*2
+
+       F(1)= U(2)
+       F(2)= U(3)
+       F(3)= U(4)
+       F(4)= R*U(1)-P*U(3)-U(1)+B*U(1)**3-C*U(1)**5
+
+       IF(IJAC.EQ.0)RETURN
+
+       DFDU(1,1)=0.0d0
+       DFDU(1,2)=1.0d0
+       DFDU(1,3)=0.0d0
+       DFDU(1,4)=0.0d0
+
+       DFDU(2,1)=0.0d0
+       DFDU(2,2)=0.0d0
+       DFDU(2,3)=1.0d0
+       DFDU(2,4)=0.0d0
+
+       DFDU(3,1)=0.0d0
+       DFDU(3,2)=0.0d0
+       DFDU(3,3)=0.0d0
+       DFDU(3,4)=1.0d0
+
+       DFDU(4,1)=R-1.0d0+3.0d0*B*U(1)**2-5.0d0*C*U(1)**4
+       DFDU(4,2)=0.0d0
+       DFDU(4,3)=-P
+       DFDU(4,4)=0.0d0
+
+      IF(IJAC.EQ.1)RETURN
+
+!      *Parameter derivatives
+       DFDP(1,1)=0.0d0
+       DFDP(2,1)=0.0d0
+       DFDP(3,1)=0.0d0
+       DFDP(4,1)=U(1)*DRDE+U(1)**3*DBDE-U(1)**5*DCDE
+
+      END SUBROUTINE FUNC
+
+      SUBROUTINE STPNT(NDIM,U,PAR,T)
+!     ---------- -----
+
+      IMPLICIT NONE
+      INTEGER, INTENT(IN) :: NDIM
+      DOUBLE PRECISION, INTENT(INOUT) :: U(NDIM),PAR(*)
+      DOUBLE PRECISION, INTENT(IN) :: T
+
+!----------------------------------------------------------------------
+! Problem parameters (only PAR(1-9) are available to the user) :
+
+       U(1)=0.0
+       U(2)=0.0
+       U(3)=0.0
+       U(4)=0.0
+       PAR(1)=0.0                ! E
+
+!----------------------------------------------------------------------
+! If IEQUIB >0 put initial equilibrium in PAR(11+i), i=1,...,NDIM :
+
+      PAR(12) = 0.0
+      PAR(13) = 0.0
+      PAR(14) = 0.0
+      PAR(15) = 0.0
+
+
+      END SUBROUTINE STPNT
+
+      SUBROUTINE PVLS(NDIM,U,PAR)
+!     ---------- ----
+
+      IMPLICIT NONE
+      INTEGER, INTENT(IN) :: NDIM
+      DOUBLE PRECISION, INTENT(IN) :: U(NDIM)
+      DOUBLE PRECISION, INTENT(INOUT) :: PAR(*)
+! Homoclinic bifurcations COMMON block needed here :
+      COMMON /BLHOM/ ITWIST,ISTART,IEQUIB,NFIXED,NPSI,NUNSTAB,NSTAB,NREV
+      INTEGER ITWIST,ISTART,IEQUIB,NFIXED,NPSI,NUNSTAB,NSTAB,NREV
+      INTEGER I
+
+      DOUBLE PRECISION E
+      DOUBLE PRECISION P
+      DOUBLE PRECISION R
+      DOUBLE PRECISION B
+      DOUBLE PRECISION C
+
+      E=PAR(1)
+      P=2
+      R=-6.9142484373744839e-01-7.3260087859986806e-02*E-2.7462906764622484e-03*E*E
+      B=1.7910887544563148e+00-3.0554994266613233e-01*E-2.4878961651300643e-02*E*E
+      C=7.5841639153560658e-01+5.5761858956235276e-02*E+5.1480291789433611e-03*E*E
+
+      PAR(2)=R
+      PAR(3)=B
+      PAR(4)=C
+
+! If IEQUIB =0 put analytic equilibrium in PAR(11+i), i=1..NDIM
+
+      IF(IEQUIB.EQ.0)THEN
+        DO I=1,NDIM
+          PAR(11+I)= 0.0
+        ENDDO
+      ENDIF
+
+      END SUBROUTINE PVLS
+
+      !----------------------------------------------------------------------
+            SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC)
+      !     ---------- ----
+
+            IMPLICIT NONE
+            INTEGER, INTENT(IN) :: NDIM,ICP(*),NBC,IJAC
+            DOUBLE PRECISION, INTENT(IN) :: PAR(*),U0(NDIM),U1(NDIM)
+            DOUBLE PRECISION, INTENT(OUT) :: FB(NBC)
+            DOUBLE PRECISION, INTENT(INOUT) :: DBC(NBC,*)
+
+             FB(1)=U0(1)
+             FB(2)=U1(1)
+             FB(3)=U0(3)
+             FB(4)=U1(3)
+
+            END SUBROUTINE BCND
+      !----------------------------------------------------------------------
+
+      SUBROUTINE ICND
+      END SUBROUTINE ICND
+
+      SUBROUTINE FOPT
+      END SUBROUTINE FOPT