add Maple code and C skeletons for Hermite polynomial interpolation

git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/LocalInterp/trunk@101 df1f8a13-aa1d-4dd4-9681-27ded5b42416

9 files changed, 131 insertions, 0 deletions

diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-I.compute.c
new file mode 100644
index 0000000..81bc4e1
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-I.compute.c
@@ -0,0 +1,12 @@
+fp t4,
+   t3,
+   t2,
+   t1;
+      t4 = x*x;
+      t3 = x*t4;
+      t2 = RATIONAL(1.0,2.0);
+      t1 = RATIONAL(-1.0,2.0);
+      coeff_I_m1 = t4+(x+t3)*t1;
+      coeff_I_0 = RATIONAL(-5.0,2.0)*t4+RATIONAL(1.0,1.0)+RATIONAL(3.0,2.0)*t3;
+      coeff_I_p1 = RATIONAL(-3.0,2.0)*t3+t2*x+RATIONAL(2.0,1.0)*t4;
+      coeff_I_p2 = t2*t3+t1*t4;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dx.compute.c
new file mode 100644
index 0000000..91da0b2
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dx.compute.c
@@ -0,0 +1,8 @@
+fp t6;
+      t6 = x*x;
+      coeff_dx_m1 = RATIONAL(2.0,1.0)*x+RATIONAL(-3.0,2.0)*t6+RATIONAL(-1.0,2.0
+);
+      coeff_dx_0 = RATIONAL(-5.0,1.0)*x+RATIONAL(9.0,2.0)*t6;
+      coeff_dx_p1 = RATIONAL(1.0,2.0)+RATIONAL(4.0,1.0)*x+RATIONAL(-9.0,2.0)*t6
+;
+      coeff_dx_p2 = -x+RATIONAL(3.0,2.0)*t6;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dxx.compute.c
new file mode 100644
index 0000000..9cb9a24
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order2/coeff-dxx.compute.c
@@ -0,0 +1,4 @@
+      coeff_dxx_m1 = RATIONAL(2.0,1.0)+RATIONAL(-3.0,1.0)*x;
+      coeff_dxx_0 = RATIONAL(-5.0,1.0)+RATIONAL(9.0,1.0)*x;
+      coeff_dxx_p1 = RATIONAL(-9.0,1.0)*x+RATIONAL(4.0,1.0);
+      coeff_dxx_p2 = RATIONAL(-1.0,1.0)+RATIONAL(3.0,1.0)*x;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-I.compute.c
new file mode 100644
index 0000000..758efe3
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-I.compute.c
@@ -0,0 +1,17 @@
+fp t10,
+   t9,
+   t8,
+   t7;
+      t10 = x*x;
+      t9 = x*t10;
+      t8 = RATIONAL(1.0,12.0);
+      t7 = RATIONAL(-1.0,12.0);
+      coeff_I_m2 = RATIONAL(-1.0,6.0)*t10+(x+t9)*t8;
+      coeff_I_m1 = RATIONAL(-2.0,3.0)*x+RATIONAL(5.0,4.0)*t10+RATIONAL(-7.0,
+12.0)*t9;
+      coeff_I_0 = RATIONAL(-7.0,3.0)*t10+RATIONAL(1.0,1.0)+RATIONAL(4.0,3.0)*t9
+;
+      coeff_I_p1 = RATIONAL(-4.0,3.0)*t9+RATIONAL(2.0,3.0)*x+RATIONAL(5.0,3.0)*
+t10;
+      coeff_I_p2 = RATIONAL(7.0,12.0)*t9+t7*x+RATIONAL(-1.0,2.0)*t10;
+      coeff_I_p3 = t7*t9+t8*t10;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dx.compute.c
new file mode 100644
index 0000000..4300a83
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dx.compute.c
@@ -0,0 +1,11 @@
+fp t12;
+      t12 = x*x;
+      coeff_dx_m2 = RATIONAL(-1.0,3.0)*x+RATIONAL(1.0,12.0)+RATIONAL(1.0,4.0)*
+t12;
+      coeff_dx_m1 = RATIONAL(-2.0,3.0)+RATIONAL(5.0,2.0)*x+RATIONAL(-7.0,4.0)*
+t12;
+      coeff_dx_0 = RATIONAL(-14.0,3.0)*x+RATIONAL(4.0,1.0)*t12;
+      coeff_dx_p1 = RATIONAL(-4.0,1.0)*t12+RATIONAL(10.0,3.0)*x+RATIONAL(2.0,
+3.0);
+      coeff_dx_p2 = RATIONAL(7.0,4.0)*t12+RATIONAL(-1.0,12.0)-x;
+      coeff_dx_p3 = RATIONAL(1.0,6.0)*x+RATIONAL(-1.0,4.0)*t12;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dxx.compute.c
new file mode 100644
index 0000000..79fc889
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order3/coeff-dxx.compute.c
@@ -0,0 +1,6 @@
+      coeff_dxx_m2 = RATIONAL(-1.0,3.0)+RATIONAL(1.0,2.0)*x;
+      coeff_dxx_m1 = RATIONAL(-7.0,2.0)*x+RATIONAL(5.0,2.0);
+      coeff_dxx_0 = RATIONAL(-14.0,3.0)+RATIONAL(8.0,1.0)*x;
+      coeff_dxx_p1 = RATIONAL(10.0,3.0)+RATIONAL(-8.0,1.0)*x;
+      coeff_dxx_p2 = RATIONAL(7.0,2.0)*x+RATIONAL(-1.0,1.0);
+      coeff_dxx_p3 = RATIONAL(1.0,6.0)+RATIONAL(-1.0,2.0)*x;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-I.compute.c
new file mode 100644
index 0000000..139a39a
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-I.compute.c
@@ -0,0 +1,33 @@
+fp t23,
+   t24,
+   t22,
+   t20,
+   t19,
+   t18,
+   t17,
+   t16,
+   t15,
+   t14,
+   t13;
+      t23 = x*x;
+      t24 = x*t23;
+      t22 = t24*t23;
+      t20 = t23*t23;
+      t19 = RATIONAL(-1.0,24.0);
+      t18 = RATIONAL(1.0,12.0);
+      t17 = RATIONAL(-7.0,12.0);
+      t16 = RATIONAL(5.0,12.0);
+      t15 = RATIONAL(-1.0,12.0);
+      t14 = RATIONAL(13.0,12.0);
+      t13 = t19*t24;
+      coeff_I_m2 = t18*x+RATIONAL(-1.0,8.0)*t23+t13+RATIONAL(1.0,8.0)*t20+t19*
+t22;
+      coeff_I_m1 = RATIONAL(-2.0,3.0)*x+t14*t23+t13+t17*t20+RATIONAL(5.0,24.0)*
+t22;
+      coeff_I_0 = RATIONAL(-25.0,12.0)*t23+t16*t24+t14*t20+RATIONAL(1.0,1.0)+
+RATIONAL(-5.0,12.0)*t22;
+      coeff_I_p1 = t17*t24+RATIONAL(2.0,3.0)*x+RATIONAL(3.0,2.0)*t23+t16*t22-
+t20;
+      coeff_I_p2 = t15*x+RATIONAL(-11.0,24.0)*t23+RATIONAL(7.0,24.0)*t24+
+RATIONAL(-5.0,24.0)*t22+RATIONAL(11.0,24.0)*t20;
+      coeff_I_p3 = t13+RATIONAL(1.0,24.0)*t22+t18*t23+t15*t20;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dx.compute.c
new file mode 100644
index 0000000..2eac534
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dx.compute.c
@@ -0,0 +1,20 @@
+fp t30,
+   t29,
+   t28,
+   t27;
+      t30 = x*x;
+      t29 = x*t30;
+      t28 = t30*t30;
+      t27 = RATIONAL(-1.0,8.0)*t30;
+      coeff_dx_m2 = RATIONAL(1.0,2.0)*t29+RATIONAL(-5.0,24.0)*t28+t27+RATIONAL(
+1.0,12.0)+RATIONAL(-1.0,4.0)*x;
+      coeff_dx_m1 = RATIONAL(-7.0,3.0)*t29+RATIONAL(13.0,6.0)*x+RATIONAL(25.0,
+24.0)*t28+t27+RATIONAL(-2.0,3.0);
+      coeff_dx_0 = RATIONAL(-25.0,6.0)*x+RATIONAL(5.0,4.0)*t30+RATIONAL(13.0,
+3.0)*t29+RATIONAL(-25.0,12.0)*t28;
+      coeff_dx_p1 = RATIONAL(-7.0,4.0)*t30+RATIONAL(3.0,1.0)*x+RATIONAL(-4.0,
+1.0)*t29+RATIONAL(2.0,3.0)+RATIONAL(25.0,12.0)*t28;
+      coeff_dx_p2 = RATIONAL(-1.0,12.0)+RATIONAL(11.0,6.0)*t29+RATIONAL(-25.0,
+24.0)*t28+RATIONAL(-11.0,12.0)*x+RATIONAL(7.0,8.0)*t30;
+      coeff_dx_p3 = RATIONAL(-1.0,3.0)*t29+RATIONAL(1.0,6.0)*x+RATIONAL(5.0,
+24.0)*t28+t27;
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dxx.compute.c
new file mode 100644
index 0000000..78113c5
--- /dev/null
+++ b/src/GeneralizedPolynomial-Uniform/Hermite/1d.coeffs/1d.cube.order4/coeff-dxx.compute.c
@@ -0,0 +1,20 @@
+fp t37,
+   t36,
+   t35,
+   t34,
+   t33;
+      t37 = x*x;
+      t36 = t37*x;
+      t35 = RATIONAL(-1.0,4.0);
+      t34 = RATIONAL(-25.0,6.0);
+      t33 = t35*x;
+      coeff_dxx_m2 = t35+t33+RATIONAL(3.0,2.0)*t37+RATIONAL(-5.0,6.0)*t36;
+      coeff_dxx_m1 = RATIONAL(13.0,6.0)+t33+RATIONAL(-7.0,1.0)*t37+RATIONAL(
+25.0,6.0)*t36;
+      coeff_dxx_0 = RATIONAL(-25.0,3.0)*t36+RATIONAL(13.0,1.0)*t37+t34+RATIONAL
+(5.0,2.0)*x;
+      coeff_dxx_p1 = RATIONAL(3.0,1.0)+RATIONAL(-7.0,2.0)*x+RATIONAL(-12.0,1.0)
+*t37+RATIONAL(25.0,3.0)*t36;
+      coeff_dxx_p2 = RATIONAL(11.0,2.0)*t37+t34*t36+RATIONAL(7.0,4.0)*x+
+RATIONAL(-11.0,12.0);
+      coeff_dxx_p3 = RATIONAL(5.0,6.0)*t36+RATIONAL(1.0,6.0)+t33-t37;