From 07df48225553adc441aa68d65a518b145b80a7f5 Mon Sep 17 00:00:00 2001 From: Dominic Steinitz Date: Wed, 14 Mar 2018 06:53:36 +0000 Subject: The full almost entirely C example tidied --- packages/sundials/MyMain.c | 19 - packages/sundials/src/Main.hs | 41 +- packages/sundials/src/Types2.hs | 10658 -------------------------------------- packages/sundials/src/helpers.c | 23 + packages/sundials/src/helpers.h | 2 + 5 files changed, 65 insertions(+), 10678 deletions(-) delete mode 100644 packages/sundials/MyMain.c delete mode 100644 packages/sundials/src/Types2.hs (limited to 'packages/sundials') diff --git a/packages/sundials/MyMain.c b/packages/sundials/MyMain.c deleted file mode 100644 index 1a7f579..0000000 --- a/packages/sundials/MyMain.c +++ /dev/null @@ -1,19 +0,0 @@ -#include -#include -#include /* prototypes for ARKODE fcts., consts. */ -#include /* serial N_Vector types, fcts., macros */ -#include /* access to dense SUNMatrix */ -#include /* access to dense SUNLinearSolver */ -#include /* access to ARKDls interface */ -#include /* definition of type realtype */ -#include - -#include "src/helpers.h" - -int main () { - sunindextype NEQ = 1; /* number of dependent vars. */ - N_Vector y = NULL; /* empty vector for storing solution */ - y = N_VNew_Serial(NEQ); /* Create serial vector for solution */ - if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1; - return 0; -} diff --git a/packages/sundials/src/Main.hs b/packages/sundials/src/Main.hs index 7388b2b..28b813a 100644 --- a/packages/sundials/src/Main.hs +++ b/packages/sundials/src/Main.hs @@ -241,6 +241,45 @@ main = do printf(" ---------------------\n"); fclose(UFID); - return 0; + /* Get/print some final statistics on how the solve progressed */ + flag = ARKodeGetNumSteps(arkode_mem, &nst); + check_flag(&flag, "ARKodeGetNumSteps", 1); + flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a); + check_flag(&flag, "ARKodeGetNumStepAttempts", 1); + flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi); + check_flag(&flag, "ARKodeGetNumRhsEvals", 1); + flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups); + check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1); + flag = ARKodeGetNumErrTestFails(arkode_mem, &netf); + check_flag(&flag, "ARKodeGetNumErrTestFails", 1); + flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni); + check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1); + flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn); + check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1); + flag = ARKDlsGetNumJacEvals(arkode_mem, &nje); + check_flag(&flag, "ARKDlsGetNumJacEvals", 1); + flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS); + check_flag(&flag, "ARKDlsGetNumRhsEvals", 1); + + printf("\nFinal Solver Statistics:\n"); + printf(" Internal solver steps = %li (attempted = %li)\n", nst, nst_a); + printf(" Total RHS evals: Fe = %li, Fi = %li\n", nfe, nfi); + printf(" Total linear solver setups = %li\n", nsetups); + printf(" Total RHS evals for setting up the linear system = %li\n", nfeLS); + printf(" Total number of Jacobian evaluations = %li\n", nje); + printf(" Total number of Newton iterations = %li\n", nni); + printf(" Total number of linear solver convergence failures = %li\n", ncfn); + printf(" Total number of error test failures = %li\n\n", netf); + + /* check the solution error */ + flag = check_ans(y, t, reltol, abstol); + + /* Clean up and return */ + N_VDestroy(y); /* Free y vector */ + ARKodeFree(&arkode_mem); /* Free integrator memory */ + SUNLinSolFree(LS); /* Free linear solver */ + SUNMatDestroy(A); /* Free A matrix */ + + return flag; } |] putStrLn $ show res diff --git a/packages/sundials/src/Types2.hs b/packages/sundials/src/Types2.hs deleted file mode 100644 index 84a46ee..0000000 --- a/packages/sundials/src/Types2.hs +++ /dev/null @@ -1,10658 +0,0 @@ -bash-3.2$ pwd -/Users/dom/Dropbox/Tidy/NumMethHaskell/symplectic-integrators -bash-3.2$ BlogLiterately Notes.lhs -BlogLiterately: CouldNotFindBibFile "DynSys.bib" -bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\tfrac h2,\tfrac12(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\tfrac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\tfrac h2,\tfrac12(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\tfrac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\tfrac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\tfrac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\tfrac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\frac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -

Introduction

-

For the midpoint method you approximate All approximations with an error O(h2)

-

This gives the method
$$ -y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) -$$
This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size where $(t+\frac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$

-bash-3.2$ BlogLiterately Notes.lhs > Notes.htmls -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\frac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -bash-3.2$ BlogLiterately Notes.lhs > Notes.html -[WARNING] Could not convert TeX math ' - y_{k+1}=y_k+hf(t+\frac{h}{2},\frac{1}{2}(y_k+y_{k+1})) - ', rendering as TeX -[WARNING] Could not convert TeX math '(t+\frac h2,y_{k+\frac12})', rendering as TeX -[WARNING] Could not convert TeX math 'y_{k+\frac12}=\frac12(y_k+y_{k+1})', rendering as TeX -bash-3.2$ pwd -/Users/dom/Dropbox/Tidy/NumMethHaskell/symplectic-integrators -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ BlogLiterately --math=mathjax Notes.lhs > Notes.html -bash-3.2$ pwd -/Users/dom/Dropbox/Tidy/NumMethHaskell/symplectic-integrators -bash-3.2$ nix-shell shell.nix -I nixpkgs=/Users/dom/nixpkgs -error: Nix database directory ‘/nix/var/nix/db’ is not writable: Permission denied -bash-3.2$ source /nix/var/nix/profiles/default/etc/profile.d/nix-daemon.sh -bash-3.2$ nix-shell shell.nix -I nixpkgs=/Users/dom/nixpkgs -error: getting status of ‘/Users/dom/Dropbox/Tidy/NumMethHaskell/symplectic-integrators/shell.nix’: No such file or directory -bash-3.2$ cp ../variational/shell.nix . -bash-3.2$ nix-shell 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/nix/store/5kblpllg7za260gw9lqhwyl9nsi9zw6a-JuicyPixels-3.2.9.4/share/doc/x86_64-osx-ghc-8.2.2/JuicyPixels-3.2.9.4/html/JuicyPixels.haddock doesn't exist or isn't a file -Warning: haddock-html: /nix/store/5kblpllg7za260gw9lqhwyl9nsi9zw6a-JuicyPixels-3.2.9.4/share/doc/x86_64-osx-ghc-8.2.2/JuicyPixels-3.2.9.4/html doesn't exist or isn't a directory -Warning: haddock-interfaces: /nix/store/mnq2djh7fbll0sgvvpzcc5qpxks30n10-nats-1.1.2/share/doc/x86_64-osx-ghc-8.2.2/nats-1.1.2/html/nats.haddock doesn't exist or isn't a file -Warning: haddock-html: /nix/store/mnq2djh7fbll0sgvvpzcc5qpxks30n10-nats-1.1.2/share/doc/x86_64-osx-ghc-8.2.2/nats-1.1.2/html doesn't exist or isn't a directory - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ ghci -GHCi, version 8.2.2: http://www.haskell.org/ghc/ :? for help -Prelude> :l Notes.lhs -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:27: error: Variable not in scope: mu - | -160 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:164:5: error: - • No instance for (Fractional [a0]) - arising from the literal ‘1.0e-6’ - • In the expression: 1.0e-6 - In an equation for ‘h’: h = 1.0e-6 - | -164 | h = 1.0e-6 - | ^^^^^^ - -Notes.lhs:166:9: error: - • Ambiguous type variable ‘a0’ arising from the literal ‘1.0’ - prevents the constraint ‘(Fractional a0)’ from being solved. - Relevant bindings include y_n0 :: [a0] (bound at Notes.lhs:166:1) - Probable fix: use a type annotation to specify what ‘a0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the expression: 1.0 - In the expression: [1.0, 0.0] - In an equation for ‘y_n0’: y_n0 = [1.0, 0.0] - | -166 | y_n0 = [1.0, 0.0] - | ^^^ - -Notes.lhs:168:37: error: - • No instance for (Num [a0]) arising from a use of ‘*’ - • In the first argument of ‘(/)’, namely - ‘h * f (0.0 + h / 2) (y_n0 + y_n1)’ - In the second argument of ‘(+)’, namely - ‘h * f (0.0 + h / 2) (y_n0 + y_n1) / 2’ - In the expression: y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2 - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:168:37: error: - • No instance for (Fractional [a0]) arising from a use of ‘/’ - • In the second argument of ‘(+)’, namely - ‘h * f (0.0 + h / 2) (y_n0 + y_n1) / 2’ - In the expression: y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2 - In the first argument of ‘map’, namely - ‘(\ y_n1 -> y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2)’ - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:168:41: error: - • Ambiguous type variable ‘a0’ arising from a use of ‘f’ - prevents the constraint ‘(Fractional a0)’ from being solved. - Relevant bindings include - y_n1 :: [a0] (bound at Notes.lhs:168:22) - y_n1s :: [[a0]] (bound at Notes.lhs:168:1) - Probable fix: use a type annotation to specify what ‘a0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the second argument of ‘(*)’, namely - ‘f (0.0 + h / 2) (y_n0 + y_n1)’ - In the first argument of ‘(/)’, namely - ‘h * f (0.0 + h / 2) (y_n0 + y_n1)’ - In the second argument of ‘(+)’, namely - ‘h * f (0.0 + h / 2) (y_n0 + y_n1) / 2’ - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f (0.0 + h / 2) (y_n0 + y_n1) / 2) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:171:1: error: - parse error (possibly incorrect indentation or mismatched brackets) -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:168:41: error: - • Couldn't match expected type ‘[a0]’ - with actual type ‘[Double] -> [Double]’ - • Probable cause: ‘f’ is applied to too few arguments - In the second argument of ‘(*)’, namely - ‘f [0.0 + h / 2, (y_n0 + y_n1) / 2]’ - In the second argument of ‘(+)’, namely - ‘h * f [0.0 + h / 2, (y_n0 + y_n1) / 2]’ - In the expression: y_n0 + h * f [0.0 + h / 2, (y_n0 + y_n1) / 2] - • Relevant bindings include - y_n1 :: [a0] (bound at Notes.lhs:168:22) - y_n1s :: [[a0]] (bound at Notes.lhs:168:1) - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f [0.0 + h / 2, (y_n0 + y_n1) / 2]) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:168:20: error: - • Couldn't match expected type ‘[a1] -> [a1]’ - with actual type ‘(p0 -> [a1], [a1])’ - • In the first argument of ‘map’, namely - ‘(\ y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1)’ - In the second argument of ‘(:)’, namely - ‘map - (\ y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s’ - In the expression: - y_n0 - : map - (\ y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - • Relevant bindings include - y_n1s :: [[a1]] (bound at Notes.lhs:168:1) - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:168:37: error: - • Couldn't match expected type ‘[a1]’ with actual type ‘a0 -> a0’ - • Probable cause: ‘(*)’ is applied to too few arguments - In the second argument of ‘(+)’, namely ‘h * f 0.0’ - In the first argument of ‘(+)’, namely ‘y_n0 + h * f 0.0’ - In the expression: y_n0 + h * f 0.0 + h / 2 - • Relevant bindings include - y_n1s :: [[a1]] (bound at Notes.lhs:168:1) - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - | ^^^^^^^^^ - -Notes.lhs:168:71: error: - • Variable not in scope: y_n1 :: [a1] - • Perhaps you meant one of these: - ‘y_n0’ (line 166), ‘y_n1s’ (line 168) - | -168 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - | ^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:168:5: error: - • No instance for (Fractional ([a0] -> [a0])) - arising from the literal ‘1.0e-6’ - (maybe you haven't applied a function to enough arguments?) - • In the expression: 1.0e-6 - In an equation for ‘h’: h = 1.0e-6 - | -168 | h = 1.0e-6 - | ^^^^^^ - -Notes.lhs:170:9: error: - • Ambiguous type variable ‘a0’ arising from the literal ‘1.0’ - prevents the constraint ‘(Fractional a0)’ from being solved. - Relevant bindings include y_n0 :: [a0] (bound at Notes.lhs:170:1) - Probable fix: use a type annotation to specify what ‘a0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the expression: 1.0 - In the expression: [1.0, 0.0] - In an equation for ‘y_n0’: y_n0 = [1.0, 0.0] - | -170 | y_n0 = [1.0, 0.0] - | ^^^ - -Notes.lhs:172:20: error: - • Couldn't match expected type ‘[a0] -> [a0]’ - with actual type ‘(p0 -> [a0] -> [a0], [a0])’ - • In the first argument of ‘map’, namely - ‘(\ y_n1 -> zipWith (+) y_n0 + h * f 0.0 + h / 2, - zipWith f y_n0 y_n1)’ - In the second argument of ‘(:)’, namely - ‘map - (\ y_n1 -> zipWith (+) y_n0 + h * f 0.0 + h / 2, - zipWith f y_n0 y_n1) - y_n1s’ - In the expression: - y_n0 - : map - (\ y_n1 -> zipWith (+) y_n0 + h * f 0.0 + h / 2, - zipWith f y_n0 y_n1) - y_n1s - • Relevant bindings include - y_n1s :: [[a0]] (bound at Notes.lhs:172:1) - | -172 | y_n1s = y_n0 : map (\y_n1 -> zipWith (+) y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:172:83: error: - • Variable not in scope: y_n1 :: [a0] - • Perhaps you meant one of these: - ‘y_n0’ (line 170), ‘y_n1s’ (line 172) - | -172 | y_n1s = y_n0 : map (\y_n1 -> zipWith (+) y_n0 + h * f 0.0 + h / 2, zipWith f y_n0 y_n1) y_n1s - | ^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:175:1: error: - parse error (possibly incorrect indentation or mismatched brackets) -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:168:5: error: - • Ambiguous type variable ‘p0’ arising from the literal ‘1.0e-6’ - prevents the constraint ‘(Fractional p0)’ from being solved. - Relevant bindings include h :: p0 (bound at Notes.lhs:168:1) - Probable fix: use a type annotation to specify what ‘p0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the expression: 1.0e-6 - In an equation for ‘h’: h = 1.0e-6 - | -168 | h = 1.0e-6 - | ^^^^^^ - -Notes.lhs:170:9: error: - • Ambiguous type variable ‘p0’ arising from the literal ‘1.0’ - prevents the constraint ‘(Fractional p0)’ from being solved. - Relevant bindings include y_n0 :: [p0] (bound at Notes.lhs:170:1) - Probable fix: use a type annotation to specify what ‘p0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the expression: 1.0 - In the expression: [1.0, 0.0] - In an equation for ‘y_n0’: y_n0 = [1.0, 0.0] - | -170 | y_n0 = [1.0, 0.0] - | ^^^ - -Notes.lhs:172:30: error: - • Ambiguous type variable ‘p0’ arising from a use of ‘+’ - prevents the constraint ‘(Num p0)’ from being solved. - Relevant bindings include - y_n1 :: [p0] (bound at Notes.lhs:172:22) - y_n1s :: [[p0]] (bound at Notes.lhs:172:1) - Probable fix: use a type annotation to specify what ‘p0’ should be. - These potential instances exist: - instance Num Integer -- Defined in ‘GHC.Num’ - instance Num Double -- Defined in ‘GHC.Float’ - instance Num Float -- Defined in ‘GHC.Float’ - ...plus three others - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the expression: - y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1)) - In the first argument of ‘map’, namely - ‘(\ y_n1 - -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1)))’ - In the second argument of ‘(:)’, namely - ‘map - (\ y_n1 - -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))) - y_n1s’ - | -172 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:172:48: error: - • Ambiguous type variable ‘p0’ arising from a use of ‘f’ - prevents the constraint ‘(Fractional p0)’ from being solved. - Relevant bindings include - y_n1 :: [p0] (bound at Notes.lhs:172:22) - y_n1s :: [[p0]] (bound at Notes.lhs:172:1) - Probable fix: use a type annotation to specify what ‘p0’ should be. - These potential instances exist: - instance Fractional Double -- Defined in ‘GHC.Float’ - instance Fractional Float -- Defined in ‘GHC.Float’ - ...plus one instance involving out-of-scope types - (use -fprint-potential-instances to see them all) - • In the second argument of ‘(*)’, namely - ‘f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))’ - In the second argument of ‘(+)’, namely - ‘(pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))’ - In the expression: - y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1)) - | -172 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))) y_n1s - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Notes.lhs:172:67: error: - • No instance for (Fractional [p0]) arising from the literal ‘0.5’ - • In the first argument of ‘(*)’, namely ‘0.5’ - In the second argument of ‘f’, namely ‘(0.5 * (y_n0 + y_n1))’ - In the second argument of ‘(*)’, namely - ‘f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))’ - | -172 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))) y_n1s - | ^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:173:67: error: - • No instance for (Fractional [Double]) - arising from the literal ‘0.5’ - • In the first argument of ‘(*)’, namely ‘0.5’ - In the second argument of ‘f’, namely ‘(0.5 * (y_n0 + y_n1))’ - In the second argument of ‘(*)’, namely - ‘f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))’ - | -173 | y_n1s = y_n0 : map (\y_n1 -> y_n0 + (pure h) * f (0.0 + 0.5 * h) (0.5 * (y_n0 + y_n1))) y_n1s - | ^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> head y_n1s -[1.0,0.0] -*Main> y_n1s!!0 -[1.0,0.0] -*Main> y_n1s!!1 -*** Exception: Notes.lhs:(164,1)-(166,13): Non-exhaustive patterns in function f - -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:175:64: error: - • Variable not in scope: y_n1 :: [Double] - • Perhaps you meant one of these: - ‘y_n0’ (line 170), ‘y_n1s’ (line 173) - | -175 | g u' = y_n0 + pure h * f (0.0 + 0.5 * h) ((pure 0.5) * (y_n0 + y_n1)) - | ^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> g y_n0 -*** Exception: Notes.lhs:(164,1)-(166,13): Non-exhaustive patterns in function f - -*Main> :t f -f :: Fractional a => p -> [a] -> [a] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:164:27: error: Variable not in scope: mu - | -164 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> g y_n0 -*** Exception: 1 -CallStack (from HasCallStack): - error, called at Notes.lhs:167:16 in main:Main -*Main> y_n0 -[1.0,0.0] -*Main> pure h * y_n0 -[1.0e-6] -*Main> (pure h) * y_n0 -[1.0e-6] -*Main> :t zipWith -zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] -*Main> :t repeat -repeat :: a -> [a] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> (pure h) * y_n0 -[1.0e-6] -*Main> (repeat h) * y_n0 -[1.0e-6,0.0] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> head y_n1s -[1.0,0.0] -*Main> head $ tail y_n1s -[1.0,-1.0e-6] -*Main> take 10 y_n1s -[[1.0,0.0],[1.0,-1.0e-6],[0.9999999999995,-1.0e-6],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7]] -*Main> take 100 y_n1s -[[1.0,0.0],[1.0,-1.0e-6],[0.9999999999995,-1.0e-6],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7]] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> take 100 y_n1s -[[1.0,0.0],[1.0,-1.0e-6],[0.9999999999995,-1.0e-6],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7],[0.9999999999995,-9.999999999997499e-7]] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:176:38: error: - • Variable not in scope: y_n1s :: [[Double]] - • Perhaps you meant ‘y_1s’ (line 176) - | -176 | y_1s = y_init : map (rk2Step y_init) y_n1s - | ^^^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> y_1 -[0.9999999999995,-9.999999999997499e-7] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> take 10 y2s - -:45:9: error: - • Variable not in scope: y2s :: [a] - • Perhaps you meant ‘y_2s’ (line 183) -*Main> take 10 y_2s -[[0.9999999999995,-9.999999999997499e-7],[0.9999999999985,-1.99999999999925e-6],[0.9999999999979999,-1.9999999999987497e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6],[0.9999999999979999,-1.9999999999985e-6]] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> take 10 y_2s -[[0.9999999999995,-9.999999999997499e-7],[0.9999999999945,-5.99999999999725e-6],[0.999999999982,-5.999999999984751e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6],[0.999999999982,-5.999999999953503e-6]] -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:160:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -160 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> take 10 y_3s -[[0.999999999982,-5.999999999953503e-6],[0.9999999998319999,-3.099999999950356e-5],[0.9999999995194999,-3.0999999997629366e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5],[0.9999999995194999,-3.099999999372456e-5]] -*Main> :q -Leaving GHCi. - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ ghci -GHCi, version 8.2.2: http://www.haskell.org/ghc/ :? for help -Prelude> :l Notes.lhs -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:248:1: warning: [-Worphans] - Orphan instance: instance Num a => Num [a] - To avoid this - move the instance declaration to the module of the class or of the type, or - wrap the type with a newtype and declare the instance on the new type. - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:248:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ - -Notes.lhs:256:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - rk2Step :: Fractional p => p -> p -> [p] -> [p] -> [p] - | -256 | rk2Step h t y_n0 y_n1 = y_n0 + (repeat h) * f (t + 0.5 * h) ((repeat 0.5) * (y_n0 + y_n1)) - | ^^^^^^^ - -Notes.lhs:263:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - f :: Fractional a => p -> [a] -> [a] - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:263:1: warning: [-Wincomplete-patterns] - Pattern match(es) are non-exhaustive - In an equation for ‘f’: - Patterns not matched: - _ [] - _ [_] - _ (_:_:_:_) - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:263:3: warning: [-Wunused-matches] - Defined but not used: ‘t’ - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:267:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_init :: [Double] - | -267 | y_init = [1.0, 0.0] - | ^^^^^^ - -Notes.lhs:277:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_1 :: [Double] - | -277 | y_1 = y_1s !! nC - | ^^^ - -Notes.lhs:279:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_2s :: [[Double]] - | -279 | y_2s = y_1 : map (rk2Step 5.0e-6 1.0e-6 y_1) y_2s - | ^^^^ - -Notes.lhs:281:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_2 :: [Double] - | -281 | y_2 = y_2s !! nC - | ^^^ - -Notes.lhs:283:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_3s :: [[Double]] - | -283 | y_3s = y_2 : map (rk2Step 2.5e-5 6.0e-6 y_2) y_3s - | ^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:248:1: warning: [-Worphans] - Orphan instance: instance Num a => Num [a] - To avoid this - move the instance declaration to the module of the class or of the type, or - wrap the type with a newtype and declare the instance on the new type. - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:248:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ - -Notes.lhs:256:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - rk2Step :: Fractional p => p -> p -> [p] -> [p] -> [p] - | -256 | rk2Step h t y_n0 y_n1 = y_n0 + (repeat h) * f (t + 0.5 * h) ((repeat 0.5) * (y_n0 + y_n1)) - | ^^^^^^^ - -Notes.lhs:263:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - f :: Fractional a => p -> [a] -> [a] - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:263:1: warning: [-Wincomplete-patterns] - Pattern match(es) are non-exhaustive - In an equation for ‘f’: - Patterns not matched: - _ [] - _ [_] - _ (_:_:_:_) - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:263:3: warning: [-Wunused-matches] - Defined but not used: ‘t’ - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:267:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_init :: [Double] - | -267 | y_init = [1.0, 0.0] - | ^^^^^^ - -Notes.lhs:277:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_1 :: [Double] - | -277 | y_1 = y_1s !! nC - | ^^^ - -Notes.lhs:281:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_2 :: [Double] - | -281 | y_2 = y_2s !! nC - | ^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:277:11: error: - The type signature for ‘y_3’ lacks an accompanying binding - | -277 | y_1, y_2, y_3 :: [Double] - | ^^^ -Failed, no modules loaded. -Prelude> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:248:1: warning: [-Worphans] - Orphan instance: instance Num a => Num [a] - To avoid this - move the instance declaration to the module of the class or of the type, or - wrap the type with a newtype and declare the instance on the new type. - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:248:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ - -Notes.lhs:256:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - rk2Step :: Fractional p => p -> p -> [p] -> [p] -> [p] - | -256 | rk2Step h t y_n0 y_n1 = y_n0 + (repeat h) * f (t + 0.5 * h) ((repeat 0.5) * (y_n0 + y_n1)) - | ^^^^^^^ - -Notes.lhs:263:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - f :: Fractional a => p -> [a] -> [a]o - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:263:1: warning: [-Wincomplete-patterns] - Pattern match(es) are non-exhaustive - In an equation for ‘f’: - Patterns not matched: - _ [] - _ [_] - _ (_:_:_:_) - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:263:3: warning: [-Wunused-matches] - Defined but not used: ‘t’ - | -263 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ - -Notes.lhs:267:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: y_init :: [Double] - | -267 | y_init = [1.0, 0.0] - | ^^^^^^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:248:1: warning: [-Worphans] - Orphan instance: instance Num a => Num [a] - To avoid this - move the instance declaration to the module of the class or of the type, or - wrap the type with a newtype and declare the instance on the new type. - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:248:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ - -Notes.lhs:256:1: warning: [-Wmissing-signatures] - Top-level binding with no type signature: - rk2Step :: Fractional a => a -> a -> [a] -> [a] -> [a] - | -256 | rk2Step h t y_n0 y_n1 = y_n0 + (repeat h) * f (t + 0.5 * h) ((repeat 0.5) * (y_n0 + y_n1)) - | ^^^^^^^ - -Notes.lhs:264:1: warning: [-Wincomplete-patterns] - Pattern match(es) are non-exhaustive - In an equation for ‘f’: - Patterns not matched: - _ [] - _ [_] - _ (_:_:_:_) - | -264 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:264:3: warning: [-Wunused-matches] - Defined but not used: ‘t’ - | -264 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:248:1: warning: [-Worphans] - Orphan instance: instance Num a => Num [a] - To avoid this - move the instance declaration to the module of the class or of the type, or - wrap the type with a newtype and declare the instance on the new type. - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:248:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -248 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ - -Notes.lhs:265:1: warning: [-Wincomplete-patterns] - Pattern match(es) are non-exhaustive - In an equation for ‘f’: - Patterns not matched: - _ [] - _ [_] - _ (_:_:_:_) - | -265 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^... - -Notes.lhs:265:3: warning: [-Wunused-matches] - Defined but not used: ‘t’ - | -265 | f t [y0, y1] = [y1, -y0 - mu * y1 * (y0 * y0 - 1)] - | ^ -Ok, one module loaded. -*Main> :r -[1 of 1] Compiling Main ( Notes.lhs, interpreted ) - -Notes.lhs:246:10: warning: [-Wmissing-methods] - • No explicit implementation for - ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’ or ‘-’) - • In the instance declaration for ‘Num [a]’ - | -246 | instance Num a => Num [a] where - | ^^^^^^^^^^^^^^^^ -Ok, one module loaded. -*Main> :q -Leaving GHCi. - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --ghci --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --ghci --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ BlogLiterately --ghci --math=mathjax Notes.lhs > Notes.html - -[nix-shell:~/Dropbox/Tidy/NumMethHaskell/symplectic-integrators]$ ghci -GHCi, version 8.2.2: http://www.haskell.org/ghc/ :? for help -Prelude> :l Notes.lhs -[1 of 1] Compiling RK2Imp ( Notes.lhs, interpreted ) -Ok, one module loaded. -*RK2Imp> :version -unknown command ':version' -use :? for help. -*RK2Imp> :? - Commands available from the prompt: - - evaluate/run - : repeat last command - :{\n ..lines.. \n:}\n multiline command - :add [*] ... add module(s) to the current target set - :browse[!] [[*]] display the names defined by module - (!: more details; *: all top-level names) - :cd change directory to - :cmd run the commands returned by ::IO String - :complete [] list completions for partial input string - :ctags[!] [] create tags file for Vi (default: "tags") - (!: use regex instead of line number) - :def define command : (later defined command has - precedence, :: is always a builtin command) - :edit edit file - :edit edit last module - :etags [] create tags file for Emacs (default: "TAGS") - :help, :? display this list of commands - :info[!] [ ...] display information about the given names - (!: do not filter instances) - :issafe [] display safe haskell information of module - :kind[!] show the kind of - (!: also print the normalised type) - :load[!] [*] ... load module(s) and their dependents - (!: defer type errors) - :main [ ...] run the main function with the given arguments - :module [+/-] [*] ... set the context for expression evaluation - :quit exit GHCi - :reload[!] reload the current module set - (!: defer type errors) - :run function [ ...] run the function with the given arguments - :script run the script - :type show the type of - :type +d show the type of , defaulting type variables - :type +v show the type of , with its specified tyvars - :undef undefine user-defined command : - :! run the shell command - - -- Commands for debugging: - - :abandon at a breakpoint, abandon current computation - :back [] go back in the history N steps (after :trace) - :break [] [] set a breakpoint at the specified location - :break set a breakpoint on the specified function - :continue resume after a breakpoint - :delete delete the specified breakpoint - :delete * delete all breakpoints - :force print , forcing unevaluated parts - :forward [] go forward in the history N step s(after :back) - :history [] after :trace, show the execution history - :list show the source code around current breakpoint - :list show the source code for - :list [] show the source code around line number - :print [ ...] show a value without forcing its computation - :sprint [ ...] simplified version of :print - :step single-step after stopping at a breakpoint - :step single-step into - :steplocal single-step within the current top-level binding - :stepmodule single-step restricted to the current module - :trace trace after stopping at a breakpoint - :trace evaluate with tracing on (see :history) - - -- Commands for changing settings: - - :set