From 2125f01f97abfe343fc5e0cc078bf1d081b2e441 Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Fri, 20 May 2016 20:30:15 +0000 Subject: Initial commit --- doc/libinum-examples/Makefile | 80 ++++++++++++++++++ doc/libinum-examples/build/integral_gauss-legendre | Bin 0 -> 127104 bytes doc/libinum-examples/build/root_newton | Bin 0 -> 18712 bytes .../objs/integral_gauss-legendre.o | Bin 0 -> 11072 bytes doc/libinum-examples/objs/root_newton.o | Bin 0 -> 9048 bytes doc/libinum-examples/src/integral_gauss-legendre.c | 92 +++++++++++++++++++++ doc/libinum-examples/src/root_newton.c | 58 +++++++++++++ 7 files changed, 230 insertions(+) create mode 100644 doc/libinum-examples/Makefile create mode 100755 doc/libinum-examples/build/integral_gauss-legendre create mode 100755 doc/libinum-examples/build/root_newton create mode 100644 doc/libinum-examples/objs/integral_gauss-legendre.o create mode 100644 doc/libinum-examples/objs/root_newton.o create mode 100644 doc/libinum-examples/src/integral_gauss-legendre.c create mode 100644 doc/libinum-examples/src/root_newton.c (limited to 'doc/libinum-examples') diff --git a/doc/libinum-examples/Makefile b/doc/libinum-examples/Makefile new file mode 100644 index 0000000..5c7ccc1 --- /dev/null +++ b/doc/libinum-examples/Makefile @@ -0,0 +1,80 @@ +# whether to link dynamically +# if static=0 then link dynamically +# if static=2 then link statically +# if static=1 then link libkondo statically but other libraries dynamically +STATIC=1 + +VERSION=0.3.1 + +# products of the compilation +PROJECT_BINS= root_newton integral_gauss-legendre + +# debug and optimization flags +#DB= -ggdb +OPT= -O3 + +# warning flags +WARNINGS= -Wall -Wextra -Wno-strict-overflow -std=c99 -pedantic -Wno-unused-parameter + +# compiler +CC=/usr/bin/gcc +LD=$(CC) + +# directories +INCLUDE = +LIB = +#INCLUDE = -I../../include +#LIB = -L../../build + +# flags +override LDFLAGS +=$(LIB) +override CFLAGS +=$(INCLUDE) $(DB) $(OPT) $(WARNINGS) + +# build directories +BUILDDIR=./build +SRCDIR=./src +OBJDIR=./objs + +# objects +OBJS = $(addprefix $(OBJDIR)/, root_newton.o integral_gauss-legendre.o) + +# flags which depend on whether to link statically or dynamically +# lib flag +LIBINUM_FLAG=-linum +# additional library required for static linking +XTRA_LIBS= + +ifeq ($(STATIC),1) + # libinum is linked against libm, libmpfr, libgmp and libpthread + XTRA_LIBS=-lm -lmpfr -lgmp -lpthread + # link binaries using the static library + LIBINUM_FLAG=-l:libinum.a +else ifeq ($(STATIC),2) + # libinum is linked against libm, libmpfr, libgmp and libpthread + XTRA_LIBS=-lm -lmpfr -lgmp -lpthread + # link binaries statically + override LDFLAGS += -static +else + # required flag for subsequent dynamic linking + override CFLAGS += -fPIC +endif + + +all: init $(PROJECT_BINS) + +# create dirs +init: + @[ -d $(OBJDIR) ] || /bin/mkdir $(OBJDIR) + @[ -d $(BUILDDIR) ] || /bin/mkdir $(BUILDDIR) + +root_newton: + $(CC) -c $(CFLAGS) src/$@.c -o objs/$@.o + $(LD) $(LDFLAGS) -o $(BUILDDIR)/$@ objs/$@.o $(LIBINUM_FLAG) $(XTRA_LIBS) + +integral_gauss-legendre: + $(CC) -c $(CFLAGS) src/$@.c -o objs/$@.o + $(LD) $(LDFLAGS) -o $(BUILDDIR)/$@ objs/$@.o $(LIBINUM_FLAG) $(XTRA_LIBS) + +clean: + @rm -rf $(OBJDIR) + @rm -rf $(BUILDDIR) diff --git a/doc/libinum-examples/build/integral_gauss-legendre b/doc/libinum-examples/build/integral_gauss-legendre new file mode 100755 index 0000000..b86cfe7 Binary files /dev/null and b/doc/libinum-examples/build/integral_gauss-legendre differ diff --git a/doc/libinum-examples/build/root_newton b/doc/libinum-examples/build/root_newton new file mode 100755 index 0000000..68a2e50 Binary files /dev/null and b/doc/libinum-examples/build/root_newton differ diff --git a/doc/libinum-examples/objs/integral_gauss-legendre.o b/doc/libinum-examples/objs/integral_gauss-legendre.o new file mode 100644 index 0000000..83841c9 Binary files /dev/null and b/doc/libinum-examples/objs/integral_gauss-legendre.o differ diff --git a/doc/libinum-examples/objs/root_newton.o b/doc/libinum-examples/objs/root_newton.o new file mode 100644 index 0000000..1e567f7 Binary files /dev/null and b/doc/libinum-examples/objs/root_newton.o differ diff --git a/doc/libinum-examples/src/integral_gauss-legendre.c b/doc/libinum-examples/src/integral_gauss-legendre.c new file mode 100644 index 0000000..f65465f --- /dev/null +++ b/doc/libinum-examples/src/integral_gauss-legendre.c @@ -0,0 +1,92 @@ +#include +#include +// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears +#define MPFR_USE_VA_LIST +#include +#include + +int func(mpfr_t* out, mpfr_t in, void* extra_args); + +int main(int argc, const char* argv[]){ + int ret; + mpfr_t tolerance, val, lower, upper; + array_mpfr abcissa, weights; + + // precision of MPFR floats + mpfr_set_default_prec(53); + + // tolerance for computing weights + mpfr_init(tolerance); + mpfr_set_d(tolerance, 1.e-11, MPFR_RNDN); + + // compute weights + ret=gauss_legendre_weights_mpfr(10, tolerance, 10000, &abcissa, &weights); + // return codes + if(ret==LIBINUM_ERROR_MAXITER){ + printf("error: maximum number of iterations reached when computing the integration abcissa\n"); + mpfr_clear(tolerance); + return(ret); + } + else if(ret==LIBINUM_ERROR_NAN){ + printf("error: infinity encountered when computing the integration abcissa\n"); + mpfr_clear(tolerance); + return(ret); + } + else{ + printf("abcissa:\n"); + array_mpfr_print(abcissa); + printf("\nweights:\n"); + array_mpfr_print(weights); + printf("\n"); + } + + mpfr_clear(tolerance); + + mpfr_inits(val, lower, upper, NULL); + + mpfr_set_ui(lower, 0, MPFR_RNDN); + mpfr_set_ui(upper, 2, MPFR_RNDN); + + ret=integrate_gauss_mpfr(&val, &func, lower, upper, abcissa, weights, NULL); + // return codes + if(ret==LIBINUM_ERROR_SIZE_MISMATCH){ + printf("error: the mpfr_arrays 'abcissa' and 'weights' must have the same length\n"); + mpfr_clears(val, upper, lower, NULL); + array_mpfr_free(abcissa); + array_mpfr_free(weights); + return(ret); + } + else if(ret==LIBINUM_ERROR_NAN){ + printf("error: the integrand is singular\n"); + array_mpfr_free(abcissa); + array_mpfr_free(weights); + mpfr_clears(val, upper, lower, NULL); + return(ret); + } + else{ + printf("\\int_0^2 x/sin(x) dx = "); + fprint_mpfr(stdout, val); + printf("\n"); + } + + mpfr_clears(val, upper, lower, NULL); + array_mpfr_free(abcissa); + array_mpfr_free(weights); + + return(0); +} + +/* +// e^x +int func(mpfr_t* out, mpfr_t in, void* extra_args){ + mpfr_exp(*out, in, MPFR_RNDN); + return(0); +} +*/ + +// x/sin(x) +int func(mpfr_t* out, mpfr_t in, void* extra_args){ + mpfr_sin(*out, in, MPFR_RNDN); + mpfr_div(*out, in, *out, MPFR_RNDN); + return(0); +} diff --git a/doc/libinum-examples/src/root_newton.c b/doc/libinum-examples/src/root_newton.c new file mode 100644 index 0000000..f307c58 --- /dev/null +++ b/doc/libinum-examples/src/root_newton.c @@ -0,0 +1,58 @@ +#include +#include +// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears +#define MPFR_USE_VA_LIST +#include +#include + +int func(mpfr_t* out, mpfr_t in, void* extra_args); +int dfunc(mpfr_t* out, mpfr_t in, void* extra_args); + +int main(int argc, const char* argv[]){ + int ret; + mpfr_t init, prec, x; + unsigned int maxiter; + int extra_arg; + + mpfr_inits(init, prec, x, NULL); + + // start at 2 + mpfr_set_ui(init, 2, MPFR_RNDN); + // precision + mpfr_set_d(prec, 1.e-30, MPFR_RNDN); + // maximum number of iterations before error + maxiter=10000; + // extra argument + extra_arg=4; + + // compute root + ret=root_newton_mpfr(&x, &func, &dfunc, init, prec, maxiter, &extra_arg); + + // return codes + if(ret==LIBINUM_ERROR_MAXITER){ + printf("error: maximum number of iterations reached\n"); + } + else if(ret==LIBINUM_ERROR_NAN){ + printf("error: infinity encountered\n"); + } + else{ + mpfr_printf("% 14.7Re\n", x); + } + + mpfr_clears(init, prec, x, NULL); + + return(0); +} + +// x^2-1 +int func(mpfr_t* out, mpfr_t in, void* extra_args){ + mpfr_pow_ui(*out, in, 2, MPFR_RNDN); + mpfr_add_d(*out, *out, -1./ *((int*)extra_args), MPFR_RNDN); + return(0); +} + +// 2*x +int dfunc(mpfr_t* out, mpfr_t in, void* extra_args){ + mpfr_mul_ui(*out, in, 2, MPFR_RNDN); + return(0); +} -- cgit v1.2.3-70-g09d2