Initial commitv1.0

2 files changed, 150 insertions, 0 deletions

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 <stdio.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
+#include <libinum.h>
+
+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 <stdio.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
+#include <libinum.h>
+
+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);
+}