added first tests for gaussian quadrature functions

Author: hsnyder

src/tests/quadrature/CMakeLists.txt

@@ -1,2 +1,3 @@
 ADDTEST(trapz)
 ADDTEST(simps)
+ADDTEST(gauss)

src/tests/quadrature/Makefile.manual

@@ -1,3 +1,5 @@
 PROGS_SRC = test_trapz.f90
+PROGS_SRC = test_simps.f90
+PROGS_SRC = test_gauss.f90
 
 include ../Makefile.manual.test.mk

src/tests/quadrature/test_gauss.f90

@@ -0,0 +1,34 @@
+program test_gauss_
+    use stdlib_kinds, only: dp
+    use stdlib_error, only: check
+    use stdlib_quadrature , only: gauss_legendre, gauss_legendre_lobatto
+
+    implicit none
+
+    call test_gauss
+    call test_gauss_lobatto
+
+contains
+
+    subroutine test_gauss
+        integer :: i
+        real(dp) :: analytic, numeric
+
+        ! x**2 from -1 to 1
+        analytic = 2.0_dp/3.0_dp
+        do i=2,6
+            block
+                real(dp), dimension(i) :: x,w
+                call gauss_legendre(x,w)
+                numeric = sum(x**2 * w)
+                !print *, i, numeric
+                call check(abs(numeric-analytic) < 2*epsilon(analytic))
+            end block
+        end do
+
+    end subroutine
+
+    subroutine test_gauss_lobatto
+    end subroutine
+
+end program