diff --git a/notebooks/fanci_tutorial.ipynb b/notebooks/fanci_tutorial.ipynb
index 26a1d52..54da886 100644
--- a/notebooks/fanci_tutorial.ipynb
+++ b/notebooks/fanci_tutorial.ipynb
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 68,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -63,9 +63,12 @@
     "from pyci.test import datafile\n",
     "\n",
     "# System information\n",
-    "filename = datafile(\"lih_sto6g.fcidump\")\n",
+    "# filename = datafile(\"lih_sto6g.fcidump\")\n",
+    "filename = datafile(\"/workspaces/PyCI/pyci/test/data/h4_2_0.0_STO-6G.fcidump\")\n",
+    "\n",
     "ham = pyci.hamiltonian(filename)\n",
-    "e_dict = {}"
+    "e_dict = {}\n",
+    "f_dict = {}"
    ]
   },
   {
@@ -79,7 +82,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 59,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -101,7 +104,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 60,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -124,13 +127,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 61,
    "metadata": {},
    "outputs": [],
    "source": [
     "# Optimize wavefunction\n",
     "ap1rog_results = ap1rog.optimize(ap1_params, use_jac=True)\n",
-    "e_dict[\"AP1roG\"] = ap1rog_results.x[-1]"
+    "e_dict[\"AP1roG\"] = (ap1rog_results.x[-1])\n",
+    "\n",
+    "# f_dict['AP1roG'] = (np.std(ap1rog_results.fun)) #Calculating the std of the residuals \n",
+    "\n",
+    "#Calculation of root mean square deviation (RMSD) \n",
+    "\"\"\" \n",
+    "RMSD = \\sqrt ( \\sum_i^n (residuals)^2 / (n - 2)) \n",
+    "n = size of sample \n",
+    "resilduals = Vector of residuals at the solution.\n",
+    "\"\"\"\n",
+    "f_dict['AP1roG'] = (np.sqrt(np.sum((ap1rog_results.fun)**2)/(len(ap1rog_results.fun)-2)))\n",
+    "\n",
+    "# print(f_dict['AP1roG'])\n",
+    "\n",
+    "# print(ap1rog_results) \n",
+    "\n"
    ]
   },
   {
@@ -146,7 +164,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 62,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -160,7 +178,22 @@
     "\n",
     "# Optimize wavefunction\n",
     "pccds_results = pccds.optimize(pccds_params, use_jac=False)\n",
-    "e_dict[\"pCCD+S\"] = pccds_results.x[-1]"
+    "e_dict[\"pCCD+S\"] = pccds_results.x[-1]\n",
+    "# f_dict[\"pCCD+S\"] = (np.std(ap1rog_results.fun))\n",
+    "\n",
+    "#Calculation of root mean square deviation (RMSD) \n",
+    "\"\"\" \n",
+    "RMSD = \\sqrt ( \\sum_i^n (residuals)^2 / (n - 2)) \n",
+    "n = size of sample \n",
+    "resilduals = Vector of residuals at the solution.\n",
+    "\"\"\"\n",
+    "\n",
+    "f_dict['pCCD+S'] = (np.sqrt(np.sum((pccds_results.fun)**2)/(len(pccds_results.fun)-2)))\n",
+    "\n",
+    "\n",
+    "# print(pccds_results)\n",
+    "# print(f_dict['pCCD+S'])\n",
+    "\n"
    ]
   },
   {
@@ -174,7 +207,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 63,
    "metadata": {},
    "outputs": [
     {
@@ -182,9 +215,9 @@
      "output_type": "stream",
      "text": [
       "  METHOD,           ENERGY\n",
-      "      HF, -8.947289175e+00\n",
-      "  AP1roG, -8.963531034e+00\n",
-      "  pCCD+S, -8.963613544e+00\n"
+      "      HF, -3.875079433e+00\n",
+      "  AP1roG, -3.955402403e+00\n",
+      "  pCCD+S, -3.816787845e+00\n"
      ]
     }
    ],
@@ -195,6 +228,54 @@
     "    print(f\"{name:>8s}, {energy:>16.9e}\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Calculate the standard deviation "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.4683556322835916e-14\n",
+      "1.9667674453325034e-09\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f_dict[\"AP1roG\"])\n",
+    "print(f_dict[\"pCCD+S\"])\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "  METHOD,             RMSD\n",
+      "  AP1roG,  2.468355632e-14\n",
+      "  pCCD+S,  1.966767445e-09\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Print RMSD from various methods\n",
+    "print(f\"{'METHOD':>8s}, {'RMSD':>16s}\")\n",
+    "for name, fun in f_dict.items():\n",
+    "    print(f\"{name:>8s}, {fun:>16.9e}\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -242,7 +323,7 @@
      "output_type": "stream",
      "text": [
       "Number of electrons = 4.1\n",
-      "Number of pairs     = 6.1\n"
+      "Number of pairs     = 6.2\n"
      ]
     }
    ],
@@ -269,7 +350,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.6"
+   "version": "3.10.13"
   }
  },
  "nbformat": 4,
diff --git a/pyci/rdm/algorithms.py b/pyci/rdm/algorithms.py
index e69de29..15b261c 100644
--- a/pyci/rdm/algorithms.py
+++ b/pyci/rdm/algorithms.py
@@ -0,0 +1,65 @@
+import numpy as np 
+from abc import ABCMeta, abstractmethod
+class Projection(metaclass=ABCMeta):
+    
+    @abstractmethod
+    def __init__(self, initial_guess,constraints):
+        self.initial_guess = initial_guess
+        self.constraints = constraints
+    
+    @abstractmethod 
+    def optimize(self):
+        pass
+
+class Dykstra(metaclass=ABCMeta):
+    def __init__(self, initial_guess:float, constraints:list, alpha:int =1, max_iterations:int =100, eps:int =1e-6):
+        """
+        Dykstra's algorithm for projection onto convex sets.
+
+        Parameters
+        ----------
+        initial_guess : float
+            Initializing with guessed density matrix \Gamma_0.
+        constraints : list
+            A list of projection operators onto all $J$ of the constraints as a single set, $\{\mathcal{P}_j\}_{j=0}^{J-1}$.
+        alpha : int, optional
+            Tunning parameter, by default 1
+        max_iterations : int, optional
+            Number of maximum iterations, by default 100
+        eps : int, optional
+            Tolerance, by default 1e-6
+        """        
+        super().__init__(initial_guess, constraints)
+        self.alpha = alpha
+        self.max_iterations = max_iterations
+        self.eps = eps
+    def optimize(self):
+        X = [np.zeros(self.initial_guess) for i in range(len(self.constraints))]
+        D = np.copy(self.initial_guess)
+        norm = []
+        for i in range (self.max_iterations):
+            for j, projection in enumerate(self.constraints):
+                C = D - X[j]
+                D = projection(C)
+                X[j] = D - C
+            norm.append(np.linalg.norm(D - self.initial_guess))
+            is_stop = self.alpha * abs(norm[i] - norm[i - 1]) + (1 - self.alpha) * norm[i] < self.eps
+            if is_stop:
+                break
+class Neumann(metaclass=ABCMeta):
+    def __init__(self, initial_guess, constraints, alpha, max_iterations=100, eps=1e-6):
+        super().__init__(initial_guess, constraints)
+        self.alpha = alpha
+        self.max_iterations = max_iterations
+        self.eps = eps
+    def optimize(self):
+        D = np.copy(self.initial_guess)
+        norm = []
+        for i in range (self.max_iterations):
+            for projection in enumerate(self.constraints):
+                D = projection(D)
+            norm.append(np.linalg.norm(D - self.initial_guess))
+            is_stop = self.alpha * abs(norm[i] - norm[i - 1]) + (1 - self.alpha) * norm[i] < self.eps
+            if is_stop:
+                break
+
diff --git a/pyci/test/data/h4_2_0.0_STO-6G.fcidump b/pyci/test/data/h4_2_0.0_STO-6G.fcidump
new file mode 100644
index 0000000..c2f8a60
--- /dev/null
+++ b/pyci/test/data/h4_2_0.0_STO-6G.fcidump
@@ -0,0 +1,115 @@
+ &FCI NORB=   4,NELEC= 4,MS2=0,
+  ORBSYM=1,1,1,1,
+  ISYM=1,
+ &END
+ 0.5068898550551018    1    1    1    1
+ 0.003794527559320846    1    1    2    1
+ 0.4098635263371225    1    1    2    2
+ 1.025916213093225e-09    1    1    3    1
+ -8.035957177465747e-10    1    1    3    2
+ 0.445100515768005    1    1    3    3
+ 0.09719871204645167    1    1    4    1
+ 0.05096181960669316    1    1    4    2
+ -2.511664404236669e-09    1    1    4    3
+ 0.5183452230109675    1    1    4    4
+ 0.003794527559320839    2    1    1    1
+ 0.08813159971644449    2    1    2    1
+ 0.07782243723669213    2    1    2    2
+ -5.653522719417658e-10    2    1    3    1
+ -4.283259379123106e-09    2    1    3    2
+ -0.08764576192895299    2    1    3    3
+ 0.02826446097635334    2    1    4    1
+ -0.08001497578900814    2    1    4    2
+ 7.330390461302017e-11    2    1    4    3
+ 0.05589849747028398    2    1    4    4
+ 0.4098635263371225    2    2    1    1
+ 0.07782243723669217    2    2    2    1
+ 0.521293056868916    2    2    2    2
+ -5.046337625547181e-09    2    2    3    1
+ 1.404773519730895e-11    2    2    3    2
+ 0.3561543663891216    2    2    3    3
+ -0.001427950323337701    2    2    4    1
+ -0.09114783741363394    2    2    4    2
+ 3.876907371525018e-09    2    2    4    3
+ 0.4713483506720944    2    2    4    4
+ 1.025916174929309e-09    3    1    1    1
+ -5.653522754112128e-10    3    1    2    1
+ -5.046337653302757e-09    3    1    2    2
+ 0.1293028829330219    3    1    3    1
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+ 4.05264671821115e-09    3    1    3    3
+ -1.581443448417374e-09    3    1    4    1
+ 7.217758335453794e-11    3    1    4    2
+ -0.0846859118356684    3    1    4    3
+ -1.893284105880522e-09    3    1    4    4
+ -8.035956726437643e-10    3    2    1    1
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+ 1.404779764735409e-11    3    2    2    2
+ -0.1072466481774506    3    2    3    1
+ 0.09458993631478847    3    2    3    2
+ 1.40467162901281e-09    3    2    3    3
+ 7.391295561709477e-11    3    2    4    1
+ 4.802033475720391e-09    3    2    4    2
+ 0.07788008022122561    3    2    4    3
+ -1.244524983068374e-09    3    2    4    4
+ 0.445100515768005    3    3    1    1
+ -0.08764576192895296    3    3    2    1
+ 0.3561543663891216    3    3    2    2
+ 4.052646773722302e-09    3    3    3    1
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+ 0.5359374140556439    3    3    3    3
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+ 2.168608539661471  0  0  0  0