From d45df44e5e3abbdd4ccf14024e87b8962317d626 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Coppens?= <francois.coppens@uvsq.fr>
Date: Wed, 27 Jan 2021 17:19:41 +0100
Subject: [PATCH] C++ implementation of algo 3 is working. Not optimised yet.

---
 .vscode/settings.json |   3 +-
 Makefile              |   9 +-
 SM-MaponiA3.cpp       | 291 +++++++++++++++++++++++++++++++++++++-----
 3 files changed, 267 insertions(+), 36 deletions(-)

diff --git a/.vscode/settings.json b/.vscode/settings.json
index 293d384..54df84e 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -1,6 +1,7 @@
 {
     "files.associations": {
         "ostream": "cpp",
-        "new": "cpp"
+        "new": "cpp",
+        "iostream": "cpp"
     }
 }
\ No newline at end of file
diff --git a/Makefile b/Makefile
index afaa43f..ccb052d 100644
--- a/Makefile
+++ b/Makefile
@@ -1,16 +1,17 @@
 CC=icc
 CXX=icpc
-CFLAGS=-xCORE-AVX2 -O0 -debug full
-CXXFLAGS=-xCORE-AVX2 -O0 -debug full
+CFLAGS=-O0 -debug full
+CXXFLAGS=-O0 -debug full -traceback
+# ARCH=-xCORE-AVX2 
 
 DEPS = SM-MaponiA3.cpp
 OBJ = SM-MaponiA3.o 
 
 %.o: %.c $(DEPS)
-	$(CXX) -c -o $@ $< $(CFLAGS)
+	$(CXX) $(ARCH) -c -o $@ $< $(CFLAGS)
 
 SM-MaponiA3: $(OBJ)
-	$(CXX) -o $@ $^ $(CFLAGS)
+	$(CXX) $(ARCH) -o $@ $^ $(CFLAGS)
 
 clean:
 	@rm -vf *.o
diff --git a/SM-MaponiA3.cpp b/SM-MaponiA3.cpp
index 4130058..3b65623 100644
--- a/SM-MaponiA3.cpp
+++ b/SM-MaponiA3.cpp
@@ -2,26 +2,46 @@
 // p. 283, doi:10.1016/j.laa.2006.07.007
 
 #include <iostream>
+#include <string>
 using namespace std;
 
-int M = 3;
+uint getMaxIndex(double* arr, uint size);
+void showScalar(uint scalar, string name);
+void showScalar(int scalar, string name);
+void showScalar(double scalar, string name);
+void showVector(uint* vector, uint size, string name);
+void showVector(int* vector, uint size, string name);
+void showVector(double* vector, uint size, string name);
+void showMatrix(uint** matrix, uint sizeR, uint sizeC, string name);
+void showMatrix(int** matrix, uint sizeR, uint sizeC, string name);
+void showMatrix(double** matrix, uint sizeR, uint sizeC, string name);
+void showMatrixT(uint** matrix, uint sizeR, uint sizeC, string name);
+void showMatrixT(int** matrix, uint sizeR, uint sizeC, string name);
+void showMatrixT(double** matrix, uint sizeR, uint sizeC, string name);
+int** matMul(int** A, int** B, uint size);
+double** matMul(double** A, double** B, uint size);
+int** outProd(int* vec1, int* vec2, uint size);
+double** outProd(double* vec1, int* vec2, uint size);
 
 int main() {
 
+    uint M = 3;
     uint i, j, k, l, lbar, tmp;
+    double alpha, beta;
+
     // Declare and allocate all vectors and matrices
-    int* p = new int[M+1];
-    int* breakdown = new int[M];
+    uint* p = new uint[M+1];
+    double* breakdown = new double[M+1];
 
     int** A = new int*[M];
     int** A0 = new int*[M];
     int** Ar = new int*[M];
     int** Id = new int*[M];
     double** A0inv = new double*[M];
-    double** Ainv = new double*[M];
+    double** Ainv; //= new double*[M];
     for (i = 0; i < M; i++) { 
         A[i] = new int[M];
-        Ainv[i] = new double[M];
+        //Ainv[i] = new double[M];
         A0[i] = new int[M];
         A0inv[i] = new double[M];
         Ar[i] = new int[M];
@@ -32,7 +52,7 @@ int main() {
     for (l = 0; l < M; l++) {
         ylk[l] = new double*[M+1];
         for (k = 0; k < M+1; k++) {
-            ylk[l][k] = new double[M];
+            ylk[l][k] = new double[M+1];
         }
     }
 
@@ -40,7 +60,7 @@ int main() {
     for (i = 0; i < M; i++) {
         for (j = 0; j < M; j++) {
             A[i][j] = 0;
-            Ainv[i][j] = 0;
+            //Ainv[i][j] = 0;
             A0[i][j] = 0;
             A0inv[i][j] = 0;
             Ar[i][j] = 0;
@@ -48,17 +68,27 @@ int main() {
         }
     }
 
-    // Initialize all vectors and matrices
+    // Initialize ylk with zeros
+    for (l = 0; l < M; l++) {
+        for (k = 0; k < M+1; k++) {
+            for (i = 0; i < M+1; i++) {
+                ylk[l][k][i] = 0;
+            }
+        }
+    }
+
+    // Initialize A
     A[0][0] = 1;    A[0][1] = 1;    A[0][2] = -1;
     A[1][0] = 1;    A[1][1] = 1;    A[1][2] = 0;
     A[2][0] = -1;   A[2][1] = 0;    A[2][2] = -1;
 
     // Define identity matrix, A0, A0inv and p
+    p[0] = 0;
     for (i = 0; i < M; i++) {
         Id[i][i] = 1;
         A0[i][i] = A[i][i];
         A0inv[i][i] = 1.0/A[i][i];
-        p[i] = i;
+        p[i+1] = i+1;
     }
 
     // Init Ar
@@ -68,48 +98,80 @@ int main() {
         }
     }
 
+    showMatrix(A, M, M, "A");
+    // showMatrix(A0, M, M, "A0");
+    // showMatrix(Ar, M, M, "Ar");
+    // showMatrix(A0inv, M, M, "A0inv");
+
     // Calculate all the y0k in M^2 multiplications instead of M^3
-    for (k = 1; i < M+1; k++) {
-        for (i = 0; i < M; i++) {
-            ylk[0][k][i] = A0inv[i][i] * Ar[i][k];
+    for (k = 1; k < M+1; k++) {
+        for (i = 1; i < M+1; i++) {
+            ylk[0][k][i] = A0inv[i-1][i-1] * Ar[i-1][k-1];
         }
+        // showVector(ylk[0][k], M+1, "y0k");
     }
+    showMatrixT(ylk[0], M+1, M+1, "y0k");
 
     // Calculate all the ylk from the y0k
+    // showVector(p, M+1, "p");
     for (l = 1; l < M; l++) {
-        for (j = l; j < M; j++) {
-            breakdown[j] = abs( 1 + ylk[l][p[j]][p[j]-1] );
+        for (j = l; j < M+1; j++) {
+            breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
         }
-        lbar = findMaxElmnt(breakdown); // NOT IMPLEMENTED YET
+        // showVector(breakdown, M+1, "break-down vector");
+        lbar = getMaxIndex(breakdown, M+1);
+        // showScalar(lbar, "lbar");
         for (i = 0; i < M; i++) {
             breakdown[i] = 0;
         }
-        tmp = p
-    }
-
-
-
-    for (i = 0; i < M; i++) {
-        for (j = 0; j < M; j++) {
-            cout << "A["<<i<<"]["<<j<<"] = " << A0inv[i][j] << " ";
+        tmp = p[l];
+        p[l] = p[lbar];
+        p[lbar] = tmp;
+        // showVector(p, M+1, "p");
+        for (k = l+1; k < M+1; k++) {
+            beta = 1 + ylk[l-1][p[l]][p[l]];
+            if (beta == 0) {
+                cout << "Break-down condition occured. Exiting..." << endl;
+                exit;
+            }
+            for (i = 1; i < M+1; i++) {
+                alpha = ylk[l-1][p[k]][p[l]] / beta;
+                ylk[l][p[k]][i] = ylk[l-1][p[k]][i] - alpha * ylk[l-1][p[l]][i];
+            }
+            // showVector(ylk[l][p[k]], M+1, "ylk");
         }
-        cout << endl;
     }
+    showMatrixT(ylk[1], M+1, M+1, "y1k");
+    showMatrixT(ylk[2], M+1, M+1, "y2k");
+    // EVERYTHING WORKS UPTO HERE
 
-
-
-
-
-
-
+    // Construct A-inverse from A0-inverse and the ylk
+    double** U;
+    double** Ap = new double*[M];
+    for (i = 0; i < M; i++) Ap[i] = new double[M];
+    Ainv = A0inv;
+    for (l = 0; l < M; l++) {
+        k = l+1;
+        U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
+        beta = 1 + ylk[l][p[k]][p[k]];
+        for (i = 0; i < M; i++) {
+            for (j = 0; j < M; j++) {
+                Ap[i][j] = Id[i][j] - U[i][j] / beta;
+            }
+        }
+        Ainv = matMul(Ap, Ainv, M);
+    }
+    showMatrixT(Ainv, M, M, "Ainv");
+    
     // Deallocate all vectors and matrices 
     for (i = 0; i < M; i++) {
         delete [] A[i];
-        delete [] Ainv[i];
         delete [] A0[i];
         delete [] A0inv[i];
         delete [] Ar[i];
         delete [] Id[i];
+        delete [] U[i];
+        delete [] Ap[i];
     }
 
     for (l = 0; l < M; l++) {
@@ -123,3 +185,170 @@ int main() {
 
     return 0;
 }
+
+uint getMaxIndex(double* arr, uint size) { 
+    uint i;     
+    uint max = arr[0]; 
+    uint maxi = 0;
+    for (i = 1; i < size; i++) {
+        if (arr[i] > max) {
+            max = arr[i];
+            maxi = i;
+        }
+    }
+    return maxi; 
+}
+
+void showScalar(uint scalar, string name) {
+    cout << name << " = " << scalar << endl << endl;
+}
+void showScalar(int scalar, string name) {
+    cout << name << " = " << scalar << endl << endl;
+}
+void showScalar(double scalar, string name) {
+    cout << name << " = " << scalar << endl << endl;
+}
+
+void showVector(uint* vector, uint size, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < size; i++) {
+        cout << "[ " << vector[i] << " ]" << endl;
+    }
+    cout << endl;
+}
+void showVector(int* vector, uint size, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < size; i++) {
+        cout << "[ " << vector[i] << " ]" << endl;
+    }
+    cout << endl;
+}
+void showVector(double* vector, uint size, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < size; i++) {
+        cout << "[ " << vector[i] << " ]" << endl;
+    }
+    cout << endl;
+}
+
+void showMatrix(uint** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[i][j] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+void showMatrix(int** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[i][j] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+
+void showMatrix(double** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[i][j] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+void showMatrixT(uint** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[j][i] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+void showMatrixT(int** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[j][i] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+void showMatrixT(double** matrix, uint sizeR, uint sizeC, string name) {
+    cout << name << " = " << endl;
+    for (uint i = 0; i < sizeR; i++) {
+        cout << "[ ";
+        for (uint j = 0; j < sizeC; j++) {
+            cout << matrix[j][i] << " ";
+        }
+        cout << " ]" << endl;
+    }
+    cout << endl;
+}
+
+int** matMul(int** A, int** B, uint size) {
+    int** C = new int*[size];
+    for (uint i = 0; i < size; i++) {
+        C[i] = new int[size];
+    }
+    for (uint i = 0; i < size; i++) {
+        for (uint j = 0; j < size; j++) {
+            for (uint k = 0; k < size; k++) {
+                C[i][j] += A[i][k] * B[k][j];
+            }
+        }
+    }
+    return C;
+}
+double** matMul(double** A, double** B, uint size) {
+    double** C = new double*[size];
+    for (uint i = 0; i < size; i++) {
+        C[i] = new double[size];
+    }
+    for (uint i = 0; i < size; i++) {
+        for (uint j = 0; j < size; j++) {
+            for (uint k = 0; k < size; k++) {
+                C[i][j] += A[i][k] * B[k][j];
+            }
+        }
+    }
+    return C;
+}
+
+int** outProd(int* vec1, int* vec2, uint size) {
+    int** C = new int*[size];
+    for (uint i = 0; i < size; i++) {
+        C[i] = new int[size];
+    }
+    for (uint i = 0; i < size; i++) {
+        for (uint j = 0; j < size; j++) {
+            C[i][j] = vec1[i+1] * vec2[j];
+        }
+    }
+    return C;
+}
+double** outProd(double* vec1, int* vec2, uint size) {
+    double** C = new double*[size];
+    for (uint i = 0; i < size; i++) {
+        C[i] = new double[size];
+    }
+    for (uint i = 0; i < size; i++) {
+        for (uint j = 0; j < size; j++) {
+            C[i][j] = vec1[i+1] * vec2[j];
+        }
+    }
+    return C;
+}
\ No newline at end of file