added diagonal dominance functions, update src

lib/numbers/matrix.js

@@ -779,7 +779,7 @@ matrix.reverseCols = function(M) {
  * @return {Array} matrix
  */
 matrix.zeros = function(n,m) {
-  var M = [];
+  var M = new Array(n);
   if (n < 1 || m < 1) {
     throw new Error('The matrix dimensions must be positive integers.');
   }
@@ -790,7 +790,7 @@ matrix.zeros = function(n,m) {
     for (var j=0; j<m; j++) {
       empty[j] = 0;
     }
-    M.push(empty);
+    M[i] = empty;
   }
   return M;
 };
@@ -1153,4 +1153,140 @@ matrix.isLowerBand = function(M,p) {
     cnt++;
   }
   return result;
+};
+
+/**
+ * Determines if a matrix is (weak) row diagonally-dominant.
+ *
+ * @param {Array} matrix
+ * @return {Boolean} true if so, false otherwise.
+ */
+matrix.isRowDD = function(M) {
+  var n = M.length;
+  if (n !== M[0].length) {
+    throw new Error("The given matrix must be square.");
+  } else if (M[0][0] === undefined) {
+    throw new Error("Input must be a matrix.");
+  }
+
+  for (var i=0; i<n; i++) {
+    var row = M[i],
+        diag = row[i],
+        sum = 0,
+        j;
+
+    for (j=0; j<i; j++) {
+      sum += Math.abs(row[j]);
+    }
+    for (j=i+1; j<n; j++) {
+      sum += Math.abs(row[j]);
+    }
+
+    if (Math.abs(diag) < sum) {
+      return false;
+    }
+  }
+  return true;
+};
+
+/**
+ * Determines if a matrix is strictly row diagonally-dominant.
+ *
+ * @param {Array} matrix
+ * @return {Boolean} true if so, false otherwise.
+ */
+matrix.isStrictlyRowDD = function(M) {
+  var n = M.length;
+  if (n !== M[0].length) {
+    throw new Error("The given matrix must be square.");
+  } else if (M[0][0] === undefined) {
+    throw new Error("Input must be a matrix.");
+  }
+
+  for (var i=0; i<n; i++) {
+    var row = M[i],
+        diag = row[i],
+        sum = 0,
+        j;
+
+    for (j=0; j<i; j++) {
+      sum += Math.abs(row[j]);
+    }
+    for (j=i+1; j<n; j++) {
+      sum += Math.abs(row[j]);
+    }
+
+    if (Math.abs(diag) <= sum) {
+      return false;
+    }
+  }
+  return true;
+};
+
+/**
+ * Determines if a matrix is (weak) column diagonally-dominant.
+ *
+ * @param {Array} matrix
+ * @return {Boolean} true if so, false otherwise.
+ */
+matrix.isColumnDD = function(M) {
+  var n = M.length;
+  if (n !== M[0].length) {
+    throw new Error("The given matrix must be square.");
+  } else if (M[0][0] === undefined) {
+    throw new Error("Input must be a matrix.");
+  }
+
+  for (var i=0; i<n; i++) {
+    var col = matrix.getCol(M,i),
+        diag = col[i],
+        sum = 0,
+        j;
+
+    for (j=0; j<i; j++) {
+      sum += Math.abs(col[j]);
+    }
+    for (j=i+1; j<n; j++) {
+      sum += Math.abs(col[j]);
+    }
+
+    if (Math.abs(diag) < sum) {
+      return false;
+    }
+  }
+  return true;
+};
+
+/**
+ * Determines if a matrix is strictly column diagonally-dominant.
+ *
+ * @param {Array} matrix
+ * @return {Boolean} true if so, false otherwise.
+ */
+matrix.isStrictlyColumnDD = function(M) {
+  var n = M.length;
+  if (n !== M[0].length) {
+    throw new Error("The given matrix must be square.");
+  } else if (M[0][0] === undefined) {
+    throw new Error("Input cannot be a vector.");
+  }
+
+  for (var i=0; i<n; i++) {
+    var col = matrix.getCol(M,i),
+        diag = col[i],
+        sum = 0,
+        j;
+
+    for (j=0; j<i; j++) {
+      sum += Math.abs(col[j]);
+    }
+    for (j=i+1; j<n; j++) {
+      sum += Math.abs(col[j]);
+    }
+
+    if (Math.abs(diag) <= sum) {
+      return false;
+    }
+  }
+  return true;
 };