Allow for eye(m,n) and speye(m,n) with n != m and use it to speed up QR and eigs

Author: lauerfab

lalolab/help/00base.js

@@ -231,15 +231,18 @@ function zeros(rows, cols) {
 	}	
 }
 
-function eye(n) {
-	if ( n == 1)
+function eye(m,n) {
+	if ( typeof(n) == "undefined") 
+		var n = m;
+	if ( m == 1 && n == 1)
 		return 1;
-
-	var I = zeros(n,n);
-	const mn = n*n;
-	for ( var i = 0; i< mn;i += n+1) {
-		I.val[i] = 1;
+		
+	var I = zeros(m,n);
+	const e = (m<n)?m:n;
+	for ( var i = 0; i< e; i ++) {
+		I.val[i*(n+1)] = 1;
 	}
+	
 	return I;
 }
 
@@ -4835,7 +4838,7 @@ function qroriginal( A, compute_Q ) {
 		if ( typeof( compute_Q ) == "number") {
 			// compute only first r columns of Q
 			r = compute_Q; 
-			Q = get( eye(m), [], range(r) );
+			Q = eye(m,r);			
 		}
 		else {
 			Q = eye(m);

lalolab/src/linalg.js

@@ -405,13 +405,18 @@ function sparse( A , rowmajor ) {
  * @param{number}
  * @return{spMatrix}
  */
-function speye(n) {
-	if ( n == 1)
+function speye(m,n) {
+	if ( typeof(n) == "undefined" ) 
+		var n = m;
+	if ( m == 1 && n == 1)
 		return 1;
-	var val = ones(n);
-	var rows = range(n+1);
-	var cols = rows.slice(0,n);
-	return new spMatrix(n,n,val,cols,rows);
+	
+	var e = (m<n)?m:n;
+	
+	var val = ones(e);
+	var rows = range(e+1);
+	var cols = rows.slice(0,e);
+	return new spMatrix(m,n,val,cols,rows);
 }
 /**
  * @param{Float64Array}