- white space cleanup

diff --git a/README b/README
index 419261a3ad4175116cfc34e667706b3e5cd93afc..91aee5153ab317f168e525dbde8b4e0f56a643a4 100644 (file)
--- a/README
+++ b/README
@@ -80,13 +80,13 @@ On other systems, consult `Makefile' to build them (e.g., see
 'Building Windows binaries' in this file) or use the pre-built
 binaries (Windows binaries are in the directory `windows').
 
-This software uses some level-1 BLAS subroutines. The needed functions are 
+This software uses some level-1 BLAS subroutines. The needed functions are
 included in this package.  If a BLAS library is available on your
 machine, you may use it by modifying the Makefile: Unmark the following line
 
         #LIBS ?= -lblas
 
-and mark 
+and mark
 
         LIBS ?= blas/blas.a
 
@@ -107,8 +107,8 @@ options:
 -e epsilon : set tolerance of termination criterion
         -s 0 and 2
                 |f'(w)|_2 <= eps*min(pos,neg)/l*|f'(w0)|_2,
-               where f is the primal function and pos/neg are # of
-               positive/negative data (default 0.01)
+                where f is the primal function and pos/neg are # of
+                positive/negative data (default 0.01)
         -s 1, 3, and 4
                 Dual maximal violation <= eps; similar to libsvm (default 0.1)
         -s 5 and 6
@@ -130,7 +130,7 @@ min_w w^Tw/2 + C \sum log(1 + exp(-y_i w^Tx_i))
 
 For L2-regularized L2-loss SVC dual (-s 1), we solve
 
-min_alpha  0.5(alpha^T (Q + I/2/C) alpha) - e^T alpha 
+min_alpha  0.5(alpha^T (Q + I/2/C) alpha) - e^T alpha
     s.t.   0 <= alpha_i,
 
 For L2-regularized L2-loss SVC (-s 2), we solve
@@ -139,7 +139,7 @@ min_w w^Tw/2 + C \sum max(0, 1- y_i w^Tx_i)^2
 
 For L2-regularized L1-loss SVC dual (-s 3), we solve
 
-min_alpha  0.5(alpha^T Q alpha) - e^T alpha 
+min_alpha  0.5(alpha^T Q alpha) - e^T alpha
     s.t.   0 <= alpha_i <= C,
 
 For L1-regularized L2-loss SVC (-s 5), we solve
@@ -154,7 +154,7 @@ where
 
 Q is a matrix with Q_ij = y_i y_j x_i^T x_j.
 
-If bias >= 0, w becomes [w; w_{n+1}] and x becomes [x; bias].  
+If bias >= 0, w becomes [w; w_{n+1}] and x becomes [x; bias].
 
 The primal-dual relationship implies that -s 1 and -s 2 gives the same
 model.
@@ -216,8 +216,8 @@ class 4         class 1,2,3.    10      10
 
 > train -c 10 -w3 1 -w2 5 two_class_data_file
 
-If there are only two classes, we train ONE model. 
-The C values for the two classes are 10 and 50. 
+If there are only two classes, we train ONE model.
+The C values for the two classes are 10 and 50.
 
 > predict -b 1 test_file data_file.model output_file
 
@@ -290,15 +290,15 @@ Library Usage
     solver_type can be one of L2R_LR, L2R_L2LOSS_SVC_DUAL, L2R_L2LOSS_SVC, L2R_L1LOSS_SVC_DUAL, MCSVM_CS, L1R_L2LOSS_SVC, L1R_LR.
 
     L2R_LR                L2-regularized logistic regression
-    L2R_L2LOSS_SVC_DUAL   L2-regularized L2-loss support vector classification (dual) 
+    L2R_L2LOSS_SVC_DUAL   L2-regularized L2-loss support vector classification (dual)
     L2R_L2LOSS_SVC        L2-regularized L2-loss support vector classification (primal)
-    L2R_L1LOSS_SVC_DUAL   L2-regularized L1-loss support vector classification (dual)  
-    MCSVM_CS multi-class support vector classification by Crammer and Singer        
+    L2R_L1LOSS_SVC_DUAL   L2-regularized L1-loss support vector classification (dual)
+    MCSVM_CS              multi-class support vector classification by Crammer and Singer
     L1R_L2LOSS_SVC        L1-regularized L2-loss support vector classification
     L1R_LR                L1-regularized logistic regression
 
-    C is the cost of constraints violation. 
-    eps is the stopping criterion. 
+    C is the cost of constraints violation.
+    eps is the stopping criterion.
 
     nr_weight, weight_label, and weight are used to change the penalty
     for some classes (If the weight for a class is not changed, it is
@@ -337,8 +337,8 @@ Library Usage
      organized in the following way
 
      +------------------+------------------+------------+
-     | nr_class weights | nr_class weights |  ...   
-     | for 1st feature  | for 2nd feature  |      
+     | nr_class weights | nr_class weights |  ...
+     | for 1st feature  | for 2nd feature  |
      +------------------+------------------+------------+
 
      If bias >= 0, x becomes [x; bias]. The number of features is
@@ -367,7 +367,7 @@ Library Usage
 
     This function gives nr_w decision values in the array
     dec_values. nr_w is 1 if there are two classes except multi-class
-    svm by Crammer and Singer (-s 4), and is the number of classes otherwise. 
+    svm by Crammer and Singer (-s 4), and is the number of classes otherwise.
 
     We implement one-vs-the rest multi-class strategy (-s 0,1,2,3) and
     multi-class svm by Crammer and Singer (-s 4) for multi-class SVM.