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#include <string> #include <fstream> #include <sstream> string read_file_into_string() { ifstream ifile( "alice_emma" ); ostringstream buf; char ch; while ( buf && ifileget( ch )) bufput( ch ); return bufstr(); }

The str() member function returns the string object associated with the ostringstream class object This string can now be manipulated the same way as any "ordinary" string object For example, in the following program, text is memberwise initialized with the string object associated with buf:

The second indicator matrix Y2 has been used in SVM, and the resulting model using Y2 is also not equivalent to LDA in general This is also the case for the indicator matrix in reference 39 One natural question is whether there exists a class indicator matrix Y IRn k , with which multivariate linear regression is equivalent to LDA If this is the case, then LDA can be formulated as a least squares problem in the multiclass case, and the generalizations of least squares can be readily applied to LDA In MLR, each xi is transformed to (f1 ( i ), , fk ( i ))T = W T xi , x x and the centered data matrix X IRd n is transformed to W T X IRk n , thus achieving dimensionality reduction if k < d.

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int main() { string text = read_file_into_string(); // marks the position of each newline within text vector< string::size_type > lines_of_text; string::size_type pos = 0; while ( pos != string::npos ) { pos = textfind( '\n', pos ); lines_of_textpush_back( pos ); } // }

10.1.2 EAP over LAN (EAPOL)

An ostringstream object can also be used to support the automatic formatting of a compound string; that is, a string consisting of multiple data types For example, the output operator converts automatically any arithmetic type into a corresponding string representation without our needing to worry about the amount of storage necessary:

Note that the transformation matrix W in MLR is dependent on the centered class indicator matrix Y as in Eq (122) To derive a class indicator matrix for MLR with which the transformation matrix is related to that of LDA, it is natural to apply the class discrimination criterion used in LDA We thus.

#include <iostream> #include <sstream> int main() { int ival = 1024; int *pival = &ival; double dval = 314159; double *pdval = &dval; ostringstream format_message; // ok: converts values to a string representation

file:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (998 / 1065) [2001-3-29 11:32:15]

look for Y , which solves the following optimization problem: maxY subject to trace (W T Sb W)(W T St W)+ + W = XXT XY , (1.23)

format_message "ival: " ival " ival's address: " pival '\n' "dval: " dval " dval's address: " pdval endl; string msg = format_messagestr(); cout " size of message string: " msgsize() " message: " msg endl; }

In some circumstances it is preferable to collect the set of nonfatal diagnostic errors and warnings rather than to display them as they are encountered A simple way of accomplishing this is to provide an overloaded set of format functions of the general form

string format( string msg, int expected, int received ) { ostringstream message; message msg " expected: " expected " received: " received "\n"; return messagestr(); } string format( string msg, vector<int> *values ); // and so on

where the pseudo-inverse is used as the matrix XXT can be singular. In reference 40, a new class indicator matrix, called Y3 , is constructed and it was shown that Y3 solves the optimization problem in Eq. (1.23). This new class indicator matrix Y3 = (Y3 (ij))ij IRn k is de ned as follows: n nj n if yi = j, n j Y3 (ij) = (1.24) nj otherwise, n where nj is the sample size of the jth class, and n is the total sample size. Note that Y3 de ned above has been centered (in terms of rows), and thus Y3 = Y3 . More importantly, it was shown in reference 40 that, under condition C1 in Eq. (1.15), multivariate linear regression with Y3 as the class indicator matrix is equivalent to LDA. We outline the main result below and the detailed proof can be found in reference 40. Recall that in LDA, the optimal transformation matrix (GLDA ) consists of the top eigenvectors of St+ Sb corresponding to the nonzero eigenvalues. On the other hand, since XXT = nSt and XY3 = nHb , where St and Hb are de ned in Eqs. (1.3) and (1.5), respectively, the optimal weight matrix W MLR for MLR in Eq. (1.22) can be expressed as W MLR = XXT

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