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65<h1>lapack.h</h1><a href="lapack_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001
66<a name="l00029"></a>00029 <span class="preprocessor">#ifndef LAPACK_H</span>
67<a name="l00030"></a>00030 <span class="preprocessor"></span><span class="preprocessor">#define LAPACK_H</span>
68<a name="l00031"></a>00031 <span class="preprocessor"></span>
69<a name="l00032"></a>00032 <span class="preprocessor">#ifndef _MSC_VER</span>
70<a name="l00033"></a>00033 <span class="preprocessor"></span><span class="preprocessor">#  include &lt;itpp/config.h&gt;</span>
71<a name="l00034"></a>00034 <span class="preprocessor">#else</span>
72<a name="l00035"></a>00035 <span class="preprocessor"></span><span class="preprocessor">#  include &lt;itpp/config_msvc.h&gt;</span>
73<a name="l00036"></a>00036 <span class="preprocessor">#endif</span>
74<a name="l00037"></a>00037 <span class="preprocessor"></span>
75<a name="l00038"></a>00038 <span class="preprocessor">#include &lt;complex&gt;</span>
76<a name="l00039"></a>00039
77<a name="l00040"></a>00040 <span class="keyword">extern</span> <span class="stringliteral">"C"</span>
78<a name="l00041"></a>00041 {
79<a name="l00042"></a>00042
80<a name="l00043"></a>00043 <span class="comment">// Fix for MKL Windows version so that naming is consistent with the 5.x and</span>
81<a name="l00044"></a>00044 <span class="comment">// 7.x MKL LAPACK libraries</span>
82<a name="l00045"></a>00045 <span class="preprocessor">#ifdef HAVE_MKL // Note: HAVE_MKL is hard-defined in &lt;itpp/config_msvc.h&gt;</span>
83<a name="l00046"></a>00046 <span class="preprocessor"></span>
84<a name="l00047"></a>00047 <span class="preprocessor">#define dgetrf_ dgetrf</span>
85<a name="l00048"></a>00048 <span class="preprocessor"></span><span class="preprocessor">#define zgetrf_ zgetrf</span>
86<a name="l00049"></a>00049 <span class="preprocessor"></span>
87<a name="l00050"></a>00050 <span class="preprocessor">#define dgetri_ dgetri</span>
88<a name="l00051"></a>00051 <span class="preprocessor"></span><span class="preprocessor">#define zgetri_ zgetri</span>
89<a name="l00052"></a>00052 <span class="preprocessor"></span>
90<a name="l00053"></a>00053 <span class="preprocessor">#define dgesvd_ dgesvd</span>
91<a name="l00054"></a>00054 <span class="preprocessor"></span><span class="preprocessor">#define zgesvd_ zgesvd</span>
92<a name="l00055"></a>00055 <span class="preprocessor"></span>
93<a name="l00056"></a>00056 <span class="preprocessor">#define dsyev_ dsyev</span>
94<a name="l00057"></a>00057 <span class="preprocessor"></span><span class="preprocessor">#define zheev_ zheev</span>
95<a name="l00058"></a>00058 <span class="preprocessor"></span>
96<a name="l00059"></a>00059 <span class="preprocessor">#define dgeev_ dgeev</span>
97<a name="l00060"></a>00060 <span class="preprocessor"></span><span class="preprocessor">#define zgeev_ zgeev</span>
98<a name="l00061"></a>00061 <span class="preprocessor"></span>
99<a name="l00062"></a>00062 <span class="preprocessor">#define dpotrf_ dpotrf</span>
100<a name="l00063"></a>00063 <span class="preprocessor"></span><span class="preprocessor">#define zpotrf_ zpotrf</span>
101<a name="l00064"></a>00064 <span class="preprocessor"></span>
102<a name="l00065"></a>00065 <span class="preprocessor">#define dgeqrf_ dgeqrf</span>
103<a name="l00066"></a>00066 <span class="preprocessor"></span><span class="preprocessor">#define zgeqrf_ zgeqrf</span>
104<a name="l00067"></a>00067 <span class="preprocessor"></span>
105<a name="l00068"></a>00068 <span class="preprocessor">#define dgeqp3_ dgeqp3</span>
106<a name="l00069"></a>00069 <span class="preprocessor"></span><span class="preprocessor">#define zgeqp3_ zgeqp3</span>
107<a name="l00070"></a>00070 <span class="preprocessor"></span>
108<a name="l00071"></a>00071 <span class="preprocessor">#define dorgqr_ dorgqr</span>
109<a name="l00072"></a>00072 <span class="preprocessor"></span><span class="preprocessor">#define zungqr_ zungqr</span>
110<a name="l00073"></a>00073 <span class="preprocessor"></span>
111<a name="l00074"></a>00074 <span class="preprocessor">#define dormqr_ dormqr</span>
112<a name="l00075"></a>00075 <span class="preprocessor"></span><span class="preprocessor">#define zunmqr_ zunmqr</span>
113<a name="l00076"></a>00076 <span class="preprocessor"></span>
114<a name="l00077"></a>00077 <span class="preprocessor">#define dgesv_ dgesv</span>
115<a name="l00078"></a>00078 <span class="preprocessor"></span><span class="preprocessor">#define zgesv_ zgesv</span>
116<a name="l00079"></a>00079 <span class="preprocessor"></span>
117<a name="l00080"></a>00080 <span class="preprocessor">#define dposv_ dposv</span>
118<a name="l00081"></a>00081 <span class="preprocessor"></span><span class="preprocessor">#define zposv_ zposv</span>
119<a name="l00082"></a>00082 <span class="preprocessor"></span>
120<a name="l00083"></a>00083 <span class="preprocessor">#define dtrtrs_ dtrtrs</span>
121<a name="l00084"></a>00084 <span class="preprocessor"></span><span class="preprocessor">#define ztrtrs_ ztrtrs</span>
122<a name="l00085"></a>00085 <span class="preprocessor"></span>
123<a name="l00086"></a>00086 <span class="preprocessor">#define dgels_ dgels</span>
124<a name="l00087"></a>00087 <span class="preprocessor"></span><span class="preprocessor">#define zgels_ zgels</span>
125<a name="l00088"></a>00088 <span class="preprocessor"></span>
126<a name="l00089"></a>00089 <span class="preprocessor">#define dgees_ dgees</span>
127<a name="l00090"></a>00090 <span class="preprocessor"></span><span class="preprocessor">#define zgees_ zgees</span>
128<a name="l00091"></a>00091 <span class="preprocessor"></span>
129<a name="l00092"></a>00092 <span class="preprocessor">#endif // #ifdef HAVE_MKL</span>
130<a name="l00093"></a>00093 <span class="preprocessor"></span>
131<a name="l00094"></a>00094   <span class="comment">// Exists in ATLAS</span>
132<a name="l00095"></a>00095   <span class="comment">/* LU factorization</span>
133<a name="l00096"></a>00096 <span class="comment">   * a is of size m*n and with lda rows.</span>
134<a name="l00097"></a>00097 <span class="comment">   * ipiv is the permutation vector of rows. Row i should be replaced by row</span>
135<a name="l00098"></a>00098 <span class="comment">   * ipiv(i).</span>
136<a name="l00099"></a>00099 <span class="comment">   * info=0 if OK. info=-i if ith value is illegal. info=i factorization OK</span>
137<a name="l00100"></a>00100 <span class="comment">   * but the system is singular if solved.</span>
138<a name="l00101"></a>00101 <span class="comment">   */</span>
139<a name="l00102"></a>00102   <span class="keywordtype">void</span> dgetrf_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv, <span class="keywordtype">int</span> *info);
140<a name="l00103"></a>00103   <span class="keywordtype">void</span> zgetrf_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv,
141<a name="l00104"></a>00104                <span class="keywordtype">int</span> *info);
142<a name="l00105"></a>00105
143<a name="l00106"></a>00106   <span class="comment">// In ATLAS</span>
144<a name="l00107"></a>00107   <span class="comment">/* Inverting a matrix of an LU-factored general matrix (first call xGETRF)</span>
145<a name="l00108"></a>00108 <span class="comment">   * a is of square size n*n with lda rows containing the factorization as</span>
146<a name="l00109"></a>00109 <span class="comment">   * returned by xGETRF</span>
147<a name="l00110"></a>00110 <span class="comment">   * ipiv is vector as returned by xGETRF</span>
148<a name="l00111"></a>00111 <span class="comment">   * lwork &gt;= n</span>
149<a name="l00112"></a>00112 <span class="comment">   * output: a is overwritten by the inverse</span>
150<a name="l00113"></a>00113 <span class="comment">   * info=0 if OK. info=-i if ith parameter is illegal. info=i the ith</span>
151<a name="l00114"></a>00114 <span class="comment">   * diagonal element = 0 and U is singular.</span>
152<a name="l00115"></a>00115 <span class="comment">   */</span>
153<a name="l00116"></a>00116   <span class="keywordtype">void</span> dgetri_(<span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv, <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork,
154<a name="l00117"></a>00117                <span class="keywordtype">int</span> *info);
155<a name="l00118"></a>00118   <span class="keywordtype">void</span> zgetri_(<span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv,
156<a name="l00119"></a>00119                std::complex&lt;double&gt; *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
157<a name="l00120"></a>00120
158<a name="l00121"></a>00121   <span class="comment">/* SVD of a general rectangular matrix A = U S V^H</span>
159<a name="l00122"></a>00122 <span class="comment">     a is of size m*n and with lda rows.</span>
160<a name="l00123"></a>00123 <span class="comment">     Output: s with sorted singular values (vector)</span>
161<a name="l00124"></a>00124 <span class="comment">     u, and vt (for U and V^H). U is m*m, and V^H is n*n</span>
162<a name="l00125"></a>00125 <span class="comment">     jobu='A','S','O','N'. Different versions. 'A' = all columns of U</span>
163<a name="l00126"></a>00126 <span class="comment">     calculated and returned in u.</span>
164<a name="l00127"></a>00127 <span class="comment">     jobvt='A','S','O','N'. Different versions. 'A' = all columns of V^H</span>
165<a name="l00128"></a>00128 <span class="comment">     calculated and returned in vt.</span>
166<a name="l00129"></a>00129 <span class="comment">     ldu = no rows in U</span>
167<a name="l00130"></a>00130 <span class="comment">     ldvt = no rows in V^H</span>
168<a name="l00131"></a>00131 <span class="comment">     info = 0 successful, = -i ith parameter is illegal, = i did not converge</span>
169<a name="l00132"></a>00132 <span class="comment"></span>
170<a name="l00133"></a>00133 <span class="comment">     work is a workspace vector of size lwork.</span>
171<a name="l00134"></a>00134 <span class="comment">     lwork &gt;= max(3*min(m,n)+max(m,n), 5*min(m,n)) for double</span>
172<a name="l00135"></a>00135 <span class="comment">     lwork &gt;= 2*min(m,n)+max(m,n) for std::complex&lt;double&gt;</span>
173<a name="l00136"></a>00136 <span class="comment">     Good performance. Make lwork larger!</span>
174<a name="l00137"></a>00137 <span class="comment">     rwork is a workspace array for complex version. Size max(1, 5*min(m,n)).</span>
175<a name="l00138"></a>00138 <span class="comment">   */</span>
176<a name="l00139"></a>00139   <span class="keywordtype">void</span> dgesvd_(<span class="keywordtype">char</span> *jobu, <span class="keywordtype">char</span> *jobvt, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda,
177<a name="l00140"></a>00140                <span class="keywordtype">double</span> *s, <span class="keywordtype">double</span> *u, <span class="keywordtype">int</span> *ldu, <span class="keywordtype">double</span> *vt, <span class="keywordtype">int</span> *ldvt,
178<a name="l00141"></a>00141                <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
179<a name="l00142"></a>00142   <span class="keywordtype">void</span> zgesvd_(<span class="keywordtype">char</span> *jobu, <span class="keywordtype">char</span> *jobvt, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a,
180<a name="l00143"></a>00143                <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *s, std::complex&lt;double&gt; *u, <span class="keywordtype">int</span> *ldu,
181<a name="l00144"></a>00144                std::complex&lt;double&gt; *vt, <span class="keywordtype">int</span> *ldvt, std::complex&lt;double&gt; *work,
182<a name="l00145"></a>00145                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">double</span> *rwork, <span class="keywordtype">int</span> *info);
183<a name="l00146"></a>00146
184<a name="l00147"></a>00147   <span class="comment">/* Eigenvalues and eigenvectors of a symmetric/hermitian matrix A */</span>
185<a name="l00148"></a>00148   <span class="keywordtype">void</span> dsyev_(<span class="keywordtype">char</span> *jobz, <span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *w,
186<a name="l00149"></a>00149               <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
187<a name="l00150"></a>00150   <span class="keywordtype">void</span> zheev_(<span class="keywordtype">char</span> *jobz, <span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda,
188<a name="l00151"></a>00151               <span class="keywordtype">double</span> *w, std::complex&lt;double&gt; *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">double</span> *rwork,
189<a name="l00152"></a>00152               <span class="keywordtype">int</span> *info);
190<a name="l00153"></a>00153
191<a name="l00154"></a>00154   <span class="comment">/* Eigenvalues and eigenvectors of a general matrix A */</span>
192<a name="l00155"></a>00155   <span class="keywordtype">void</span> dgeev_(<span class="keywordtype">char</span> *jobvl, <span class="keywordtype">char</span> *jobvr, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *wr,
193<a name="l00156"></a>00156               <span class="keywordtype">double</span> *wi, <span class="keywordtype">double</span> *vl, <span class="keywordtype">int</span> *ldvl, <span class="keywordtype">double</span> *vr, <span class="keywordtype">int</span> *ldvr,
194<a name="l00157"></a>00157               <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
195<a name="l00158"></a>00158   <span class="keywordtype">void</span> zgeev_(<span class="keywordtype">char</span> *jobvl, <span class="keywordtype">char</span> *jobvr, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a,
196<a name="l00159"></a>00159               <span class="keywordtype">int</span> *lda, std::complex&lt;double&gt; *w, std::complex&lt;double&gt; *vl,
197<a name="l00160"></a>00160               <span class="keywordtype">int</span> *ldvl, std::complex&lt;double&gt; *vr, <span class="keywordtype">int</span> *ldvr,
198<a name="l00161"></a>00161               std::complex&lt;double&gt; *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">double</span> *rwork, <span class="keywordtype">int</span> *info);
199<a name="l00162"></a>00162
200<a name="l00163"></a>00163   <span class="comment">// In ATLAS</span>
201<a name="l00164"></a>00164   <span class="comment">/* Cholesky factorization */</span>
202<a name="l00165"></a>00165   <span class="keywordtype">void</span> dpotrf_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *info);
203<a name="l00166"></a>00166   <span class="keywordtype">void</span> zpotrf_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda,
204<a name="l00167"></a>00167                <span class="keywordtype">int</span> *info);
205<a name="l00168"></a>00168
206<a name="l00169"></a>00169   <span class="comment">/* QR factorization of a general matrix A  */</span>
207<a name="l00170"></a>00170   <span class="keywordtype">void</span> dgeqrf_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *tau, <span class="keywordtype">double</span> *work,
208<a name="l00171"></a>00171                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
209<a name="l00172"></a>00172   <span class="keywordtype">void</span> zgeqrf_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda,
210<a name="l00173"></a>00173                std::complex&lt;double&gt; *tau, std::complex&lt;double&gt; *work,
211<a name="l00174"></a>00174                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
212<a name="l00175"></a>00175
213<a name="l00176"></a>00176   <span class="comment">/* QR factorization of a general matrix A with pivoting */</span>
214<a name="l00177"></a>00177   <span class="keywordtype">void</span> dgeqp3_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *jpvt, <span class="keywordtype">double</span> *tau,
215<a name="l00178"></a>00178                <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
216<a name="l00179"></a>00179   <span class="keywordtype">void</span> zgeqp3_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *jpvt,
217<a name="l00180"></a>00180                std::complex&lt;double&gt; *tau, std::complex&lt;double&gt; *work,
218<a name="l00181"></a>00181                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">double</span> *rwork, <span class="keywordtype">int</span> *info);
219<a name="l00182"></a>00182
220<a name="l00183"></a>00183   <span class="comment">/* Calculation of Q matrix from QR-factorization */</span>
221<a name="l00184"></a>00184   <span class="keywordtype">void</span> dorgqr_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *k, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *tau,
222<a name="l00185"></a>00185                <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
223<a name="l00186"></a>00186   <span class="keywordtype">void</span> zungqr_(<span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *k, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda,
224<a name="l00187"></a>00187                std::complex&lt;double&gt; *tau, std::complex&lt;double&gt; *work,
225<a name="l00188"></a>00188                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
226<a name="l00189"></a>00189
227<a name="l00190"></a>00190   <span class="comment">/*</span>
228<a name="l00191"></a>00191 <span class="comment">   * Multiplies a real matrix by the orthogonal matix Q of the QR</span>
229<a name="l00192"></a>00192 <span class="comment">   * factorization formed by dgeqp3_()</span>
230<a name="l00193"></a>00193 <span class="comment">   */</span>
231<a name="l00194"></a>00194   <span class="keywordtype">void</span> dormqr_(<span class="keywordtype">char</span> *side, <span class="keywordtype">char</span> *trans, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *k, <span class="keywordtype">double</span> *a,
232<a name="l00195"></a>00195                <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *tau, <span class="keywordtype">double</span> *c, <span class="keywordtype">int</span> *ldc, <span class="keywordtype">double</span> *work,
233<a name="l00196"></a>00196                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
234<a name="l00197"></a>00197   <span class="comment">/*</span>
235<a name="l00198"></a>00198 <span class="comment">   * Multiplies a complex matrix by the unitary matix Q of the QR</span>
236<a name="l00199"></a>00199 <span class="comment">   * factorization formed by zgeqp3_()</span>
237<a name="l00200"></a>00200 <span class="comment">   */</span>
238<a name="l00201"></a>00201   <span class="keywordtype">void</span> zunmqr_(<span class="keywordtype">char</span> *side, <span class="keywordtype">char</span> *trans, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *k,
239<a name="l00202"></a>00202                std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, std::complex&lt;double&gt; *tau,
240<a name="l00203"></a>00203                std::complex&lt;double&gt; *c, <span class="keywordtype">int</span> *ldc, std::complex&lt;double&gt; *work,
241<a name="l00204"></a>00204                <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
242<a name="l00205"></a>00205
243<a name="l00206"></a>00206   <span class="comment">// In ATLAS</span>
244<a name="l00207"></a>00207   <span class="comment">/*</span>
245<a name="l00208"></a>00208 <span class="comment">   * Solves a system on linear equations, Ax=b, with a square matrix A,</span>
246<a name="l00209"></a>00209 <span class="comment">   * Using LU-factorization</span>
247<a name="l00210"></a>00210 <span class="comment">   */</span>
248<a name="l00211"></a>00211   <span class="keywordtype">void</span> dgesv_(<span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv, <span class="keywordtype">double</span> *b,
249<a name="l00212"></a>00212               <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
250<a name="l00213"></a>00213   <span class="keywordtype">void</span> zgesv_(<span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *ipiv,
251<a name="l00214"></a>00214               std::complex&lt;double&gt; *b, <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
252<a name="l00215"></a>00215
253<a name="l00216"></a>00216   <span class="comment">// In ATLAS</span>
254<a name="l00217"></a>00217   <span class="comment">/*</span>
255<a name="l00218"></a>00218 <span class="comment">   * Solves a system on linear equations, Ax=b, with a square</span>
256<a name="l00219"></a>00219 <span class="comment">   * symmetric/hermitian positive definite matrix A, using</span>
257<a name="l00220"></a>00220 <span class="comment">   * Cholesky-factorization</span>
258<a name="l00221"></a>00221 <span class="comment">   */</span>
259<a name="l00222"></a>00222   <span class="keywordtype">void</span> dposv_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *b,
260<a name="l00223"></a>00223               <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
261<a name="l00224"></a>00224   <span class="keywordtype">void</span> zposv_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda,
262<a name="l00225"></a>00225               std::complex&lt;double&gt; *b, <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
263<a name="l00226"></a>00226
264<a name="l00227"></a>00227   <span class="comment">/*</span>
265<a name="l00228"></a>00228 <span class="comment">   * Solves a system of linear equations with a triangular matrix with</span>
266<a name="l00229"></a>00229 <span class="comment">   * multiple right-hand sides</span>
267<a name="l00230"></a>00230 <span class="comment">   */</span>
268<a name="l00231"></a>00231   <span class="keywordtype">void</span> dtrtrs_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">char</span> *trans, <span class="keywordtype">char</span> *<a class="code" href="group__diag.html#gb0938c932c1cbc19b2ce6c5ac1007553" title="Get the diagonal elements of the input matrix m.">diag</a>, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs,
269<a name="l00232"></a>00232                <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">double</span> *b, <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
270<a name="l00233"></a>00233   <span class="keywordtype">void</span> ztrtrs_(<span class="keywordtype">char</span> *uplo, <span class="keywordtype">char</span> *trans, <span class="keywordtype">char</span> *<a class="code" href="group__diag.html#gb0938c932c1cbc19b2ce6c5ac1007553" title="Get the diagonal elements of the input matrix m.">diag</a>, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs,
271<a name="l00234"></a>00234                std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, std::complex&lt;double&gt; *b,
272<a name="l00235"></a>00235                <span class="keywordtype">int</span> *ldb, <span class="keywordtype">int</span> *info);
273<a name="l00236"></a>00236
274<a name="l00237"></a>00237   <span class="comment">/*</span>
275<a name="l00238"></a>00238 <span class="comment">   * Solves a linear over/underdetermined system using QR or LQ</span>
276<a name="l00239"></a>00239 <span class="comment">   * factorization. Assumes a full rank matrix</span>
277<a name="l00240"></a>00240 <span class="comment">   */</span>
278<a name="l00241"></a>00241   <span class="keywordtype">void</span> dgels_(<span class="keywordtype">char</span> *trans, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, <span class="keywordtype">double</span> *a, <span class="keywordtype">int</span> *lda,
279<a name="l00242"></a>00242               <span class="keywordtype">double</span> *b, <span class="keywordtype">int</span> *ldb, <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
280<a name="l00243"></a>00243   <span class="keywordtype">void</span> zgels_(<span class="keywordtype">char</span> *trans, <span class="keywordtype">int</span> *m, <span class="keywordtype">int</span> *n, <span class="keywordtype">int</span> *nrhs, std::complex&lt;double&gt; *a,
281<a name="l00244"></a>00244               <span class="keywordtype">int</span> *lda, std::complex&lt;double&gt; *b, <span class="keywordtype">int</span> *ldb,
282<a name="l00245"></a>00245               std::complex&lt;double&gt; *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *info);
283<a name="l00246"></a>00246
284<a name="l00247"></a>00247   <span class="comment">/*</span>
285<a name="l00248"></a>00248 <span class="comment">   * Compute for an N-by-N real nonsymmetric matrix A, the eigenvalues,</span>
286<a name="l00249"></a>00249 <span class="comment">   * the real Schur form T, and, optionally, the matrix of Schur vectors Z</span>
287<a name="l00250"></a>00250 <span class="comment">   */</span>
288<a name="l00251"></a>00251   <span class="keywordtype">void</span> dgees_(<span class="keywordtype">char</span> *jobvs, <span class="keywordtype">char</span> *<a class="code" href="classitpp_1_1Vec.html#6d62d1911501ca2b7884c7506eb17125" title="Sort the data vector in increasing order.">sort</a>, <span class="keywordtype">int</span>* select, <span class="keywordtype">int</span> *n, <span class="keywordtype">double</span> *a,
289<a name="l00252"></a>00252               <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *sdim, <span class="keywordtype">double</span> *wr, <span class="keywordtype">double</span> *wi, <span class="keywordtype">double</span> *vs,
290<a name="l00253"></a>00253               <span class="keywordtype">int</span> *ldvs, <span class="keywordtype">double</span> *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">int</span> *bwork, <span class="keywordtype">int</span> *info);
291<a name="l00254"></a>00254
292<a name="l00255"></a>00255   <span class="comment">/*</span>
293<a name="l00256"></a>00256 <span class="comment">   * Compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues,</span>
294<a name="l00257"></a>00257 <span class="comment">   * the Schur form T, and, optionally, the matrix of Schur vectors Z</span>
295<a name="l00258"></a>00258 <span class="comment">   */</span>
296<a name="l00259"></a>00259   <span class="keywordtype">void</span> zgees_(<span class="keywordtype">char</span> *jobvs, <span class="keywordtype">char</span> *<a class="code" href="classitpp_1_1Vec.html#6d62d1911501ca2b7884c7506eb17125" title="Sort the data vector in increasing order.">sort</a>, <span class="keywordtype">int</span>* select, <span class="keywordtype">int</span> *n,
297<a name="l00260"></a>00260               std::complex&lt;double&gt; *a, <span class="keywordtype">int</span> *lda, <span class="keywordtype">int</span> *sdim,
298<a name="l00261"></a>00261               std::complex&lt;double&gt; *w, std::complex&lt;double&gt; *vs, <span class="keywordtype">int</span> *ldvs,
299<a name="l00262"></a>00262               std::complex&lt;double&gt; *work, <span class="keywordtype">int</span> *lwork, <span class="keywordtype">double</span> *rwork,
300<a name="l00263"></a>00263               <span class="keywordtype">int</span> *bwork, <span class="keywordtype">int</span> *info);
301<a name="l00264"></a>00264
302<a name="l00265"></a>00265 } <span class="comment">// extern C</span>
303<a name="l00266"></a>00266
304<a name="l00267"></a>00267 <span class="preprocessor">#endif // #ifndef LAPACK_H</span>
305</pre></div></div>
306<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:11 2009 for mixpp by&nbsp;
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308<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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