1 /*
  2  *   Copyright (c) 2011, Michael Lehn
  3  *
  4  *   All rights reserved.
  5  *
  6  *   Redistribution and use in source and binary forms, with or without
  7  *   modification, are permitted provided that the following conditions
  8  *   are met:
  9  *
 10  *   1) Redistributions of source code must retain the above copyright
 11  *      notice, this list of conditions and the following disclaimer.
 12  *   2) Redistributions in binary form must reproduce the above copyright
 13  *      notice, this list of conditions and the following disclaimer in
 14  *      the documentation and/or other materials provided with the
 15  *      distribution.
 16  *   3) Neither the name of the FLENS development group nor the names of
 17  *      its contributors may be used to endorse or promote products derived
 18  *      from this software without specific prior written permission.
 19  *
 20  *   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 21  *   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 22  *   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 23  *   A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 24  *   OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 25  *   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 26  *   LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 27  *   DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 28  *   THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 29  *   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 30  *   OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 31  */
 32 
 33 /* Based on
 34  *
 35        SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
 36  *
 37  *  -- LAPACK auxiliary routine (version 3.2) --
 38  *     Univ. of Tennessee, Univ. of California Berkeley,
 39  *     Univ. of Colorado Denver and NAG Ltd..
 40  *     November 2006
 41  */
 42 
 43 #ifndef FLENS_LAPACK_EIG_LAQR1_TCC
 44 #define FLENS_LAPACK_EIG_LAQR1_TCC 1
 45 
 46 #include <flens/blas/blas.h>
 47 #include <flens/lapack/lapack.h>
 48 
 49 namespace flens { namespace lapack {
 50 
 51 //== generic lapack implementation =============================================
 52 
 53 template <typename MH, typename T, typename VV>
 54 void
 55 laqr1_generic(GeMatrix<MH>              &H,
 56               const T                   &sr1,
 57               const T                   &si1,
 58               const T                   &sr2,
 59               const T                   &si2,
 60               DenseVector<VV>           &v)
 61 {
 62     using std::abs;
 63 
 64     typedef typename GeMatrix<MH>::IndexType    IndexType;
 65 
 66     const IndexType n   = H.numRows();
 67     const T         Zero(0);
 68 
 69     if (n==2) {
 70         const T s = abs(H(1,1)-sr2) + abs(si2) + abs(H(2,1));
 71         if (s==Zero) {
 72             v(1) = Zero;
 73             v(2) = Zero;
 74         } else {
 75             const T H21s = H(2,1)/s;
 76             v(1) = H21s*H(1,2) + (H(1,1)-sr1)*((H(1,1)-sr2)/s) - si1*(si2/s);
 77             v(2) = H21s*(H(1,1) + H(2,2)-sr1-sr2);
 78         }
 79     } else {
 80         const T s = abs(H(1,1)-sr2) + abs(si2) + abs(H(2,1)) + abs(H(3,1));
 81         if (s==Zero) {
 82             v(1) = Zero;
 83             v(2) = Zero;
 84             v(3) = Zero;
 85         } else {
 86             const T H21s = H(2,1) / s;
 87             const T H31s = H(3,1) / s;
 88             v(1) = (H(1,1)-sr1)*((H(1,1)-sr2)/s) - si1*(si2/s)
 89                     + H(1,2)*H21s + H(1,3)*H31s;
 90             v(2) = H21s*(H(1,1) + H(2,2)-sr1-sr2) + H(2,3 )*H31s;
 91             v(3) = H31s*(H(1,1) + H(3,3)-sr1-sr2) + H21s*H(3,2);
 92         }
 93     }
 94 }
 95 
 96 //== interface for native lapack ===============================================
 97 
 98 #ifdef CHECK_CXXLAPACK
 99 
100 template <typename MH, typename T, typename VV>
101 void
102 laqr1_native(GeMatrix<MH>              &H,
103              const T                   &sr1,
104              const T                   &si1,
105              const T                   &sr2,
106              const T                   &si2,
107              DenseVector<VV>           &v)
108 {
109     const INTEGER   N   = H.numRows();
110     const INTEGER   LDH = H.leadingDimension();
111 
112     if (IsSame<T,DOUBLE>::value) {
113         LAPACK_IMPL(dlaqr1)(&N,
114                             H.data(),
115                             &LDH,
116                             &sr1,
117                             &si1,
118                             &sr2,
119                             &si2,
120                             v.data());
121     } else {
122         ASSERT(0);
123     }
124 }
125 
126 #endif // CHECK_CXXLAPACK
127 
128 //== public interface ==========================================================
129 
130 template <typename MH, typename T, typename VV>
131 void
132 laqr1(GeMatrix<MH>              &H,
133       const T                   &sr1,
134       const T                   &si1,
135       const T                   &sr2,
136       const T                   &si2,
137       DenseVector<VV>           &v)
138 {
139     LAPACK_DEBUG_OUT("laqr1");
140 
141 //
142 //  Test the input parameters
143 //
144 #   ifndef NDEBUG
145     typedef typename GeMatrix<MH>::IndexType    IndexType;
146 
147     ASSERT(H.firstRow()==1);
148     ASSERT(H.firstCol()==1);
149     ASSERT(H.numRows()==H.numCols());
150 
151     const IndexType n = H.numRows();
152 
153     ASSERT(n==2 || n==3);
154 
155     ASSERT(v.length()==n);
156 #   endif
157 
158 //
159 //  Make copies of output arguments
160 //
161 #   ifdef CHECK_CXXLAPACK
162     typename GeMatrix<MH>::NoView       H_org  = H;
163     typename DenseVector<VV>::NoView    v_org  = v;
164 #   endif
165 
166 //
167 //  Call implementation
168 //
169     laqr1_generic(H, sr1, si1, sr2, si2, v);
170 
171 #   ifdef CHECK_CXXLAPACK
172 //
173 //  Make copies of results computed by the generic implementation
174 //
175     typename GeMatrix<MH>::NoView       H_generic  = H;
176     typename DenseVector<VV>::NoView    v_generic  = v;
177 //
178 //  restore output arguments
179 //
180     H = H_org;
181     v = v_org;
182 //
183 //  Compare results
184 //
185     laqr1_native(H, sr1, si1, sr2, si2, v);
186 
187     bool failed = false;
188     if (! isIdentical(H_generic, H, "H_generic""H")) {
189         std::cerr << "CXXLAPACK: H_generic = " << H_generic << std::endl;
190         std::cerr << "F77LAPACK: H = " << H << std::endl;
191         failed = true;
192     }
193 
194     if (! isIdentical(v_generic, v, "v_generic""v")) {
195         std::cerr << "CXXLAPACK: v_generic = " << v_generic << std::endl;
196         std::cerr << "F77LAPACK: v = " << v << std::endl;
197         failed = true;
198     }
199 
200     if (failed) {
201         std::cerr << "error in: laqr1.tcc" << std::endl;
202         ASSERT(0);
203     } else {
204         // std::cerr << "passed: laqr1.tcc" << std::endl;
205     }
206 #   endif
207 }
208 
209 //-- forwarding ----------------------------------------------------------------
210 
211 template <typename MH, typename T, typename VV>
212 void
213 laqr1(MH                        &&H,
214       const T                   &sr1,
215       const T                   &si1,
216       const T                   &sr2,
217       const T                   &si2,
218       VV                        &&v)
219 {
220     CHECKPOINT_ENTER;
221     laqr1(H, sr1, si1, sr2, si2, v);
222     CHECKPOINT_LEAVE;
223 }
224 
225 } } // namespace lapack, flens
226 
227 #endif // FLENS_LAPACK_EIG_LAQR1_TCC