lapack-tests.lisp 8.13 KB
 rtoy committed Nov 25, 2006 1 ``````;;; `````` rtoy committed Nov 25, 2006 2 ``````;;; Simple tests for selected LAPACK routines. `````` rtoy committed Nov 25, 2006 3 4 5 6 ``````;;; ;;; \$Id\$ ;;; `````` rtoy committed Nov 25, 2006 7 ``````;; Convert the eigenvalues returned by DGEEV into an array `````` rtoy committed Nov 25, 2006 8 9 10 11 12 13 14 15 16 17 18 ``````(defun make-eigval (wr wi) (let ((e-val (make-array (length wr)))) (map-into e-val #'(lambda (r i) ;; Do we really want to do this? Should we ;; just make all of the eigenvalues complex? (if (zerop i) r (complex r i))) wr wi) e-val)) `````` rtoy committed Nov 25, 2006 19 20 ``````;; Convert the eigenvalues returned by DGEEV into a more typical ;; matrix form. `````` rtoy committed Nov 25, 2006 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 ``````(defun make-eigvec (n vr wi) (let ((evec (make-array (list n n)))) (do ((col 0 (incf col)) (posn 0)) ((>= col n)) (cond ((zerop (aref wi col)) (dotimes (row n) (setf (aref evec row col) (aref vr posn)) (incf posn))) (t (dotimes (row n) (let* ((next-posn (+ posn n)) (val+ (complex (aref vr posn) (aref vr next-posn))) (val- (conjugate val+))) (setf (aref evec row col) val+) (setf (aref evec row (1+ col)) val-) (incf posn))) ;; Skip over the next column, which we've already used (incf col) (incf posn n)))) evec)) `````` rtoy committed Nov 26, 2006 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 ``````;; Expected results from http://www.nag.co.uk/lapack-ex/examples/results/dgeev-ex.r ;; ;; DGEEV Example Program Results ;; ;; Eigenvalue( 1) = 7.9948E-01 ;; ;; Eigenvector( 1) ;; -6.5509E-01 ;; -5.2363E-01 ;; 5.3622E-01 ;; -9.5607E-02 ;; ;; Eigenvalue( 2) = (-9.9412E-02, 4.0079E-01) ;; ;; Eigenvector( 2) ;; (-1.9330E-01, 2.5463E-01) ;; ( 2.5186E-01,-5.2240E-01) ;; ( 9.7182E-02,-3.0838E-01) ;; ( 6.7595E-01, 0.0000E+00) ;; ;; Eigenvalue( 3) = (-9.9412E-02,-4.0079E-01) ;; ;; Eigenvector( 3) ;; (-1.9330E-01,-2.5463E-01) ;; ( 2.5186E-01, 5.2240E-01) ;; ( 9.7182E-02, 3.0838E-01) ;; ( 6.7595E-01,-0.0000E+00) ;; ;; Eigenvalue( 4) = -1.0066E-01 ;; ;; Eigenvector( 4) ;; 1.2533E-01 ;; 3.3202E-01 ;; 5.9384E-01 ;; 7.2209E-01 ;; `````` rtoy committed Nov 25, 2006 79 80 81 82 83 84 85 86 87 ``````(defun print-dgeev-results (e-val e-vec) (let ((n (length e-val))) (dotimes (k n) (format t "Eigenvalue(~D) = ~A~%" k (aref e-val k)) (format t "~%Eigenvector(~D)~%" k) (dotimes (row n) (format t "~A~%" (aref e-vec row k))) (terpri)))) `````` rtoy committed Nov 25, 2006 88 89 ``````;; DGEEV example based on the example from ;; http://www.nag.co.uk/lapack-ex/node87.html `````` rtoy committed Nov 25, 2006 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 ``````(defun test-dgeev () ;; The matrix is ;; ;; 0.35 0.45 -0.14 -0.17 ;; 0.09 0.07 -0.54 0.35 ;; -0.44 -0.33 -0.03 0.17 ;; 0.25 -0.32 -0.13 0.11 ;; ;; Recall that Fortran arrays are column-major order! (let* ((n 4) (a-mat (make-array (* n n) :element-type 'double-float :initial-contents '(0.35d0 0.09d0 -0.44d0 0.25d0 0.45d0 0.07d0 -0.33d0 -0.32d0 -0.14d0 -0.54d0 -0.03d0 -0.13d0 -0.17d0 0.35d0 0.17d0 0.11d0))) (wr (make-array n :element-type 'double-float)) (wi (make-array n :element-type 'double-float)) (vl (make-array 0 :element-type 'double-float)) (vr (make-array (* n n) :element-type 'double-float)) (lwork 660) (work (make-array lwork :element-type 'double-float))) (multiple-value-bind (z-jobvl z-jobvr z-n z-a z-lda z-wr z-wi z-vl z-ldvl z-vr z-ldvr z-work z-lwork info) (dgeev "N" "V" n a-mat n wr wi vl n vr n work lwork 0) `````` rtoy committed Nov 26, 2006 114 115 `````` (declare (ignore z-jobvl z-jobvr z-n z-a z-lda z-wr z-wi z-vl z-ldvl z-vr z-ldvr z-work z-lwork)) `````` rtoy committed Nov 25, 2006 116 117 118 119 120 121 122 123 124 125 `````` ;; Display solution (cond ((zerop info) (print-dgeev-results (make-eigval wr wi) (make-eigvec n vr wi))) (t (format t "Failure in DGEEV. INFO = ~D~%" info))) ;; Display workspace info (format t "Optimum workspace required = ~D~%" (truncate (aref work 0))) (format t "Workspace provided = ~D~%" lwork)))) `````` rtoy committed Nov 26, 2006 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 ``````;; Expected results http://www.nag.co.uk/lapack-ex/examples/results/dgeevx-ex.r ;; ;; DGEEVX Example Program Results ;; ;; Eigenvalue( 1) = 7.9948E-01 ;; ;; Reciprocal condition number = 9.9E-01 ;; Error bound = 1.3E-16 ;; ;; Eigenvector( 1) ;; -6.5509E-01 ;; -5.2363E-01 ;; 5.3622E-01 ;; -9.5607E-02 ;; ;; Reciprocal condition number = 8.2E-01 ;; Error bound = 1.6E-16 ;; ;; Eigenvalue( 2) = (-9.9412E-02, 4.0079E-01) ;; ;; Reciprocal condition number = 7.0E-01 ;; Error bound = 1.8E-16 ;; ;; Eigenvector( 2) ;; (-1.9330E-01, 2.5463E-01) ;; ( 2.5186E-01,-5.2240E-01) ;; ( 9.7182E-02,-3.0838E-01) ;; ( 6.7595E-01, 0.0000E+00) ;; ;; Reciprocal condition number = 4.0E-01 ;; Error bound = 3.3E-16 ;; ;; Eigenvalue( 3) = (-9.9412E-02,-4.0079E-01) ;; ;; Reciprocal condition number = 7.0E-01 ;; Error bound = 1.8E-16 ;; ;; Eigenvector( 3) ;; (-1.9330E-01,-2.5463E-01) ;; ( 2.5186E-01, 5.2240E-01) ;; ( 9.7182E-02, 3.0838E-01) ;; ( 6.7595E-01,-0.0000E+00) ;; ;; Reciprocal condition number = 4.0E-01 ;; Error bound = 3.3E-16 ;; ;; Eigenvalue( 4) = -1.0066E-01 ;; ;; Reciprocal condition number = 5.7E-01 ;; Error bound = 2.3E-16 ;; ;; Eigenvector( 4) ;; 1.2533E-01 ;; 3.3202E-01 ;; 5.9384E-01 ;; 7.2209E-01 ;; ;; Reciprocal condition number = 3.1E-01 ;; Error bound = 4.2E-16 ;; (defun print-dgeevx-results (tol e-val e-vec rconde rcondv) (let ((n (length e-val))) (dotimes (k n) (format t "Eigenvalue(~D) = ~A~%" k (aref e-val k)) (let ((rcnd (aref rconde k))) (format t "Reciprocal condition number = ~A~%" rcnd) (if (plusp rcnd) (format t "Error bound = ~A~%" (/ tol rcnd)) (format t "Error bound is infinite~%"))) (format t "~%Eigenvector(~D)~%" k) (dotimes (row n) (format t "~A~%" (aref e-vec row k))) (let ((rcnd (aref rcondv k))) (format t "Reciprocal condition number = ~A~%" rcnd) (if (plusp rcnd) (format t "Error bound = ~A~%" (/ tol rcnd)) (format t "Error bound is infinity~%"))) (terpri)))) (defun test-dgeevx () (let* ((n 4) (a-mat (make-array (* n n) :element-type 'double-float :initial-contents '(0.35d0 0.09d0 -0.44d0 0.25d0 0.45d0 0.07d0 -0.33d0 -0.32d0 -0.14d0 -0.54d0 -0.03d0 -0.13d0 -0.17d0 0.35d0 0.17d0 0.11d0))) (wr (make-array n :element-type 'double-float)) (wi (make-array n :element-type 'double-float)) (vl (make-array (* n n) :element-type 'double-float)) (vr (make-array (* n n) :element-type 'double-float)) (scale (make-array n :element-type 'double-float)) (rconde (make-array n :element-type 'double-float)) (rcondv (make-array n :element-type 'double-float)) (lwork 660) (work (make-array lwork :element-type 'double-float)) (iwork (make-array (- (* n 2) 2) :element-type 'f2cl-lib::integer4))) (multiple-value-bind (z-balanc z-jobvl z-jobvr z-sense z-n z-a z-lda z-wr z-wi z-vl z-ldvl z-vr z-ldvr ilo ihi z-scale abnrm z-rconde z-rcondv z-work z-lwork z-iwork info) (dgeevx "Balance" "Vectors (left)" "Vectors (right)" "Both reciprocal condition numbers" n a-mat n wr wi vl n vr n 0 0 scale 0d0 rconde rcondv work lwork iwork 0) (declare (ignore z-balanc z-jobvl z-jobvr z-sense z-n z-a z-lda z-wr z-wi z-vl z-ldvl z-vr z-ldvr z-scale z-rconde z-rcondv z-work z-lwork z-iwork)) ;; Display solution (cond ((zerop info) (let* ((eps (dlamch "Eps")) (tol (* eps abnrm))) (print-dgeevx-results tol (make-eigval wr wi) (make-eigvec n vr wi) rconde rcondv))) (t (format t "Failure in DGEEV. INFO = ~D~%" info))) ;; Display workspace info (format t "Optimum workspace required = ~D~%" (truncate (aref work 0))) (format t "Workspace provided = ~D~%" lwork)))) `````` rtoy committed Nov 25, 2006 245 246 `````` ;;; \$Log\$ `````` rtoy committed Nov 26, 2006 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 ``````;;; Revision 1.3 2006/11/26 05:31:16 rtoy ;;; packages/lapack.system: ;;; o Add DGEEVX and dependencies ;;; ;;; packages/lapack/lapack-tests.lisp: ;;; o Add test for DGEEVX ;;; o Add comments ;;; ;;; packages/lapack/dgeevx.f: ;;; packages/lapack/dlacon.f: ;;; packages/lapack/dlaexc.f: ;;; packages/lapack/dlaqtr.f: ;;; packages/lapack/dlasy2.f: ;;; packages/lapack/dtrexc.f: ;;; packages/lapack/dtrsna.f: ;;; o New files for DGEEVX and dependencies. ;;; `````` rtoy committed Nov 25, 2006 264 265 266 ``````;;; Revision 1.2 2006/11/26 04:53:22 rtoy ;;; Add comments ;;; `````` rtoy committed Nov 25, 2006 267 268 269 270 271 272 273 ``````;;; Revision 1.1 2006/11/26 04:51:05 rtoy ;;; packages/lapack.system: ;;; o Add defsystem for LAPACK tests ;;; ;;; packages/lapack/lapack-tests.lisp: ;;; o Add simple tests for LAPACK. (Currently only DGEEV). ;;;``````