lapack-tests.lisp 28 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 30, 2006 7 8 ``````(in-package "LAPACK") `````` rtoy committed Nov 25, 2006 9 ``````;; Convert the eigenvalues returned by DGEEV into an array `````` rtoy committed Nov 25, 2006 10 11 12 13 14 15 16 17 18 19 20 ``````(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 21 22 ``````;; Convert the eigenvalues returned by DGEEV into a more typical ;; matrix form. `````` rtoy committed Nov 25, 2006 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 ``````(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 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 79 80 ``````;; 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 81 ``````(defun print-dgeev-results (e-val e-vec) `````` rtoy committed Nov 28, 2006 82 `````` (format t "~2%DGEEV Example Program Results~%") `````` rtoy committed Nov 25, 2006 83 84 85 86 87 88 89 90 `````` (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)))) `````` Raymond Toy committed Dec 02, 2011 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 ``````(defun check-eigen-val-vec (n e-val e-vec true-val true-vec &key (tol 1d-14)) (flet ((relerr-ok (est true) (let* ((re (/ (abs (- est true)) (abs true))) (ok (<= re tol))) ;; Return NIL if it's ok. Otherwise return a list to ;; indicate what failed. (unless ok (format t "est = ~S~%true = ~S~% rel = ~S~%" est true re) (list est true re))))) (or (relerr-ok (aref e-val n) true-val) (dotimes (k n t) (let ((res (relerr-ok (aref e-vec k n) (aref true-vec k)))) (when res (return res))))))) `````` rtoy committed Nov 25, 2006 108 109 ``````;; DGEEV example based on the example from ;; http://www.nag.co.uk/lapack-ex/node87.html `````` rtoy committed Nov 25, 2006 110 111 112 113 114 115 116 117 118 119 120 ``````(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 `````` Raymond Toy committed Dec 02, 2011 121 122 123 124 `````` :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))) `````` rtoy committed Nov 25, 2006 125 126 127 128 129 130 131 `````` (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 `````` Raymond Toy committed Dec 02, 2011 132 `````` z-ldvr z-work z-lwork info) `````` rtoy committed Nov 25, 2006 133 `````` (dgeev "N" "V" n a-mat n wr wi vl n vr n work lwork 0) `````` rtoy committed Nov 26, 2006 134 135 `````` (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)) `````` Raymond Toy committed Dec 02, 2011 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 `````` (let ((e-val (make-eigval wr wi)) (e-vec (make-eigvec n vr wi))) ;; Display solution (cond ((zerop info) (print-dgeev-results e-val e-vec)) (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) (values e-val e-vec))))) (rt:deftest dgeev.1 (multiple-value-bind (e-val e-vec) (test-dgeev) (list (check-eigen-val-vec 0 e-val e-vec 0.799482122586210d0 #(-0.6550887675124076d0 -0.5236294609021240d0 0.5362184613722345d0 -0.0956067782012298d0)) (check-eigen-val-vec 1 e-val e-vec #c(-0.0994124532950747d0 0.4007924719897546d0) #(#c(-0.193301548264222d0 0.254631571927584d0) #c(0.251856531726740d0 -0.522404734711629d0) #c(0.097182458443282d0 -0.308383755897228d0) #c(0.675954054254748 0d0))) (check-eigen-val-vec 2 e-val e-vec #c(-0.0994124532950747d0 -0.4007924719897546d0) #(#c(-0.193301548264222d0 -0.254631571927584d0) #c(0.251856531726740d0 0.522404734711629d0) #c(0.097182458443282d0 0.308383755897228d0) #c(0.675954054254748 0d0))) (check-eigen-val-vec 3 e-val e-vec -0.100657215996059d0 #(0.125332697230903d0 0.332022215571751d0 0.593837759557331d0 0.722087029862455d0 -0.6550887675124076d0)))) (t t t t)) `````` rtoy committed Nov 25, 2006 179 `````` `````` rtoy committed Nov 26, 2006 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 ``````;; 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) `````` rtoy committed Nov 28, 2006 241 `````` (format t "~2%DGEEVX Example Program Results~%") `````` rtoy committed Nov 26, 2006 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 `````` (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 26, 2006 300 `````` `````` rtoy committed Nov 26, 2006 301 302 303 304 305 306 307 308 309 310 311 312 313 314 ``````;; Expected results (from http://www.nag.co.uk/lapack-ex/examples/results/dgesv-ex.r) ;; Solution ;; 1.0000 -1.0000 3.0000 -5.0000 ;; ;; Details of factorization ;; 1 2 3 4 ;; 1 5.2500 -2.9500 -0.9500 -3.8000 ;; 2 0.3429 3.8914 2.3757 0.4129 ;; 3 0.3010 -0.4631 -1.5139 0.2948 ;; 4 -0.2114 -0.3299 0.0047 0.1314 ;; ;; Pivot indices ;; 2 2 3 4 ;; `````` rtoy committed Nov 26, 2006 315 ``````(defun print-dgesv-results (n a b ipiv) `````` rtoy committed Nov 28, 2006 316 `````` (format t "~2%DGESV Example Program Results~%") `````` rtoy committed Nov 26, 2006 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 `````` (format t "Solution~%") (dotimes (k n) (format t "~21,14e " (aref b k))) (format t "~&Details of factorization~%") (dotimes (r n) (dotimes (c n) (format t "~21,14e" (aref a (+ r (* c n))))) (terpri)) (format t "Pivot indices~%") (dotimes (k n) (format t " ~d" (aref ipiv k))) (terpri)) (defun test-dgesv () ;; ;; Matrix A: ;; 1.80 2.88 2.05 -0.89 ;; 5.25 -2.95 -0.95 -3.80 ;; 1.58 -2.69 -2.90 -1.04 ;; -1.11 -0.66 -0.59 0.80 ;; ;; RHS: ;; 9.52 24.35 0.77 -6.22 (let* ((n 4) (a-mat (make-array (* n n) :element-type 'double-float :initial-contents '(1.80d0 5.25d0 1.58d0 -1.11d0 2.88d0 -2.95d0 -2.69d0 -0.66d0 2.05d0 -0.95d0 -2.90d0 -0.59d0 -0.89d0 -3.80d0 -1.04d0 0.8d0))) (b (make-array n :element-type 'double-float :initial-contents '(9.52d0 24.35d0 0.77d0 -6.22d0))) (ipiv (make-array n :element-type 'f2cl-lib:integer4))) (multiple-value-bind (z-n z-nrhs z-a z-lda z-ipiv z-b z-ldb info) (dgesv n 1 a-mat n ipiv b n 0) (declare (ignore z-n z-nrhs z-a z-lda z-ipiv z-b z-ldb)) ;; Display solution (cond ((zerop info) (print-dgesv-results n a-mat b ipiv)) (t (format t "The (~D, ~D) element of the factor U is zero~%" info info)))))) `````` rtoy committed Nov 26, 2006 357 `````` `````` rtoy committed Nov 27, 2006 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 ``````;; Expected results (from ) ;; ;; It seems, however, that the result from that page are wrong. At ;; least they seem wrong when I run the actual test program. The main ;; difference is that the singular vectors have the signs of some ;; entries wrong. ;; ;; The result below is what the test program actually produces. ;; DGESDD Example Program Results ;; ;; Singular values ;; 9.9966 3.6831 1.3569 0.5000 ;; Left singular vectors ;; 1 2 3 4 ;; 1 -0.1921 0.8030 -0.0041 0.5642 ;; 2 0.8794 0.3926 0.0752 -0.2587 ;; 3 -0.2140 0.2980 -0.7827 -0.5027 ;; 4 0.3795 -0.3351 -0.6178 0.6017 ;; ;; Right singular vectors by row (first m rows of V**T) ;; 1 2 3 4 5 6 ;; 1 -0.2774 -0.2020 -0.2918 0.0938 0.4213 -0.7816 ;; 2 0.6003 0.0301 -0.3348 0.3699 -0.5266 -0.3353 ;; 3 0.1277 -0.2805 -0.6453 -0.6781 -0.0413 0.1645 ;; 4 -0.1323 -0.7034 -0.1906 0.5399 0.0575 0.3957 ;; ;; Error estimate for the singular values ;; 1.1E-15 ;; ;; Error estimates for the left singular vectors ;; 1.8E-16 4.8E-16 1.3E-15 1.3E-15 ;; ;; Error estimates for the right singular vectors ;; 1.8E-16 4.8E-16 1.3E-15 2.2E-15 ;; `````` rtoy committed Nov 26, 2006 394 ``````(defun print-dgesdd-results (m n s u a) `````` rtoy committed Nov 28, 2006 395 `````` (format t "~2%DGESDD Example Program Results~%") `````` rtoy committed Nov 26, 2006 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 `````` (format t "Singular values~%") (dotimes (k m) (format t "~20,14e" (aref s k))) (format t "~2%Left singular vectors~%") (dotimes (r m) (dotimes (c m) (format t "~16,7e" (aref u (+ r (* c m))))) (terpri)) (format t "~%Right singular vectors (first m rows of V**T)~%") (dotimes (r m) (dotimes (c n) (format t "~16,7e" (aref a (+ r (* c m))))) (terpri)) ;; Compute error estimates for the singular vectors (let ((serrbd (* (aref s 0) (dlamch "Eps"))) (rcondu (make-array m :element-type 'double-float)) (rcondv (make-array m :element-type 'double-float)) (uerrbd (make-array m :element-type 'double-float)) (verrbd (make-array m :element-type 'double-float))) (ddisna "Left" m n s rcondu 0) (ddisna "Right" m n s rcondv 0) (dotimes (k m) (setf (aref uerrbd k) (/ serrbd (aref rcondu k))) (setf (aref verrbd k) (/ serrbd (aref rcondv k)))) (format t "Error estimate for the singular values~%") (format t "~20,15g~%" serrbd) (format t "~%~%Error estimates for the left singular values~%") (format t "~{~15,4e~^ ~}~%" (coerce uerrbd 'list)) (format t "~%~%Error estimates for the right singular values~%") (format t "~{~15,4e~^ ~}~%" (coerce verrbd 'list)))) (defun test-dgesdd () ;; ;; Matrix A: ;; 2.27 0.28 -0.48 1.07 -2.35 0.62 ;; -1.54 -1.67 -3.09 1.22 2.93 -7.39 ;; 1.15 0.94 0.99 0.79 -1.45 1.03 ;; -1.94 -0.78 -0.21 0.63 2.30 -2.57 (let* ((m 4) ; rows (n 6) ; cols (a-mat (make-array (* m n) :element-type 'double-float :initial-contents '(2.27d0 -1.54d0 1.15d0 -1.94d0 0.28d0 -1.67d0 0.94d0 -0.78d0 -0.48d0 -3.09d0 0.99d0 -0.21d0 1.07d0 1.22d0 0.79d0 0.63d0 -2.35d0 2.93d0 -1.45d0 2.30d0 0.62d0 -7.39d0 1.03d0 -2.57d0))) (s (make-array (min m n) :element-type 'double-float)) (u (make-array (* m (min m n)):element-type 'double-float)) (vt (make-array (* n n) :element-type 'double-float)) (lwork 1000) (work (make-array lwork :element-type 'double-float)) (iwork (make-array (* 8 (min m n)) :element-type 'f2cl-lib:integer4))) (multiple-value-bind (z-jobz z-m z-n z-a z-lda z-s z-u z-ldu z-vt z-ldvt z-work z-lwork z-iwork info) (dgesdd "Overwrite A by transpose(V)" m n a-mat m s u m vt n work lwork iwork 0) (declare (ignore z-jobz z-m z-n z-a z-lda z-s z-u z-ldu z-vt z-ldvt z-work z-lwork z-iwork )) ;; Display solution (cond ((zerop info) (print-dgesdd-results m n s u a-mat)) (t (format t "Failure in DGESDD. Info = ~D~%" info))) (format t "Optimum workspace required = ~D~%" (truncate (aref work 0))) (format t "Workspace provided = ~D~%" lwork)))) `````` rtoy committed Nov 27, 2006 459 `````` `````` rtoy committed Nov 27, 2006 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 ``````;; Expected results (from http://www.nag.co.uk/lapack-ex/examples/results/dgesvd-ex.r) ;; DGESVD Example Program Results ;; ;; Singular values ;; 9.9966 3.6831 1.3569 0.5000 ;; Left singular vectors (first n columns of U) ;; 1 2 3 4 ;; 1 -0.2774 -0.6003 -0.1277 0.1323 ;; 2 -0.2020 -0.0301 0.2805 0.7034 ;; 3 -0.2918 0.3348 0.6453 0.1906 ;; 4 0.0938 -0.3699 0.6781 -0.5399 ;; 5 0.4213 0.5266 0.0413 -0.0575 ;; 6 -0.7816 0.3353 -0.1645 -0.3957 ;; ;; Right singular vectors by row (V**T) ;; 1 2 3 4 ;; 1 -0.1921 0.8794 -0.2140 0.3795 ;; 2 -0.8030 -0.3926 -0.2980 0.3351 ;; 3 0.0041 -0.0752 0.7827 0.6178 ;; 4 -0.5642 0.2587 0.5027 -0.6017 ;; ;; Error estimate for the singular values ;; 1.1E-15 ;; ;; Error estimates for the left singular vectors ;; 1.8E-16 4.8E-16 1.3E-15 2.2E-15 ;; ;; Error estimates for the right singular vectors ;; 1.8E-16 4.8E-16 1.3E-15 1.3E-15 ;; `````` rtoy committed Nov 27, 2006 490 ``````(defun print-dgesvd-results (m n s vt a) `````` rtoy committed Nov 28, 2006 491 `````` (format t "~2%DGESVD Example Program Results~%") `````` rtoy committed Nov 27, 2006 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 `````` (format t "Singular values~%") (dotimes (k n) (format t "~20,14e" (aref s k))) (format t "~2%Left singular vectors~%") (dotimes (r m) (dotimes (c n) (format t "~16,7e" (aref a (+ r (* c m))))) (terpri)) (format t "~%Right singular vectors (first m rows of V**T)~%") (dotimes (r n) (dotimes (c n) (format t "~16,7e" (aref vt (+ r (* c n))))) (terpri)) ;; Compute error estimates for the singular vectors (let ((serrbd (* (aref s 0) (dlamch "Eps"))) (rcondu (make-array n :element-type 'double-float)) (rcondv (make-array n :element-type 'double-float)) (uerrbd (make-array n :element-type 'double-float)) (verrbd (make-array n :element-type 'double-float))) (ddisna "Left" m n s rcondu 0) (ddisna "Right" m n s rcondv 0) (dotimes (k n) (setf (aref uerrbd k) (/ serrbd (aref rcondu k))) (setf (aref verrbd k) (/ serrbd (aref rcondv k)))) (format t "Error estimate for the singular values~%") (format t "~20,15g~%" serrbd) (format t "~%~%Error estimates for the left singular values~%") (format t "~{~15,4e~^ ~}~%" (coerce uerrbd 'list)) (format t "~%~%Error estimates for the right singular values~%") (format t "~{~15,4e~^ ~}~%" (coerce verrbd 'list)))) (defun test-dgesvd () ;; ;; Matrix A: ;; 2.27 -1.54 1.15 -1.94 ;; 0.28 -1.67 0.94 -0.78 ;; -0.48 -3.09 0.99 -0.21 ;; 1.07 1.22 0.79 0.63 ;; -2.35 2.93 -1.45 2.30 ;; 0.62 -7.39 1.03 -2.57 (let* ((m 6) ; rows (n 4) ; cols (a-mat (make-array (* m n) :element-type 'double-float :initial-contents '(2.27d0 0.28d0 -0.48d0 1.07d0 -2.35d0 0.62d0 -1.54d0 -1.67d0 -3.09d0 1.22d0 2.93d0 -7.39d0 1.15d0 0.94d0 0.99d0 0.79d0 -1.45d0 1.03d0 -1.94d0 -0.78d0 -0.21d0 0.63d0 2.30d0 -2.57d0))) (s (make-array (min m n) :element-type 'double-float)) (u (make-array (* m (min m n)):element-type 'double-float)) (vt (make-array (* n n) :element-type 'double-float)) (lwork (+ 10 (* 4 8) (* 64 (+ 10 8)))) (work (make-array lwork :element-type 'double-float))) (multiple-value-bind (z-jobz z-jobvt z-m z-n z-a z-lda z-s z-u z-ldu z-vt z-ldvt z-work z-lwork info) (dgesvd "Overwrite A by U" "Singular vectors (V)" m n a-mat m s u m vt n work lwork 0) (declare (ignore z-jobz z-jobvt z-m z-n z-a z-lda z-s z-u z-ldu z-vt z-ldvt z-work z-lwork)) ;; Display solution (cond ((zerop info) (print-dgesvd-results m n s vt a-mat)) (t (format t "Failure in DGESDD. Info = ~D~%" info))) (format t "Optimum workspace required = ~D~%" (truncate (aref work 0))) (format t "Workspace provided = ~D~%" lwork)))) `````` rtoy committed Nov 27, 2006 556 `````` `````` Raymond Toy committed Nov 25, 2011 557 558 559 560 561 ``````(defun make-complex-eigvec (n vr) (make-array (list n n) :displaced-to vr :element-type (array-element-type vr))) `````` Raymond Toy committed Dec 04, 2011 562 563 564 565 566 567 568 569 570 571 ``````(defun transpose (mat) (let* ((nrows (array-dimension mat 0)) (ncols (array-dimension mat 1)) (trans (make-array (list ncols nrows) :element-type (array-element-type mat)))) (dotimes (r nrows) (dotimes (c ncols) (setf (aref trans c r) (aref mat r c)))) trans)) `````` Raymond Toy committed Nov 25, 2011 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 ``````(defun print-zgeev-results (e-val e-vec) (format t "~2%ZGEEV Example Program Results~%") (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)))) (defun test-zgeev () ;; The matrix is ;; ;; #c(-3.97, -5.04) #c(-4.11, 3.70) #c(-0.34, 1.01) #c( 1.29, -0.86) ;; #c( 0.34, -1.50) #c( 1.52, -0.43) #c( 1.88, -5.38) #c( 3.36, 0.65) ;; #c( 3.31, -3.85) #c( 2.50, 3.45) #c( 0.88, -1.08) #c( 0.64, -1.48) ;; #c(-1.10, 0.82) #c( 1.81, -1.59) #c( 3.25, 1.33) #c( 1.57, -3.44) ;; ;; Recall that Fortran arrays are column-major order! (let* ((n 4) (a-mat (make-array (* n n) :element-type '(complex double-float) :initial-contents '(#c(-3.97d0 -5.04d0) #c( 0.34d0 -1.50d0) #c( 3.31d0 -3.85d0) #c(-1.10d0 0.82d0) #c(-4.11d0 3.70d0) #c( 1.52d0 -0.43d0) #c( 2.50d0 3.45d0) #c( 1.81d0 -1.59d0) #c(-0.34d0 1.01d0) #c( 1.88d0 -5.38d0) #c( 0.88d0 -1.08d0) #c( 3.25d0 1.33d0) #c( 1.29d0 -0.86d0) #c( 3.36d0 0.65d0) #c( 0.64d0 -1.48d0) #c( 1.57d0 -3.44d0)))) (lwork 660) (w (make-array n :element-type '(complex double-float))) (rw (make-array lwork :element-type 'double-float)) (vl (make-array 0 :element-type '(complex double-float))) (vr (make-array (* n n) :element-type '(complex double-float))) (work (make-array lwork :element-type '(complex double-float)))) (multiple-value-bind (z-jobvl z-jobvr z-n z-a z-lda z-w z-vl z-ldvl z-vr z-ldvr z-work z-lwork z-rwork info) (zgeev "N" "V" n a-mat n w vl n vr n work lwork rw 0) (declare (ignore z-jobvl z-jobvr z-n z-a z-lda z-w z-vl z-ldvl z-vr z-ldvr z-work z-lwork z-rwork)) ;; Display solution (cond ((zerop info) (print-zgeev-results w `````` Raymond Toy committed Dec 04, 2011 624 `````` (transpose (make-complex-eigvec n vr)))) `````` Raymond Toy committed Nov 25, 2011 625 626 627 628 `````` (t (format t "Failure in DGEEV. INFO = ~D~%" info))) ;; Display workspace info (format t "Optimum workspace required = ~D~%" (truncate (realpart (aref work 0)))) `````` Raymond Toy committed Dec 04, 2011 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 `````` (format t "Workspace provided = ~D~%" lwork) (values w (transpose (make-complex-eigvec n vr)))))) (rt:deftest zgeev.1 (multiple-value-bind (val vec) (test-zgeev) (list (check-eigen-val-vec 0 val vec #c(-6.00042534294924d0 -6.99984337157039d0) #(#c(0.845722126909561d0 +0.000000000000000d0) #c(-0.017722752537655d0 +0.303607402208809d0) #c(0.087521244669520d0 +0.311452829815249d0) #c(-0.056147220899372d0 -0.290597986123314d0))) (check-eigen-val-vec 1 val vec #c(-5.00003345759697d0 +2.00602716231652d0) #(#c( -0.386549111838405d0 +0.173234631742952d0) #c(-0.353928813160122d0 +0.452880967035810d0) #c(0.612370054896136d0 +0.000000000000000d0) #c(-0.085928358258907d0 -0.328362611341537d0))) (check-eigen-val-vec 2 val vec #c(7.998194516208244d0 -0.996365091392899d0) #(#c(-0.172974121492221d0 +0.266896080554183d0) #c(0.692423212284643d0 +0.000000000000000d0) #c(0.332402268453410d0 +0.495979987128303d0) #c(0.250388389801717d0 -0.014655003103538d0))) (check-eigen-val-vec 3 val vec #c(3.00226428433797d0 -3.99981869935322d0) #(#c(-0.035613578794424d0 -0.178218041420316d0) #c(0.126374262079091d0 +0.266632374107522d0) #c(0.012932561333282d0 -0.296568203073541d0) #c(0.889824013759239d0 +0.000000000000000d0))))) (t t t t)) `````` Raymond Toy committed Nov 13, 2013 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 `````` (defun print-zheev-results (e-val e-vec) (format t "~2%ZHEEV Example Program Results~2%") (let ((n (length e-val))) (format t "Eigenvalues~%") (dotimes (k n) (format t " ~A" (aref e-val k))) (format t "~2%Eigenvectors~%") (dotimes (k n) (format t "~%Eigenvector(~D)~%" k) (dotimes (row n) (format t "~A~%" (aref e-vec row k))) (terpri)))) (defun test-zheev () ;; The matrix is ;; 1 #c(2 -1) #c(3 -1) #c(4 -1) ;; #c(2 1) 2 #c(3 -2) #c(4 -2) ;; #c(3 1) #c(3 2) 3 #c(4 -3) ;; #c(4 1) #c(4 2) #c(4 3) 4 ;; Recall that Fortran arrays are column-major order! (let* ((n 4) (a-mat (make-array (* n n) :element-type '(complex double-float) :initial-contents '(#c(1d0 0) #c(2d0 1d0) #c(3d0 1d0) #c(4d0 1d0) #c(2d0 -1d0) #c(2d0 0) #c(3d0 2d0) #c(4d0 2d0) #c(3d0 -1d0) #c(3d0 -2d0) #c(3d0 0) #c(4d0 3d0) #c(4d0 -1d0) #c(4d0 -2d0) #c(4d0 -3d0) #c(4d0 0)))) (lwork 132) (w (make-array n :element-type 'double-float)) (work (make-array lwork :element-type '(complex double-float))) (rwork (make-array (- (* 3 n) 2) :element-type 'double-float))) (multiple-value-bind (z-jobz z-uplo z-n z-a z-lda z-w z-work z-lwork z-rwork info) (zheev "V" "U" n a-mat n w work lwork rwork 0) (declare (ignore z-jobz z-uplo z-n z-a z-lda z-w z-work z-lwork z-rwork)) (cond ((zerop info) (print-zheev-results w (transpose (make-complex-eigvec n a-mat)))) (t (format t "Failure in ZHEEV. INFO = ~D~%" info))) (format t "Optimum workspace required = ~D~%" (truncate (realpart (aref work 0)))) (format t "Workspace provided = ~D~%" lwork) (values w (transpose (make-complex-eigvec n a-mat)))))) (rt:deftest zheev.1 (multiple-value-bind (val vec) (test-zheev) (let ((cval (make-array 4 :element-type '(complex double-float)))) (map-into cval #'(lambda (x) (complex x 0d0)) val) (list (check-eigen-val-vec 0 cval vec #c(-4.244305402383179d0 0) #(#C(0.38390086708134163d0 0.29405658581351474d0) #C(0.4512081881756226d0 -0.11018120938621835d0) #C(-0.026341826788003057d0 -0.48569831719444095d0) #C(-0.5602011901552105d0 -0.0d0))) (check-eigen-val-vec 1 cval vec #c(-0.6885811461174348d0 0d0) #(#C(-0.3975174811710425d0 0.5105011667992776d0) #C(0.39532449113598805d0 -0.323828267501095d0) #C(-0.43094682808194457d0 0.0382543464880426d0) #C(0.36475148673610636d0 0.0d0))) (check-eigen-val-vec 2 cval vec #c(1.1412485214653287d0 0d0) #(#C(0.37459176938191946d0 0.24136603676776178d0) #C(-0.28951694726673083d0 0.4917390332315046d0) #C(-0.37679299781495784d0 -0.3993997903501625d0) #C(0.4174960446688179d0 0.0d0))) (check-eigen-val-vec 3 cval vec #c(13.791638027035287d0 0d0) #(#C(0.3309009213351469d0 -0.19861339914465895d0) #C(0.3727831818692677d0 -0.24193063397200412d0) #C(0.4869962523459657d0 -0.19381997741123178d0) #C(0.6154900747846208d0 0.0d0)))))) (t t t t)) `````` rtoy committed Nov 27, 2006 754 755 756 757 ``````(defun do-all-lapack-tests () (test-dgeev) (test-dgeevx) (test-dgesv) `````` rtoy committed Nov 27, 2006 758 `````` (test-dgesdd) `````` Raymond Toy committed Dec 02, 2011 759 `````` (test-dgesvd) `````` Raymond Toy committed Nov 13, 2013 760 761 `````` (test-zgeev) (test-zheev)) `````` rtoy committed Nov 27, 2006 762 `````` `````` rtoy committed Nov 25, 2006 763 ``````;;; \$Log\$ `````` rtoy committed Nov 30, 2006 764 765 766 767 768 769 770 771 772 773 774 775 776 777 ``````;;; Revision 1.11 2006/12/01 04:29:29 rtoy ;;; Create packages for BLAS and LAPACK routines. ;;; ;;; blas.system: ;;; o Converted files are in the BLAS package. ;;; o Add blas-package defsystem to load the package definition. ;;; ;;; lapack.system: ;;; o Converted files are in the LAPACK package. ;;; o Add lapack-package defsystem to load the package definition. ;;; ;;; lapack/lapack-tests.lisp: ;;; o Tests are in the LAPACK package ;;; `````` rtoy committed Nov 28, 2006 778 779 780 ``````;;; Revision 1.10 2006/11/28 15:49:01 rtoy ;;; Print out short title for each test. ;;; `````` rtoy committed Nov 27, 2006 781 782 783 ``````;;; Revision 1.9 2006/11/27 22:22:23 rtoy ;;; Add expected results. ;;; `````` rtoy committed Nov 27, 2006 784 785 786 ``````;;; Revision 1.8 2006/11/27 20:04:33 rtoy ;;; Add DGESVD and update files and tests appropriately. ;;; `````` rtoy committed Nov 27, 2006 787 788 789 ``````;;; Revision 1.7 2006/11/27 15:23:29 rtoy ;;; Add function to run all the tests. ;;; `````` rtoy committed Nov 26, 2006 790 791 792 793 794 795 796 797 798 799 800 ``````;;; Revision 1.6 2006/11/26 23:26:47 rtoy ;;; packages/lapack.system: ;;; o Add DGESDD and dependencies ;;; o Add DDISNA to compute condition number of singular vectors ;;; ;;; packages/lapack/.cvsignore: ;;; o Ignore new generated Lisp files. ;;; ;;; packages/lapack/lapack-tests.lisp: ;;; o Add test for DGESDD ;;; `````` rtoy committed Nov 26, 2006 801 802 803 ``````;;; Revision 1.5 2006/11/26 14:26:42 rtoy ;;; Add expected results for DGESV. ;;; `````` rtoy committed Nov 26, 2006 804 805 806 807 808 809 810 811 812 813 ``````;;; Revision 1.4 2006/11/26 14:24:46 rtoy ;;; packages/lapack.system: ;;; o DGESV and dependencies ;;; ;;; packages/.cvsignore: ;;; o Ignore generated dgesv.lisp and dependencies ;;; ;;; packages/lapack/lapack-tests.lisp: ;;; o Test routine for DGESV ;;; `````` rtoy committed Nov 26, 2006 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 ``````;;; 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 831 832 833 ``````;;; Revision 1.2 2006/11/26 04:53:22 rtoy ;;; Add comments ;;; `````` rtoy committed Nov 25, 2006 834 835 836 837 838 839 ``````;;; 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). `````` rtoy committed Nov 27, 2006 840 ``;;;``