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comparison src/DLD-FUNCTIONS/qz.cc @ 10840:89f4d7e294cc

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Grammarcheck .cc files
author Rik <octave@nomad.inbox5.com>
date Sat, 31 Jul 2010 11:18:11 -0700
parents 3140cb7a05a1
children fd0a3ac60b0e
comparison
equal deleted inserted replaced
10839:65bc065bec95 10840:89f4d7e294cc
302 @end tex\n\ 302 @end tex\n\
303 @ifnottex\n\ 303 @ifnottex\n\
304 @var{lambda}\n\ 304 @var{lambda}\n\
305 @end ifnottex\n\ 305 @end ifnottex\n\
306 of @math{(A - s B)}.\n\ 306 of @math{(A - s B)}.\n\
307 \n\
307 @item @code{[AA, BB, Q, Z, V, W, lambda] = qz (A, B)}\n\ 308 @item @code{[AA, BB, Q, Z, V, W, lambda] = qz (A, B)}\n\
308 \n\ 309 \n\
309 Computes qz decomposition, generalized eigenvectors, and \n\ 310 Computes qz decomposition, generalized eigenvectors, and \n\
310 generalized eigenvalues of @math{(A - sB)}\n\ 311 generalized eigenvalues of @math{(A - sB)}\n\
311 @tex\n\ 312 @tex\n\
312 $$ AV = BV{ \\rm diag }(\\lambda) $$\n\ 313 $$ AV = BV{ \\rm diag }(\\lambda) $$\n\
313 $$ W^T A = { \\rm diag }(\\lambda)W^T B $$\n\ 314 $$ W^T A = { \\rm diag }(\\lambda)W^T B $$\n\
314 $$ AA = Q^T AZ, BB = Q^T BZ $$\n\ 315 $$ AA = Q^T AZ, BB = Q^T BZ $$\n\
315 @end tex\n\ 316 @end tex\n\
316 @ifnottex\n\ 317 @ifnottex\n\
318 \n\
317 @example\n\ 319 @example\n\
318 @group\n\ 320 @group\n\
319 \n\ 321 \n\
320 A * V = B * V * diag (lambda)\n\ 322 A * V = B * V * diag (lambda)\n\
321 W' * A = diag (lambda) * W' * B\n\ 323 W' * A = diag (lambda) * W' * B\n\
322 AA = Q * A * Z, BB = Q * B * Z\n\ 324 AA = Q * A * Z, BB = Q * B * Z\n\
323 \n\ 325 \n\
324 @end group\n\ 326 @end group\n\
325 @end example\n\ 327 @end example\n\
328 \n\
326 @end ifnottex\n\ 329 @end ifnottex\n\
327 with @var{Q} and @var{Z} orthogonal (unitary)= @var{I}\n\ 330 with @var{Q} and @var{Z} orthogonal (unitary)= @var{I}\n\
328 \n\ 331 \n\
329 @item @code{[AA,BB,Z@{, lambda@}] = qz(A,B,opt)}\n\ 332 @item @code{[AA,BB,Z@{, lambda@}] = qz(A,B,opt)}\n\
330 \n\ 333 \n\
331 As in form [2], but allows ordering of generalized eigenpairs\n\ 334 As in form [2], but allows ordering of generalized eigenpairs\n\
332 for (e.g.) solution of discrete time algebraic Riccati equations.\n\ 335 for (e.g.) solution of discrete time algebraic Riccati equations.\n\
333 Form 3 is not available for complex matrices, and does not compute\n\ 336 Form 3 is not available for complex matrices, and does not compute\n\
334 the generalized eigenvectors @var{V}, @var{W}, nor the orthogonal matrix @var{Q}.\n\ 337 the generalized eigenvectors @var{V}, @var{W}, nor the orthogonal matrix\n\
338 @var{Q}.\n\
335 \n\ 339 \n\
336 @table @var\n\ 340 @table @var\n\
337 @item opt\n\ 341 @item opt\n\
338 for ordering eigenvalues of the GEP pencil. The leading block\n\ 342 for ordering eigenvalues of the GEP pencil. The leading block\n\
339 of the revised pencil contains all eigenvalues that satisfy:\n\ 343 of the revised pencil contains all eigenvalues that satisfy:\n\
340 @table @code\n\ 344 @table @code\n\
341 @item \"N\"\n\ 345 @item \"N\"\n\
342 = unordered (default) \n\ 346 = unordered (default) \n\
343 \n\ 347 \n\
344 @item \"S\"\n\ 348 @item \"S\"\n\
345 = small: leading block has all |lambda| <= 1 \n\ 349 = small: leading block has all |lambda| @leq{} 1 \n\
346 \n\ 350 \n\
347 @item \"B\"\n\ 351 @item \"B\"\n\
348 = big: leading block has all |lambda| >= 1 \n\ 352 = big: leading block has all |lambda| @geq{} 1 \n\
349 \n\ 353 \n\
350 @item \"-\"\n\ 354 @item \"-\"\n\
351 = negative real part: leading block has all eigenvalues\n\ 355 = negative real part: leading block has all eigenvalues\n\
352 in the open left half-plane\n\ 356 in the open left half-plane\n\
353 \n\ 357 \n\