From help-octave-request at bevo dot che dot wisc dot edu Thu Nov 7 14:48:00 2002 Subject: not equivalent? From: "Albert F. Niessner" To: Octave Help Date: 07 Nov 2002 15:46:15 -0500 --=-a7Mcbqjj69hcwK+bw4qf Content-Type: text/plain Content-Transfer-Encoding: 7bit I have two vectors (series and spacing) of 500x1 elements each. If I then do the following (N = length(series);): k=0:N-1; W = e.^(-j*2*pi*(spacing*k)/N); spectrum = W' * series; I get some answer. Because of the size of W, it may be worth while to loop over very large vectors so I can also do it this way: w = -j*2*pi*spacing/N; for k=1:N W = e.^(w*(k-1)); spectrum(k) = sum (series .* W); endfor; I then used the same vectors in both cases and get different results -- max (abs((abs(r1) - abs(r2))) < 10^-10 but max(abs(r1 - r2)) > 450. I have not checked the phase angle because I am not sure that information would reduce my confusion. So, why are the results different? Is there some implied precision difference between the matrix-vector multiplication and multiplying followed by and accumulation? Example data has been attached. Al Niessner --=-a7Mcbqjj69hcwK+bw4qf Content-Disposition: attachment; filename=example.oct.gz Content-Type: application/x-gzip; name=example.oct.gz Content-Transfer-Encoding: base64 H4sICODPyj0CA2V4YW1wbGUub2N0AJVbya4cxxG88ysG0NUY1JK1NGEYBny3L/6BZ/lBliAuICna +nt3Zg5fR0bVA6g5DMlCTy9RWRGRUc0fbn/79Pz05fnft3/9fvvHj1+evj7fyj3fa/vT7Z//+e32 9w9fb2nccnkr+W2SW0mp3D5+/nL78/ufnz9/fv/86a/vPnz68nz/5eOv9/dPn5/uP334+pc3P9ze P717fnv7/PzpPOz855ffP57/fPf05dPP/zv/+enDfz+/vbWUzr//+OHX3969P/+Z39zSvUsu/Zjf vt/o6Hk7Y2Qps9l315Eh46i9Jfs+jyn31HuqeYh9Nx2p8zpRGToy29FnadW+5c2t3uX6jXQdGEW/ 25Fk9Pz41pGSW6kzHfpt15sjnKrcW2nXXR46ksvLEfUYetuz9OtjIy0/TqrfoiMpx4dNdxkvl9Zv Hcrtuu1UbajA057fhmZLuc1R/dtOfp3GnuPEln51YtvkKKlX/zZsLyySTB0h3BSOeD8ntHlcn2nY 1utmkh3Tk8DHcL4Q69MuPifj2sq8Po50TVAPhnSNM3gifT3T+W1glICOAn3dX26HAw2PProDHato j3O77mg4zgi91zDA3B41HMrjrOGD52JSnSvQ8eoKNI+0I5aZFjQ8VvEp5Gu1gqvRSzqOaEnzc7WM teklHYpOgV5QzY3gSPfK1ar8MOPcP/gB59axLVA2hm3j5+XKV2yZDqRyWQ9a5optuz79QRah0BXb WI5lQenENkUATmyX1XpyZrhDrTTmBum0Yowu8PMAN5xJseWrpcRL5kQ60vOyqBXpOBuK9EIXjalA FioYRJ9KF/F+lC54nueM57EqDrWmVWzo5gVcONejcCOvaOW2ONsK7sIaNUXpOcHtVBMr0StHxLWt XIxL2TmCCbIecW61jgt8nCPinChHCFzM0YVVacxSKl99HhXIz9Cl8yi6XEc72UNJczTiHSrUL8if 3/Jg41gTCvVS7VuseeT7sK5ASl7JS701ljlJkSO1krm2N3xc2L/MCZfPD+ELT69YxzlTrOPca1nH 8jTOiEtfusTznFAHBq0ufBLvUTmjx0rXk8eHVdKIgqn0TGyYWlwLW84gfjqRLpHBT6TDbRvSc3Fy eMwrwkeu7AQ60yNMOk2+yxEVZksfDfnTUM11GSqrD+m1rh4j/k6BZhs0KqteaszX7Ey0puN5VAfZ EO+QjqWw10EG9rTNcLHXanrlj6jLijWThYyFLHIbka2UPyQuV7VzPd7TevYT64MZbPTo+U6sJ5Uw WzUF5AI6zVeKWnik50jDStVs0efBS6oRn6pv5pU5KwN7VmygIfXNzAwSRNeputc41aaKzPG98Q0k ejRl6tjrKVPHm9QOhbnbyblHS7UXQi727zPLjDeXpHFGOEZJo8LHyTlKzNo6vMLOLcJ0ksac2Ds5 aSxNR0rkn+91KfZRo8lT0uC6rYONwJR45j0949Ue9EzHhDbtYWfYOyfunALRuudIXLayKhUDJn0p 7SzUlKkOEvepDjY2c4nt5QkZTf4Q9nKpMxdvu5RwjDqO+KzmnWkyeorTrI4jioxSBjv3VuM9F5Ir pwxmQo5ClDIYROEVpJRBzd1JGZkqWN0drXU9O5f52TeHGVJ2jpOtnBGptyw9yLrMtajjglV6jjgq PbMQSmzSyv3gBdWWjjVXqtdZo0/JS4OuVReZah9q9IfyMa1slY89xVnO0YgMYeu6a7bZSu9awNU4 c9Humu2Fm+crbV+OE658zMEBJzlu2pZk7ZynaLOVFWitGCsweCnxjNURG4hXaIGcxLYRCQy0b6lX PLnAS1kIh21MI4emno1X/K4P4XwjJW7dpHfuTbYETJhZBMcKcEodxa/bDI4y4tQZWPYf+xw5sotC HZe8Qh2Xr0K9OO/JLLXzx7xGJ6UghvUidrzYpS8eIgtxq2KN8UZ/Je7MPFInxa87z8aZWKXFbWln mPu9gYvrTrWO9bCUZS/goEC/La1SXOTOwBELc8fUhKXCTbJwP6UMTPscrwQZyyL6PqnjmCDNGJyp 1HFZ0YaGIk0qtsvvV6AXUzE5rW+Lv8wUIinS0Skq0nFpKBZMyw8f0RbTsO3yluZn01GvWrcSxhra L7FZZ5cricOMURjLDWFsGmq+1q4P4Z5uLnHYJvtcwvfv24eqnLXt90fWZJlLYJfhcwPLKZ5ln+FX 5o7DrO6S5XZwG366B9rgm8si2uyPbKDmfnaXx30X1JsNkoWuexucS+066mXPT+L0mw4G6rH9VOq6 Nlhv9qKIRfpC4KVyxc4j6rvZY7qdLMyEs0b5yFE8xx9pRLgz3DUiPEfn2ZddR1kKfXRWnm/NB/cI c8Rg3/ZUyeONylakZ5bDUjl0OxIbjw2+m2yI84wNJ2/6j81e3ybG3xD0ppS5+ayTeWuQX1GjwVtt 9Yjqsmdo3g7Zuec1xueAbzXPkY7U0HFUsTF0mw2TxNvXm42/nXle8uYudX0L4TvSCy6i1Egbd11f rA+NlrnKR2Yy3r2PwcHE7KzMLROD58wEMZc9uE2XstkE3LFznLK1pF/eivn49OPP73/6I6/FnBSO 5O8zVOnptEm8lqyCdJrFgjQqd15l7fxVXGT9/NUIpTa0GAKNTl3mobU8FKUjBJnpzu9AWHIcbEdR y1UxjjxvWiR4MFGfF4i+aePYUEHPm65jIhEN3eRKONfnTUsXaKvzoZshwQQr0jEBUpxPIwIlbECH XxnQFSx4MaDxWsWARh4wnLGsiuEcOhDDueO7L4ozHHROssKcQ6aqMB+CPb3CfNpLWD8Kc8Nbrgpz E8zBFebzSUHeFeYZPKrBHEYM5gntclWYA5OKwTxAbcRgxsIUz0JhPUusZy1nhTmNaw1IW36kMPcD ZlSGzTGIiCjMEyterJxxKppVMzJis2ouUAfNqhknp3k1w4+smA/QombFjLg3K2asjKYoFyzvZiij r2hWzLgoutHGAeTWDWUkt06scY54MYOl7lbMyNDdihnNejeYB9LI0N3zhscozOG5+qHOF6dinPcs B9LRUJiDqA2FOajKUJgrcv9QnE+3ct3zUJylwbMPwzmc2XBGpzAU59aA6YfijFM6DWaUomncjNI8 DeYEhmdWXdpYCNNgRlCnwVyAL6eRRgYvP62aURqnVzNw6rRqRst9WDVj0R2+qwdXP5ybYVUcXM2H cQY+1mHVDE9+GGVkvLYzMxTqYcWMBHE4M4P3TEYZBV58SlbMeEjBqlR1SVbLqOXJQMYIOBnIHZKy ZCB3UJdkzJyhX0qBmVVLkjFzuVpc178DnL/p35FhG9v1b0I+bPr3DVJ9KpO/cO0ceVlHDOQGT+7y h2moy98Ap5Odl68lkl3+8A0Gl78JGWpZUHb5wwd9yB+kwS5/uGfj+he8gJUyYlq8lCGeN/1DScrV S/ni3Gz6N9Gpmv71DGiY/oVrmf7FEatlTCRM/8YAJ1IDM9sxxhgH+BfTvzCDpn8Vn0uindORGPrr iFEGzo7rX4OmwAUQK94FECtenJmhflwAM/7KmHnC7DRjZsTHBNDenDLhawW2MEz4Qv2Z8lWsUVM+ EXjPw5SvY5WY8iHfZVO+4P1M+YKv65GSdcTwxTXTbZOqwplV+XLwkKp8FTk6q/KdPR/0RaZ8Yb6j 8umTmvKFVrpbHePexIiUrCOBkvU8I9hlfXZTvhc/oQNWxjhxww0GLJCxlLELH3baw90yLOHhdAFT asqHepBN+UKXasqHtDgXtnDhw1l34UNanMEt2zHGyQ2ieBW+kjAyNuEL1WPCl/FNIhO+I3QF7pYh dDfhC3LkyofrzJQvzI1L37iExZUPl70pX0gvTPnCexWmfJdV1xFDGXtflz4QsWLSl2G2iklfSZAC JYa5PKQP9v5c+rDJT7H50xGDGRZXib2ftVFOyhCMmPbhwine+wEhlEfvB2/mee+H9+O9H24jmfiV BumOix8mjN77IaoufpgfuPghYt774Z6yiZ/+6VQMW1cmefFYo2IokVKMKnAmXfIKhN4ueZcjKNWY GNtEUzxc0MUUr4EyFFM8xL86IcOsmeCFnMwEr+NGrwsevivpggeLo7jgaRfMOlceOgclZzqnf7K6 FVc3gffpXN3CSOg77DwjtPA6gu2dNeceVkDS6t1dGDFawLa/hSbajqmhOdARpoViIocmqzRvoqHu 24CX+O0QowXICkziwkaDSRzSXzGJe+lH7RhjBXydx5o7YONivV3JkFNYb4c9RzGFQ3dQupFCh10X U7hjQHxsChcoyRTuCkV0xED+hpfesikcPvlw6oWnMoULEaspHNqGYgqHUl6GYwxrbzj3QrW7wuH6 dIW75LVM98NAGy5wSLSucIiOK1w4sfthePfIFU7gtbfJXUeZTr1QBq5weHVv7XA5Huwjird2ODeu cPoXQ1f/0sLbGTritgE2ZY4Br9DZIc4F+CM3v/BylOkZEFE1OUOSqSZnCd9wSyH7sRHPMuE03GLU Rc2qqxlUU3U1u2a4upjhGweZ67Z6I4dRmYkZCnn1Rg73GJdOrrqY4e3kmP3oiLfLF8nUzNasuphN 2PJxMcM7dDED+qolZD96h6USGK5qoNHVGzkouOqNHKyjujRytRAF16WPqzX4X72bGl801hGrW/zf WN7H4XN6Hwcmoj76OHhO7+Ogw6+VDXCtMWHTEQ4lqueY0ENUzzHrFWhV7+OADarnmCAbVbiWJcTy enFheqgudOD0qwkdhp9VKJSoJnR4xEPn4L+8uc7hfC46V13ncPpc5xpkzq5z/YqcG2cStcWsWEdC VqyJs+lcxhF2v9V1Dle+6xxOnoeYeCkPMfFtQxc62Dmsi9BVFzrMuxehqw+hg9l7CB3sE7rQ4bs0 rnSY7LvSIel5LwfNU3WlQzodC8yudOFa7ifgzcDJfqLOBWeXOpCx+mjm4CW3GXc+dKSRC6nTM3lA 3lNMXLSeYnbYFYwpph7jUod1uUhddamDyfEQE6fi4OSnHiGTt19xy1wPTn6qx5gIjzdzwFfiMSZ0 m+IxZsaRQi5XUqWiE1M/1ENJjXhGTP5Q5cXkTyCAFJM/NKOSPJm4mFC8mYMlKKZ/47hKVbyZA1Mm 3szhTozpH3YDkmMmryPecMA2kDdz4I7F9Q8stcSNPNs8Svykrn94nof+wZO6/oGLlcI9iCxtnXhb B6ZVFgEU38kreAxRs/hGHiiruAAeF49I5bxYXACxNFwAoZGSRQDlIYCXFZFFAMUFEG/QUb5IXyRR ryWPfTyoFdc/rIxF/8T1r15TI2yPRTiUF/Ht0ssqiXAoL65/wMTyEMDrblwAQcPFBRBaXHEBBOcm 7WGTpbFNlsZUIb59h/feOI+Qxj5ZPMSEjkU8xBxXTyqdQ2Lx7TuwzmLKFybAlQ8XUI+7pDoymKg8 xByws2pMgfPou3eXfxTfvAOSFNM9VFTxCDNd6i2eYeLi9c078DriGWa6Wkcx3UM9F9+8Qyx88w7s ovjuHTS34rt3iM60qBgXr+3e4caETIuKweKK6V6gTde9cGbLf9KVGonpHnLJtCQeeVRlT3AijsxE b6oXZs9kL1zJZK8i9Zvs4asOYrKHbw/J4YE8IOg9H1Kk93wvidX/AcSjJkhkRgAA --=-a7Mcbqjj69hcwK+bw4qf-- ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html -------------------------------------------------------------