Changeset 98b30b4 in sasview for src/sas/perspectives/fitting/media
- Timestamp:
- Feb 17, 2015 8:35:07 AM (9 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
- Children:
- 3702c12
- Parents:
- a37b4e6
- File:
-
- 1 edited
Legend:
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src/sas/perspectives/fitting/media/fitting_help.rst
rec392464 r98b30b4 10 10 .. |phi| unicode:: U+03C6 11 11 .. |theta| unicode:: U+03B8 12 .. |chi| unicode:: U+03C7 13 14 .. |inlineimage004| image:: sm_image004.gif 15 .. |inlineimage005| image:: sm_image005.gif 16 .. |inlineimage008| image:: sm_image008.gif 17 .. |inlineimage009| image:: sm_image009.gif 18 .. |inlineimage010| image:: sm_image010.gif 19 .. |inlineimage011| image:: sm_image011.gif 20 .. |inlineimage012| image:: sm_image012.gif 21 .. |inlineimage018| image:: sm_image018.gif 22 .. |inlineimage019| image:: sm_image019.gif 23 12 24 13 25 Fitting Perspective … … 61 73 One of two fit-engines can be chosen from the Fitting menu bar. The Simple Fit- 62 74 engine uses Scipy's leasqr and the Complex Fit-Engine is a custom optimizer 63 that provides a better chance to find the global minimum of the chi2 but that75 that provides a better chance to find the global minimum of the |chi| 2 but that 64 76 requires longer computation time. In order to set a data to a control panel 65 77 (FitPage), see the "DataLoader Help". Once a data set to the FiPage, select a … … 532 544 533 545 We use only these array values in the computation, therefore the mean value 534 given in the control panel, for example âradius = 60â, will be ignored.546 given in the control panel, for example ââ¬Ëradius = 60ââ¬â¢, will be ignored. 535 547 536 548 .. _Gaussian_Distribution: … … 560 572 normalization factor which will be determined during the numerical calculation. 561 573 The median value is the value given in the size parameter in the control panel, 562 for example, âradius = 60â.574 for example, ââ¬Åradius = 60ââ¬ï¿œ. 563 575 564 576 The PD (polydispersity) is given by /sigma/ … … 588 600 which is determined during the numerical calculation. 589 601 590 The z = 1/p2 â1.602 The z = 1/p2ââ¬â 1. 591 603 592 604 The PD (polydispersity) is … … 628 640 Equation 1 629 641 630 The functions .. image:: sm_image004.gif and .. image:: sm_image005.gif642 The functions |inlineimage004| and |inlineimage005| 631 643 refer to the slit width weighting function and the slit height weighting 632 644 determined at the q point, respectively. Here, we assumes that the weighting … … 643 655 Equation 3 644 656 645 so that .. image:: sm_image008.gif .. image:: sm_image009.gif for 646 .. image:: sm_image010.gif and u. 647 648 The .. image:: sm_image011.gif and .. image:: sm_image012.gif stand for 657 so that |inlineimage008| |inlineimage009| for |inlineimage010| and u. 658 659 The |inlineimage011| and |inlineimage012| stand for 649 660 the slit height (FWHM/2) and the slit width (FWHM/2) in the q space. Now the 650 661 integral of Equation 1 is simplified to … … 660 671 ------ 661 672 662 For .. image:: sm_image012.gif = 0 and .. image:: sm_image011.gif = 663 constant. 673 For |inlineimage012| = 0 and |inlineimage011| = constant. 664 674 665 675 .. image:: sm_image016.gif 666 676 667 677 For discrete q values, at the q values from the data points and at the q 668 values extended up to qN= qi + .. image:: sm_image011.gifthe smeared678 values extended up to qN= qi + |inlineimage011| the smeared 669 679 intensity can be calculated approximately 670 680 … … 673 683 Equation 5 674 684 675 .. image:: sm_image018.gif= 0 for *Is* in *j* < *i* or *j* > N-1*.685 |inlineimage018| = 0 for *Is* in *j* < *i* or *j* > N-1*. 676 686 677 687 Case 2 678 688 ------ 679 689 680 For .. image:: sm_image012.gif = constant and 681 .. image:: sm_image011.gif = 0. 690 For |inlineimage012| = constant and |inlineimage011| = 0. 682 691 683 692 Similarly to Case 1, we get 684 693 685 .. image:: sm_image019.gif for qp= qi- .. image:: sm_image012.gif 686 687 and qN= qi+ .. image:: sm_image012.gif. .. image:: sm_image018.gif = 0 694 |inlineimage019| for qp= qi- |inlineimage012| and qN= qi+ |inlineimage012|. |inlineimage018| = 0 688 695 for *Is* in *j* < *p* or *j* > *N-1*. 689 696 … … 691 698 ------ 692 699 693 For .. image:: sm_image011.gif= constant and694 .. image:: sm_image011.gif= constant.700 For |inlineimage011| = constant and 701 |inlineimage011| = constant. 695 702 696 703 In this case, the best way is to perform the integration, Equation 1, … … 707 714 Equation 7 708 715 709 for qp= qi- .. image:: sm_image012.gifand710 qN= qi+ .. image:: sm_image012.gif. .. image:: sm_image018.gif= 0 for716 for qp= qi- |inlineimage012| and 717 qN= qi+ |inlineimage012|. |inlineimage018| = 0 for 711 718 *Is* in *j* < *p* or *j* > *N-1*. 712 719 … … 745 752 In Equation 9, x0 = qcos/theta/ and y0 = qsin/theta/, and the primed axes 746 753 are in the coordinate rotated by an angle /theta/ around the z-axis (below) 747 so that x â0= x0cos/theta/+y0sin/theta/ and yâ0= -x0sin/theta/+y0cos/theta/.754 so that xââ¬â¢0= x0cos/theta/+y0sin/theta/ and yââ¬â¢0= -x0sin/theta/+y0cos/theta/. 748 755 749 756 Note that the rotation angle is zero for x-y symmetric elliptical Gaussian … … 754 761 Now we consider a numerical integration where each bins in /theta/ and R are 755 762 *evenly* (this is to simplify the equation below) distributed by /delta//theta/ 756 and /delta/R, respectively, and it is assumed that I(x â, yâ) is constant763 and /delta/R, respectively, and it is assumed that I(xââ¬â¢, yââ¬â¢) is constant 757 764 within the bins which in turn becomes 758 765 … … 762 769 763 770 Since we have found the weighting factor on each bin points, it is convenient 764 to transform x â-yâback to x-y coordinate (rotating it by -/theta/ around z771 to transform xââ¬â¢-yââ¬â¢ back to x-y coordinate (rotating it by -/theta/ around z 765 772 axis). Then, for the polar symmetric smear 766 773 … … 940 947 If this operation is successful, the new ftol value will be displayed in the 941 948 info line at the bottom of the SV window.Note that increasing the ftol value 942 may cause for the fitting to terminate with higher chisq.949 may cause for the fitting to terminate with higher |chi| sq. 943 950 944 951 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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