{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":1000,"title":"Image Processing 004: Zernike Coefficients","description":"*Fit Zernike Terms to a wavefront.*\r\n\r\nThe class notes of \u003chttp://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf Schwiegerling UofA\u003e on ANSI Standard Zernike terms is the basis for this challenge.  Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/_/rsrc/1350774824076/matlab_cody/Zernike_UA_480.jpg\u003e\u003e\r\n\r\n\r\nANSI Standard Zernike Chart:\r\n\r\n\r\n\r\n*Algorithm Description:*\r\n\r\n  M=surface array to be fit by Zernike terms; \r\n  -valid data is circle of normalized radius\u003c=1\r\n  Use the R and T arrays to create the A array\r\n  R=radial normalized distance from center of array\r\n  T=angular radian value from center of array\r\n  A=fitting array [valid_data_pts,terms]\r\n\r\n  Create A * z_fit = M(valid_data_pts)\r\n  [valid_pts,terms] * [terms,1] = [valid_pts,1]\r\n\r\n  Loop term=0:terms-1\r\n  - Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\r\n  - A(:,term+1) = z(valid_data_pts)\r\n  End Loop\r\n  \r\n  Solve for z_fit: pinv(A)*M(valid_pts)  or A\\M(valid_pts)\r\n\r\n*Inputs:* [M N R T] where N is number of Zernike terms for fit\r\n\r\n*Outputs:* [v] Zernike fit vector of length N\r\n\r\nCreation of the M surface and expected v fit vector can be seen in the Test Suite.\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 888.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 444.433px; transform-origin: 407px 444.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.15px 7.91667px; transform-origin: 109.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFit Zernike Terms to a wavefront.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe class notes of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwiegerling UofA\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.6px 7.91667px; transform-origin: 253.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 319.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 159.967px; text-align: center; transform-origin: 384px 159.967px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9667px 7.91667px; transform-origin: 92.9667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eANSI Standard Zernike Chart:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8333px 7.91667px; transform-origin: 75.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAlgorithm Description:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eM=surface array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003eto be fit by Zernike terms\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 7.91667px; transform-origin: 46.2px 7.91667px; \"\u003e-valid data \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 127.05px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 127.05px 7.91667px; \"\u003eis circle of normalized radius\u0026lt;=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eUse \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 154px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 154px 7.91667px; \"\u003ethe R and T arrays to create the A array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 77px 7.91667px; transform-origin: 77px 7.91667px; \"\u003eR=radial normalized \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003edistance from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 165.55px 7.91667px; transform-origin: 165.55px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; \"\u003eT=angular radian \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003evalue from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eA=fitting array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 84.7px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 84.7px 7.91667px; \"\u003e[valid_data_pts,terms]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 7.91667px; transform-origin: 138.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003eCreate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003eA * z_fit = M(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[valid_pts,terms] * [terms,1] = [valid_pts,1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 7.91667px; transform-origin: 73.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003eLoop \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 53.9px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 7.91667px; \"\u003eterm=0:terms-1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 250.25px 7.91667px; transform-origin: 250.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 7.91667px; transform-origin: 50.05px 7.91667px; \"\u003e- Create the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 200.2px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 200.2px 7.91667px; \"\u003e2-D array of z-terms uisng z=zern_data_v01(term,R,T)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 7.91667px; transform-origin: 127.05px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e- A(:,term+1) = z(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eEnd \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 15.4px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 15.4px 7.91667px; \"\u003eLoop\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 215.6px 7.91667px; transform-origin: 215.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 23.1px 7.91667px; transform-origin: 23.1px 7.91667px; \"\u003eSolve \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 119.35px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 119.35px 7.91667px; \"\u003efor z_fit: pinv(A)*M(valid_pts)\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 65.45px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 65.45px 7.91667px; \"\u003eor A\\M(valid_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3333px 7.91667px; transform-origin: 23.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162.55px 7.91667px; transform-origin: 162.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [M N R T] where N is number of Zernike terms for fit\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 7.91667px; transform-origin: 29.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7833px 7.91667px; transform-origin: 98.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [v] Zernike fit vector of length N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 7.91667px; transform-origin: 250.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreation of the M surface and expected v fit vector can be seen in the Test Suite.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = Zernike_Fit(M,N,R,T)\r\n% M surface array\r\n% N Number of Zernike terms for fit  0:N-1\r\n% R Radial distance from center of M array for each M location\r\n% T angle from center of M array to each M location\r\n  v=zeros(N,1);\r\nend\r\n\r\n% The function zern_data_v01 has been loaded and rehashed\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n\r\n%% zern_data_v01.m\r\n% Author: Team\r\n% function to create a zernike polynomial\r\n% Using ANSI standard zernikes\r\n\r\n% input\r\n%  j = term #\r\n%  r = normalized radial vector\r\n%  t = theta\r\n\r\nfunction z = zern_data_v01(j,r,t)\r\n\r\n    % Convert single index term to standard\r\n    n= ceil((sqrt(9+8*j)-1)/2)-1; % 0-0; 2-1; 5-2; 9-3; ...\r\n    m= 2*j-n*(n+2);\r\n    \r\n    % zernike term\r\n   \r\n    z = r*0; %zeros(size(r));\r\n        \r\n        % radial component\r\n    for s = 0:(n-abs(m))/2\r\n     z = z + (-1)^s * factorial(n-s) * r.^(n-2*s) ./ ...\r\n        (factorial(s) * factorial((n+abs(m))/2 - s) * factorial((n-abs(m))/2 - s));\r\n    end\r\n        \r\n        % angular component\r\n    z = z .* ((m\u003e=0)*cos(m*t) - (m\u003c0)*sin(m*t));\r\n    \r\n    % normalization\r\n    z = z * sqrt(2*(n+1)/(1+(m==0)));\r\n    \r\n    % value added processing\r\n    z = z .* (r\u003c=1);\r\n    \r\nend\r\n\r\n","test_suite":"fname='https://sites.google.com/site/razapor/matlab_cody/zern_data_v01.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'zern_data_v01.m')\r\n%urlwrite('http://tinyurl.com/matlab-zernike','zern_data_v01.m')\r\nrehash path\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n%%\r\nM=zeros(256);\r\nterms=6; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n% Create surface\r\nz_fit=zeros(terms,1); % Map 0:9 to 1:10\r\nz_fit(2)=1.0;\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\n% Data is a circle\r\n% Non-data is assigned NaN\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01,sprintf('v=%i %i %i %i %i %i',v))\r\n\r\n\r\n%%\r\nM=zeros(256);\r\nterms=10; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n%%\r\nM=zeros(128);\r\nterms=15; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2020-09-29T23:07:58.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-10-18T13:25:52.000Z","updated_at":"2020-09-29T23:08:49.000Z","published_at":"2012-10-21T01:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFit Zernike Terms to a wavefront.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe class notes of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwiegerling UofA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eANSI Standard Zernike Chart:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Description:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=surface array to be fit by Zernike terms; \\n-valid data is circle of normalized radius\u003c=1\\nUse the R and T arrays to create the A array\\nR=radial normalized distance from center of array\\nT=angular radian value from center of array\\nA=fitting array [valid_data_pts,terms]\\n\\nCreate A * z_fit = M(valid_data_pts)\\n[valid_pts,terms] * [terms,1] = [valid_pts,1]\\n\\nLoop term=0:terms-1\\n- Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\\n- A(:,term+1) = z(valid_data_pts)\\nEnd Loop\\n\\nSolve for z_fit: pinv(A)*M(valid_pts)  or A\\\\M(valid_pts)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M N R T] where N is number of Zernike terms for fit\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v] Zernike fit vector of length N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreation of the M surface and expected v fit vector can be seen in the Test 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Processing 004: Zernike Coefficients","description":"*Fit Zernike Terms to a wavefront.*\r\n\r\nThe class notes of \u003chttp://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf Schwiegerling UofA\u003e on ANSI Standard Zernike terms is the basis for this challenge.  Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/_/rsrc/1350774824076/matlab_cody/Zernike_UA_480.jpg\u003e\u003e\r\n\r\n\r\nANSI Standard Zernike Chart:\r\n\r\n\r\n\r\n*Algorithm Description:*\r\n\r\n  M=surface array to be fit by Zernike terms; \r\n  -valid data is circle of normalized radius\u003c=1\r\n  Use the R and T arrays to create the A array\r\n  R=radial normalized distance from center of array\r\n  T=angular radian value from center of array\r\n  A=fitting array [valid_data_pts,terms]\r\n\r\n  Create A * z_fit = M(valid_data_pts)\r\n  [valid_pts,terms] * [terms,1] = [valid_pts,1]\r\n\r\n  Loop term=0:terms-1\r\n  - Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\r\n  - A(:,term+1) = z(valid_data_pts)\r\n  End Loop\r\n  \r\n  Solve for z_fit: pinv(A)*M(valid_pts)  or A\\M(valid_pts)\r\n\r\n*Inputs:* [M N R T] where N is number of Zernike terms for fit\r\n\r\n*Outputs:* [v] Zernike fit vector of length N\r\n\r\nCreation of the M surface and expected v fit vector can be seen in the Test Suite.\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 888.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 444.433px; transform-origin: 407px 444.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.15px 7.91667px; transform-origin: 109.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFit Zernike Terms to a wavefront.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe class notes of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwiegerling UofA\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.6px 7.91667px; transform-origin: 253.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 319.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 159.967px; text-align: center; transform-origin: 384px 159.967px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9667px 7.91667px; transform-origin: 92.9667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eANSI Standard Zernike Chart:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8333px 7.91667px; transform-origin: 75.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAlgorithm Description:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eM=surface array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003eto be fit by Zernike terms\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 7.91667px; transform-origin: 46.2px 7.91667px; \"\u003e-valid data \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 127.05px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 127.05px 7.91667px; \"\u003eis circle of normalized radius\u0026lt;=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eUse \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 154px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 154px 7.91667px; \"\u003ethe R and T arrays to create the A array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 77px 7.91667px; transform-origin: 77px 7.91667px; \"\u003eR=radial normalized \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003edistance from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 165.55px 7.91667px; transform-origin: 165.55px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; \"\u003eT=angular radian \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003evalue from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eA=fitting array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 84.7px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 84.7px 7.91667px; \"\u003e[valid_data_pts,terms]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 7.91667px; transform-origin: 138.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003eCreate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003eA * z_fit = M(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[valid_pts,terms] * [terms,1] = [valid_pts,1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 7.91667px; transform-origin: 73.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003eLoop \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 53.9px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 7.91667px; \"\u003eterm=0:terms-1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 250.25px 7.91667px; transform-origin: 250.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 7.91667px; transform-origin: 50.05px 7.91667px; \"\u003e- Create the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 200.2px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 200.2px 7.91667px; \"\u003e2-D array of z-terms uisng z=zern_data_v01(term,R,T)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 7.91667px; transform-origin: 127.05px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e- A(:,term+1) = z(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eEnd \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 15.4px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 15.4px 7.91667px; \"\u003eLoop\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 215.6px 7.91667px; transform-origin: 215.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 23.1px 7.91667px; transform-origin: 23.1px 7.91667px; \"\u003eSolve \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 119.35px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 119.35px 7.91667px; \"\u003efor z_fit: pinv(A)*M(valid_pts)\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 65.45px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 65.45px 7.91667px; \"\u003eor A\\M(valid_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3333px 7.91667px; transform-origin: 23.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162.55px 7.91667px; transform-origin: 162.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [M N R T] where N is number of Zernike terms for fit\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 7.91667px; transform-origin: 29.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7833px 7.91667px; transform-origin: 98.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [v] Zernike fit vector of length N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 7.91667px; transform-origin: 250.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreation of the M surface and expected v fit vector can be seen in the Test Suite.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = Zernike_Fit(M,N,R,T)\r\n% M surface array\r\n% N Number of Zernike terms for fit  0:N-1\r\n% R Radial distance from center of M array for each M location\r\n% T angle from center of M array to each M location\r\n  v=zeros(N,1);\r\nend\r\n\r\n% The function zern_data_v01 has been loaded and rehashed\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n\r\n%% zern_data_v01.m\r\n% Author: Team\r\n% function to create a zernike polynomial\r\n% Using ANSI standard zernikes\r\n\r\n% input\r\n%  j = term #\r\n%  r = normalized radial vector\r\n%  t = theta\r\n\r\nfunction z = zern_data_v01(j,r,t)\r\n\r\n    % Convert single index term to standard\r\n    n= ceil((sqrt(9+8*j)-1)/2)-1; % 0-0; 2-1; 5-2; 9-3; ...\r\n    m= 2*j-n*(n+2);\r\n    \r\n    % zernike term\r\n   \r\n    z = r*0; %zeros(size(r));\r\n        \r\n        % radial component\r\n    for s = 0:(n-abs(m))/2\r\n     z = z + (-1)^s * factorial(n-s) * r.^(n-2*s) ./ ...\r\n        (factorial(s) * factorial((n+abs(m))/2 - s) * factorial((n-abs(m))/2 - s));\r\n    end\r\n        \r\n        % angular component\r\n    z = z .* ((m\u003e=0)*cos(m*t) - (m\u003c0)*sin(m*t));\r\n    \r\n    % normalization\r\n    z = z * sqrt(2*(n+1)/(1+(m==0)));\r\n    \r\n    % value added processing\r\n    z = z .* (r\u003c=1);\r\n    \r\nend\r\n\r\n","test_suite":"fname='https://sites.google.com/site/razapor/matlab_cody/zern_data_v01.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'zern_data_v01.m')\r\n%urlwrite('http://tinyurl.com/matlab-zernike','zern_data_v01.m')\r\nrehash path\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n%%\r\nM=zeros(256);\r\nterms=6; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n% Create surface\r\nz_fit=zeros(terms,1); % Map 0:9 to 1:10\r\nz_fit(2)=1.0;\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\n% Data is a circle\r\n% Non-data is assigned NaN\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01,sprintf('v=%i %i %i %i %i %i',v))\r\n\r\n\r\n%%\r\nM=zeros(256);\r\nterms=10; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n%%\r\nM=zeros(128);\r\nterms=15; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2020-09-29T23:07:58.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-10-18T13:25:52.000Z","updated_at":"2020-09-29T23:08:49.000Z","published_at":"2012-10-21T01:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFit Zernike Terms to a wavefront.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe class notes of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwiegerling UofA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eANSI Standard Zernike Chart:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Description:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=surface array to be fit by Zernike terms; \\n-valid data is circle of normalized radius\u003c=1\\nUse the R and T arrays to create the A array\\nR=radial normalized distance from center of array\\nT=angular radian value from center of array\\nA=fitting array [valid_data_pts,terms]\\n\\nCreate A * z_fit = M(valid_data_pts)\\n[valid_pts,terms] * [terms,1] = [valid_pts,1]\\n\\nLoop term=0:terms-1\\n- Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\\n- A(:,term+1) = z(valid_data_pts)\\nEnd Loop\\n\\nSolve for z_fit: pinv(A)*M(valid_pts)  or A\\\\M(valid_pts)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M N R T] where N is number of Zernike terms for fit\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v] Zernike fit vector of length N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreation of the M surface and expected v fit vector can be seen in the Test 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