{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":49652,"title":"Find the spot diameter from the intensity distribution matrix of single spot (circle)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 445.903px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 222.951px; transform-origin: 406.493px 222.951px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIntensity distribution will be same as \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Normal_distribution\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egaussian dsitribution\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and check for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egaussian beam distribution\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; 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: 383.49px 20px; text-align: left; transform-origin: 383.498px 20px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDistance between each index will be equal to 1 mm. Grid will be n*n matrix of distribution . n will be odd number . If n=3 center of the spot will be (2,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind spot diameter in mm.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint : w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of Intensity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex 0.0000 0.0045 0.0335 0.0045 0.0000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0335 13.5335 \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e100.0000 \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 13.5335 0.0335\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0000 0.0045 0.0335 0.0045 0.0000]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI=100 (max intensity);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI(13.5 %)=13.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eradius=1 mm;Spot diameter=2 mm\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Int(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('Int.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\nassert(isempty(strfind(filetext, 'if')),'if is forbidden')\r\nassert(isempty(strfind(filetext, 'str')),'str is forbidden')\r\nassert(isempty(strfind(filetext, 'while')),'while is forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch is forbidden')\r\n\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0002 0.0045 0.0123 0.0045 0.0002 0.0000 0.0000\r\n 0.0000 0.0002 0.0335 0.6738 1.8316 0.6738 0.0335 0.0002 0.0000\r\n 0.0000 0.0045 0.6738 13.5335 36.7879 13.5335 0.6738 0.0045 0.0000\r\n 0.0000 0.0123 1.8316 36.7879 100.0000 36.7879 1.8316 0.0123 0.0000\r\n 0.0000 0.0045 0.6738 13.5335 36.7879 13.5335 0.6738 0.0045 0.0000\r\n 0.0000 0.0002 0.0335 0.6738 1.8316 0.6738 0.0335 0.0002 0.0000\r\n 0.0000 0.0000 0.0002 0.0045 0.0123 0.0045 0.0002 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),4))\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0003 0.0069 0.0189 0.0069 0.0003 0.0000 0.0000\r\n 0.0000 0.0003 0.0513 1.0309 2.8023 1.0309 0.0513 0.0003 0.0000\r\n 0.0000 0.0069 1.0309 20.7063 56.2856 20.7063 1.0309 0.0069 0.0000\r\n 0.0000 0.0189 2.8023 56.2856 153.0000 56.2856 2.8023 0.0189 0.0000\r\n 0.0000 0.0069 1.0309 20.7063 56.2856 20.7063 1.0309 0.0069 0.0000\r\n 0.0000 0.0003 0.0513 1.0309 2.8023 1.0309 0.0513 0.0003 0.0000\r\n 0.0000 0.0000 0.0003 0.0069 0.0189 0.0069 0.0003 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),4))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0188 0.1387 0.0188 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0003 0.1387 1.0250 0.1387 0.0003 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0188 0.1387 0.0188 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),2))\r\n\r\n%%\r\nx = [ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0007 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0091 0.0407 0.0671 0.0407 0.0091 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0247 0.3007 1.3476 2.2218 1.3476 0.3007 0.0247 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0091 0.3007 3.6631 16.4170 27.0671 16.4170 3.6631 0.3007 0.0091 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0005 0.0407 1.3476 16.4170 73.5759 121.3061 73.5759 16.4170 1.3476 0.0407 0.0005 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0007 0.0671 2.2218 27.0671 121.3061 200.0000 121.3061 27.0671 2.2218 0.0671 0.0007 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0005 0.0407 1.3476 16.4170 73.5759 121.3061 73.5759 16.4170 1.3476 0.0407 0.0005 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0091 0.3007 3.6631 16.4170 27.0671 16.4170 3.6631 0.3007 0.0091 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0247 0.3007 1.3476 2.2218 1.3476 0.3007 0.0247 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0091 0.0407 0.0671 0.0407 0.0091 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0007 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),8))\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0036 0.0070 0.0036 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 0.0517 0.3818 0.7436 0.3818 0.0517 0.0018 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0517 1.4484 10.7022 20.8450 10.7022 1.4484 0.0517 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0036 0.3818 10.7022 79.0791 154.0251 79.0791 10.7022 0.3818 0.0036 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0070 0.7436 20.8450 154.0251 300.0000 154.0251 20.8450 0.7436 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0036 0.3818 10.7022 79.0791 154.0251 79.0791 10.7022 0.3818 0.0036 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0517 1.4484 10.7022 20.8450 10.7022 1.4484 0.0517 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 0.0517 0.3818 0.7436 0.3818 0.0517 0.0018 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0036 0.0070 0.0036 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000]\r\n\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0018 0.0035 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0009 0.0262 0.1934 0.3768 0.1934 0.0262 0.0009 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0002 0.0262 0.7338 5.4224 10.5615 5.4224 0.7338 0.0262 0.0002 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0018 0.1934 5.4224 40.0668 78.0394 40.0668 5.4224 0.1934 0.0018 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0035 0.3768 10.5615 78.0394 152.0000 78.0394 10.5615 0.3768 0.0035 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0018 0.1934 5.4224 40.0668 78.0394 40.0668 5.4224 0.1934 0.0018 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0002 0.0262 0.7338 5.4224 10.5615 5.4224 0.7338 0.0262 0.0002 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0009 0.0262 0.1934 0.3768 0.1934 0.0262 0.0009 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0018 0.0035 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0120 0.0233 0.0120 0.0016 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0001 0.0061 0.1721 1.2714 2.4763 1.2714 0.1721 0.0061 0.0001 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0016 0.1721 4.8231 35.6383 69.4140 35.6383 4.8231 0.1721 0.0016 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0120 1.2714 35.6383 263.3335 512.9037 263.3335 35.6383 1.2714 0.0120 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0001 0.0233 2.4763 69.4140 512.9037 999.0000 512.9037 69.4140 2.4763 0.0233 0.0001 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0120 1.2714 35.6383 263.3335 512.9037 263.3335 35.6383 1.2714 0.0120 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0016 0.1721 4.8231 35.6383 69.4140 35.6383 4.8231 0.1721 0.0016 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0001 0.0061 0.1721 1.2714 2.4763 1.2714 0.1721 0.0061 0.0001 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0120 0.0233 0.0120 0.0016 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0001 0.0007 0.0044 0.0197 0.0633 0.1456 0.2401 0.2837 0.2401 0.1456 0.0633 0.0197 0.0044 0.0007 0.0001\r\n 0.0007 0.0061 0.0384 0.1721 0.5525 1.2714 2.0961 2.4763 2.0961 1.2714 0.5525 0.1721 0.0384 0.0061 0.0007\r\n 0.0044 0.0384 0.2401 1.0762 3.4559 7.9520 13.1106 15.4883 13.1106 7.9520 3.4559 1.0762 0.2401 0.0384 0.0044\r\n 0.0197 0.1721 1.0762 4.8231 15.4883 35.6383 58.7577 69.4140 58.7577 35.6383 15.4883 4.8231 1.0762 0.1721 0.0197\r\n 0.0633 0.5525 3.4559 15.4883 49.7373 114.4443 188.6867 222.9070 188.6867 114.4443 49.7373 15.4883 3.4559 0.5525 0.0633\r\n 0.1456 1.2714 7.9520 35.6383 114.4443 263.3335 434.1636 512.9037 434.1636 263.3335 114.4443 35.6383 7.9520 1.2714 0.1456\r\n 0.2401 2.0961 13.1106 58.7577 188.6867 434.1636 715.8148 845.6352 715.8148 434.1636 188.6867 58.7577 13.1106 2.0961 0.2401\r\n 0.2837 2.4763 15.4883 69.4140 222.9070 512.9037 845.6352 999.0000 845.6352 512.9037 222.9070 69.4140 15.4883 2.4763 0.2837\r\n 0.2401 2.0961 13.1106 58.7577 188.6867 434.1636 715.8148 845.6352 715.8148 434.1636 188.6867 58.7577 13.1106 2.0961 0.2401\r\n 0.1456 1.2714 7.9520 35.6383 114.4443 263.3335 434.1636 512.9037 434.1636 263.3335 114.4443 35.6383 7.9520 1.2714 0.1456\r\n 0.0633 0.5525 3.4559 15.4883 49.7373 114.4443 188.6867 222.9070 188.6867 114.4443 49.7373 15.4883 3.4559 0.5525 0.0633\r\n 0.0197 0.1721 1.0762 4.8231 15.4883 35.6383 58.7577 69.4140 58.7577 35.6383 15.4883 4.8231 1.0762 0.1721 0.0197\r\n 0.0044 0.0384 0.2401 1.0762 3.4559 7.9520 13.1106 15.4883 13.1106 7.9520 3.4559 1.0762 0.2401 0.0384 0.0044\r\n 0.0007 0.0061 0.0384 0.1721 0.5525 1.2714 2.0961 2.4763 2.0961 1.2714 0.5525 0.1721 0.0384 0.0061 0.0007\r\n 0.0001 0.0007 0.0044 0.0197 0.0633 0.1456 0.2401 0.2837 0.2401 0.1456 0.0633 0.0197 0.0044 0.0007 0.0001];\r\n\r\nassert(isequal(Int(x),24))\r\n\r\n%%\r\nx=[ 0.0000 0.0001 0.0005 0.0023 0.0077 0.0208 0.0454 0.0790 0.1103 0.1233 0.1103 0.0790 0.0454 0.0208 0.0077 0.0023 0.0005 0.0001 0.0000\r\n 0.0001 0.0007 0.0035 0.0149 0.0507 0.1378 0.2999 0.5227 0.7294 0.8152 0.7294 0.5227 0.2999 0.1378 0.0507 0.0149 0.0035 0.0007 0.0001\r\n 0.0005 0.0035 0.0186 0.0790 0.2683 0.7294 1.5877 2.7673 3.8621 4.3159 3.8621 2.7673 1.5877 0.7294 0.2683 0.0790 0.0186 0.0035 0.0005\r\n 0.0023 0.0149 0.0790 0.3351 1.1377 3.0925 6.7312 11.7319 16.3732 18.2973 16.3732 11.7319 6.7312 3.0925 1.1377 0.3351 0.0790 0.0149 0.0023\r\n 0.0077 0.0507 0.2683 1.1377 3.8621 10.4982 22.8506 39.8265 55.5824 62.1143 55.5824 39.8265 22.8506 10.4982 3.8621 1.1377 0.2683 0.0507 0.0077\r\n 0.0208 0.1378 0.7294 3.0925 10.4982 28.5369 62.1143 108.2597 151.0885 168.8443 151.0885 108.2597 62.1143 28.5369 10.4982 3.0925 0.7294 0.1378 0.0208\r\n 0.0454 0.2999 1.5877 6.7312 22.8506 62.1143 135.1999 235.6412 328.8638 367.5116 328.8638 235.6412 135.1999 62.1143 22.8506 6.7312 1.5877 0.2999 0.0454\r\n 0.0790 0.5227 2.7673 11.7319 39.8265 108.2597 235.6412 410.7012 573.1797 640.5392 573.1797 410.7012 235.6412 108.2597 39.8265 11.7319 2.7673 0.5227 0.0790\r\n 0.1103 0.7294 3.8621 16.3732 55.5824 151.0885 328.8638 573.1797 799.9367 893.9445 799.9367 573.1797 328.8638 151.0885 55.5824 16.3732 3.8621 0.7294 0.1103\r\n 0.1233 0.8152 4.3159 18.2973 62.1143 168.8443 367.5116 640.5392 893.9445 999.0000 893.9445 640.5392 367.5116 168.8443 62.1143 18.2973 4.3159 0.8152 0.1233\r\n 0.1103 0.7294 3.8621 16.3732 55.5824 151.0885 328.8638 573.1797 799.9367 893.9445 799.9367 573.1797 328.8638 151.0885 55.5824 16.3732 3.8621 0.7294 0.1103\r\n 0.0790 0.5227 2.7673 11.7319 39.8265 108.2597 235.6412 410.7012 573.1797 640.5392 573.1797 410.7012 235.6412 108.2597 39.8265 11.7319 2.7673 0.5227 0.0790\r\n 0.0454 0.2999 1.5877 6.7312 22.8506 62.1143 135.1999 235.6412 328.8638 367.5116 328.8638 235.6412 135.1999 62.1143 22.8506 6.7312 1.5877 0.2999 0.0454\r\n 0.0208 0.1378 0.7294 3.0925 10.4982 28.5369 62.1143 108.2597 151.0885 168.8443 151.0885 108.2597 62.1143 28.5369 10.4982 3.0925 0.7294 0.1378 0.0208\r\n 0.0077 0.0507 0.2683 1.1377 3.8621 10.4982 22.8506 39.8265 55.5824 62.1143 55.5824 39.8265 22.8506 10.4982 3.8621 1.1377 0.2683 0.0507 0.0077\r\n 0.0023 0.0149 0.0790 0.3351 1.1377 3.0925 6.7312 11.7319 16.3732 18.2973 16.3732 11.7319 6.7312 3.0925 1.1377 0.3351 0.0790 0.0149 0.0023\r\n 0.0005 0.0035 0.0186 0.0790 0.2683 0.7294 1.5877 2.7673 3.8621 4.3159 3.8621 2.7673 1.5877 0.7294 0.2683 0.0790 0.0186 0.0035 0.0005\r\n 0.0001 0.0007 0.0035 0.0149 0.0507 0.1378 0.2999 0.5227 0.7294 0.8152 0.7294 0.5227 0.2999 0.1378 0.0507 0.0149 0.0035 0.0007 0.0001\r\n 0.0000 0.0001 0.0005 0.0023 0.0077 0.0208 0.0454 0.0790 0.1103 0.1233 0.1103 0.0790 0.0454 0.0208 0.0077 0.0023 0.0005 0.0001 0.0000];\r\n\r\nassert(isequal(Int(x),36))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":610936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2021-01-05T18:44:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-28T20:35:54.000Z","updated_at":"2025-12-09T19:47:07.000Z","published_at":"2020-12-28T21:31:27.000Z","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:t\u003eIntensity distribution will be same as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Normal_distribution\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egaussian dsitribution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and check for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egaussian beam distribution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eDistance between each index will be equal to 1 mm. Grid will be n*n matrix of distribution . n will be odd number . If n=3 center of the spot will be (2,2)\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\u003eFind spot diameter in mm.\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\u003eHint : w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of Intensity\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\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:t\u003eexample \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\u003ex 0.0000 0.0045 0.0335 0.0045 0.0000\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\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\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\u003e 0.0335 13.5335 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e100.0000 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 13.5335 0.0335\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\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\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\u003e 0.0000 0.0045 0.0335 0.0045 0.0000]\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\u003eI=100 (max intensity);\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\u003eI(13.5 %)=13.5\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\u003eradius=1 mm;Spot diameter=2 mm\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\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":49652,"title":"Find the spot diameter from the intensity distribution matrix of single spot (circle)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 445.903px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 222.951px; transform-origin: 406.493px 222.951px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIntensity distribution will be same as \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Normal_distribution\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egaussian dsitribution\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and check for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egaussian beam distribution\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; 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: 383.49px 20px; text-align: left; transform-origin: 383.498px 20px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDistance between each index will be equal to 1 mm. Grid will be n*n matrix of distribution . n will be odd number . If n=3 center of the spot will be (2,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind spot diameter in mm.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint : w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of Intensity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex 0.0000 0.0045 0.0335 0.0045 0.0000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0335 13.5335 \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e100.0000 \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 13.5335 0.0335\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 0.0000 0.0045 0.0335 0.0045 0.0000]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI=100 (max intensity);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI(13.5 %)=13.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eradius=1 mm;Spot diameter=2 mm\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; 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: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Int(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('Int.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\nassert(isempty(strfind(filetext, 'if')),'if is forbidden')\r\nassert(isempty(strfind(filetext, 'str')),'str is forbidden')\r\nassert(isempty(strfind(filetext, 'while')),'while is forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch is forbidden')\r\n\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0002 0.0045 0.0123 0.0045 0.0002 0.0000 0.0000\r\n 0.0000 0.0002 0.0335 0.6738 1.8316 0.6738 0.0335 0.0002 0.0000\r\n 0.0000 0.0045 0.6738 13.5335 36.7879 13.5335 0.6738 0.0045 0.0000\r\n 0.0000 0.0123 1.8316 36.7879 100.0000 36.7879 1.8316 0.0123 0.0000\r\n 0.0000 0.0045 0.6738 13.5335 36.7879 13.5335 0.6738 0.0045 0.0000\r\n 0.0000 0.0002 0.0335 0.6738 1.8316 0.6738 0.0335 0.0002 0.0000\r\n 0.0000 0.0000 0.0002 0.0045 0.0123 0.0045 0.0002 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),4))\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0003 0.0069 0.0189 0.0069 0.0003 0.0000 0.0000\r\n 0.0000 0.0003 0.0513 1.0309 2.8023 1.0309 0.0513 0.0003 0.0000\r\n 0.0000 0.0069 1.0309 20.7063 56.2856 20.7063 1.0309 0.0069 0.0000\r\n 0.0000 0.0189 2.8023 56.2856 153.0000 56.2856 2.8023 0.0189 0.0000\r\n 0.0000 0.0069 1.0309 20.7063 56.2856 20.7063 1.0309 0.0069 0.0000\r\n 0.0000 0.0003 0.0513 1.0309 2.8023 1.0309 0.0513 0.0003 0.0000\r\n 0.0000 0.0000 0.0003 0.0069 0.0189 0.0069 0.0003 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),4))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0188 0.1387 0.0188 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0003 0.1387 1.0250 0.1387 0.0003 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0188 0.1387 0.0188 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),2))\r\n\r\n%%\r\nx = [ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0007 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0091 0.0407 0.0671 0.0407 0.0091 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0247 0.3007 1.3476 2.2218 1.3476 0.3007 0.0247 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0091 0.3007 3.6631 16.4170 27.0671 16.4170 3.6631 0.3007 0.0091 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0005 0.0407 1.3476 16.4170 73.5759 121.3061 73.5759 16.4170 1.3476 0.0407 0.0005 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0007 0.0671 2.2218 27.0671 121.3061 200.0000 121.3061 27.0671 2.2218 0.0671 0.0007 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0005 0.0407 1.3476 16.4170 73.5759 121.3061 73.5759 16.4170 1.3476 0.0407 0.0005 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0091 0.3007 3.6631 16.4170 27.0671 16.4170 3.6631 0.3007 0.0091 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0247 0.3007 1.3476 2.2218 1.3476 0.3007 0.0247 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0091 0.0407 0.0671 0.0407 0.0091 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0007 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),8))\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0036 0.0070 0.0036 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 0.0517 0.3818 0.7436 0.3818 0.0517 0.0018 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0517 1.4484 10.7022 20.8450 10.7022 1.4484 0.0517 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0036 0.3818 10.7022 79.0791 154.0251 79.0791 10.7022 0.3818 0.0036 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0070 0.7436 20.8450 154.0251 300.0000 154.0251 20.8450 0.7436 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0036 0.3818 10.7022 79.0791 154.0251 79.0791 10.7022 0.3818 0.0036 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0517 1.4484 10.7022 20.8450 10.7022 1.4484 0.0517 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 0.0517 0.3818 0.7436 0.3818 0.0517 0.0018 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0036 0.0070 0.0036 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000]\r\n\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0018 0.0035 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0009 0.0262 0.1934 0.3768 0.1934 0.0262 0.0009 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0002 0.0262 0.7338 5.4224 10.5615 5.4224 0.7338 0.0262 0.0002 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0018 0.1934 5.4224 40.0668 78.0394 40.0668 5.4224 0.1934 0.0018 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0035 0.3768 10.5615 78.0394 152.0000 78.0394 10.5615 0.3768 0.0035 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0018 0.1934 5.4224 40.0668 78.0394 40.0668 5.4224 0.1934 0.0018 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0002 0.0262 0.7338 5.4224 10.5615 5.4224 0.7338 0.0262 0.0002 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0009 0.0262 0.1934 0.3768 0.1934 0.0262 0.0009 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0018 0.0035 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0120 0.0233 0.0120 0.0016 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0001 0.0061 0.1721 1.2714 2.4763 1.2714 0.1721 0.0061 0.0001 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0016 0.1721 4.8231 35.6383 69.4140 35.6383 4.8231 0.1721 0.0016 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0120 1.2714 35.6383 263.3335 512.9037 263.3335 35.6383 1.2714 0.0120 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0001 0.0233 2.4763 69.4140 512.9037 999.0000 512.9037 69.4140 2.4763 0.0233 0.0001 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0120 1.2714 35.6383 263.3335 512.9037 263.3335 35.6383 1.2714 0.0120 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0016 0.1721 4.8231 35.6383 69.4140 35.6383 4.8231 0.1721 0.0016 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0001 0.0061 0.1721 1.2714 2.4763 1.2714 0.1721 0.0061 0.0001 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0120 0.0233 0.0120 0.0016 0.0001 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\r\n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];\r\n\r\nassert(isequal(Int(x),6))\r\n\r\n%%\r\nx=[ 0.0001 0.0007 0.0044 0.0197 0.0633 0.1456 0.2401 0.2837 0.2401 0.1456 0.0633 0.0197 0.0044 0.0007 0.0001\r\n 0.0007 0.0061 0.0384 0.1721 0.5525 1.2714 2.0961 2.4763 2.0961 1.2714 0.5525 0.1721 0.0384 0.0061 0.0007\r\n 0.0044 0.0384 0.2401 1.0762 3.4559 7.9520 13.1106 15.4883 13.1106 7.9520 3.4559 1.0762 0.2401 0.0384 0.0044\r\n 0.0197 0.1721 1.0762 4.8231 15.4883 35.6383 58.7577 69.4140 58.7577 35.6383 15.4883 4.8231 1.0762 0.1721 0.0197\r\n 0.0633 0.5525 3.4559 15.4883 49.7373 114.4443 188.6867 222.9070 188.6867 114.4443 49.7373 15.4883 3.4559 0.5525 0.0633\r\n 0.1456 1.2714 7.9520 35.6383 114.4443 263.3335 434.1636 512.9037 434.1636 263.3335 114.4443 35.6383 7.9520 1.2714 0.1456\r\n 0.2401 2.0961 13.1106 58.7577 188.6867 434.1636 715.8148 845.6352 715.8148 434.1636 188.6867 58.7577 13.1106 2.0961 0.2401\r\n 0.2837 2.4763 15.4883 69.4140 222.9070 512.9037 845.6352 999.0000 845.6352 512.9037 222.9070 69.4140 15.4883 2.4763 0.2837\r\n 0.2401 2.0961 13.1106 58.7577 188.6867 434.1636 715.8148 845.6352 715.8148 434.1636 188.6867 58.7577 13.1106 2.0961 0.2401\r\n 0.1456 1.2714 7.9520 35.6383 114.4443 263.3335 434.1636 512.9037 434.1636 263.3335 114.4443 35.6383 7.9520 1.2714 0.1456\r\n 0.0633 0.5525 3.4559 15.4883 49.7373 114.4443 188.6867 222.9070 188.6867 114.4443 49.7373 15.4883 3.4559 0.5525 0.0633\r\n 0.0197 0.1721 1.0762 4.8231 15.4883 35.6383 58.7577 69.4140 58.7577 35.6383 15.4883 4.8231 1.0762 0.1721 0.0197\r\n 0.0044 0.0384 0.2401 1.0762 3.4559 7.9520 13.1106 15.4883 13.1106 7.9520 3.4559 1.0762 0.2401 0.0384 0.0044\r\n 0.0007 0.0061 0.0384 0.1721 0.5525 1.2714 2.0961 2.4763 2.0961 1.2714 0.5525 0.1721 0.0384 0.0061 0.0007\r\n 0.0001 0.0007 0.0044 0.0197 0.0633 0.1456 0.2401 0.2837 0.2401 0.1456 0.0633 0.0197 0.0044 0.0007 0.0001];\r\n\r\nassert(isequal(Int(x),24))\r\n\r\n%%\r\nx=[ 0.0000 0.0001 0.0005 0.0023 0.0077 0.0208 0.0454 0.0790 0.1103 0.1233 0.1103 0.0790 0.0454 0.0208 0.0077 0.0023 0.0005 0.0001 0.0000\r\n 0.0001 0.0007 0.0035 0.0149 0.0507 0.1378 0.2999 0.5227 0.7294 0.8152 0.7294 0.5227 0.2999 0.1378 0.0507 0.0149 0.0035 0.0007 0.0001\r\n 0.0005 0.0035 0.0186 0.0790 0.2683 0.7294 1.5877 2.7673 3.8621 4.3159 3.8621 2.7673 1.5877 0.7294 0.2683 0.0790 0.0186 0.0035 0.0005\r\n 0.0023 0.0149 0.0790 0.3351 1.1377 3.0925 6.7312 11.7319 16.3732 18.2973 16.3732 11.7319 6.7312 3.0925 1.1377 0.3351 0.0790 0.0149 0.0023\r\n 0.0077 0.0507 0.2683 1.1377 3.8621 10.4982 22.8506 39.8265 55.5824 62.1143 55.5824 39.8265 22.8506 10.4982 3.8621 1.1377 0.2683 0.0507 0.0077\r\n 0.0208 0.1378 0.7294 3.0925 10.4982 28.5369 62.1143 108.2597 151.0885 168.8443 151.0885 108.2597 62.1143 28.5369 10.4982 3.0925 0.7294 0.1378 0.0208\r\n 0.0454 0.2999 1.5877 6.7312 22.8506 62.1143 135.1999 235.6412 328.8638 367.5116 328.8638 235.6412 135.1999 62.1143 22.8506 6.7312 1.5877 0.2999 0.0454\r\n 0.0790 0.5227 2.7673 11.7319 39.8265 108.2597 235.6412 410.7012 573.1797 640.5392 573.1797 410.7012 235.6412 108.2597 39.8265 11.7319 2.7673 0.5227 0.0790\r\n 0.1103 0.7294 3.8621 16.3732 55.5824 151.0885 328.8638 573.1797 799.9367 893.9445 799.9367 573.1797 328.8638 151.0885 55.5824 16.3732 3.8621 0.7294 0.1103\r\n 0.1233 0.8152 4.3159 18.2973 62.1143 168.8443 367.5116 640.5392 893.9445 999.0000 893.9445 640.5392 367.5116 168.8443 62.1143 18.2973 4.3159 0.8152 0.1233\r\n 0.1103 0.7294 3.8621 16.3732 55.5824 151.0885 328.8638 573.1797 799.9367 893.9445 799.9367 573.1797 328.8638 151.0885 55.5824 16.3732 3.8621 0.7294 0.1103\r\n 0.0790 0.5227 2.7673 11.7319 39.8265 108.2597 235.6412 410.7012 573.1797 640.5392 573.1797 410.7012 235.6412 108.2597 39.8265 11.7319 2.7673 0.5227 0.0790\r\n 0.0454 0.2999 1.5877 6.7312 22.8506 62.1143 135.1999 235.6412 328.8638 367.5116 328.8638 235.6412 135.1999 62.1143 22.8506 6.7312 1.5877 0.2999 0.0454\r\n 0.0208 0.1378 0.7294 3.0925 10.4982 28.5369 62.1143 108.2597 151.0885 168.8443 151.0885 108.2597 62.1143 28.5369 10.4982 3.0925 0.7294 0.1378 0.0208\r\n 0.0077 0.0507 0.2683 1.1377 3.8621 10.4982 22.8506 39.8265 55.5824 62.1143 55.5824 39.8265 22.8506 10.4982 3.8621 1.1377 0.2683 0.0507 0.0077\r\n 0.0023 0.0149 0.0790 0.3351 1.1377 3.0925 6.7312 11.7319 16.3732 18.2973 16.3732 11.7319 6.7312 3.0925 1.1377 0.3351 0.0790 0.0149 0.0023\r\n 0.0005 0.0035 0.0186 0.0790 0.2683 0.7294 1.5877 2.7673 3.8621 4.3159 3.8621 2.7673 1.5877 0.7294 0.2683 0.0790 0.0186 0.0035 0.0005\r\n 0.0001 0.0007 0.0035 0.0149 0.0507 0.1378 0.2999 0.5227 0.7294 0.8152 0.7294 0.5227 0.2999 0.1378 0.0507 0.0149 0.0035 0.0007 0.0001\r\n 0.0000 0.0001 0.0005 0.0023 0.0077 0.0208 0.0454 0.0790 0.1103 0.1233 0.1103 0.0790 0.0454 0.0208 0.0077 0.0023 0.0005 0.0001 0.0000];\r\n\r\nassert(isequal(Int(x),36))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":610936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2021-01-05T18:44:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-28T20:35:54.000Z","updated_at":"2025-12-09T19:47:07.000Z","published_at":"2020-12-28T21:31:27.000Z","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:t\u003eIntensity distribution will be same as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Normal_distribution\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egaussian dsitribution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and check for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egaussian beam distribution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eDistance between each index will be equal to 1 mm. Grid will be n*n matrix of distribution . n will be odd number . If n=3 center of the spot will be (2,2)\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\u003eFind spot diameter in mm.\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\u003eHint : w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of Intensity\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\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:t\u003eexample \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\u003ex 0.0000 0.0045 0.0335 0.0045 0.0000\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\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\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\u003e 0.0335 13.5335 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e100.0000 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 13.5335 0.0335\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\u003e 0.0045 1.8316 13.5335 1.8316 0.0045\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\u003e 0.0000 0.0045 0.0335 0.0045 0.0000]\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\u003eI=100 (max intensity);\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\u003eI(13.5 %)=13.5\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 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