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111 KiB
JavaScript
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72, 129, 130, 209, 210, 236, 241, 242, 245, 265], "them": [1, 3, 203, 223, 233, 279], "both": [1, 11, 73, 74, 98, 99, 102, 103, 104, 111, 116, 119, 121, 132, 165, 214, 273, 278, 279], "some": [1, 2, 3, 4, 223, 233], "coeffici": [1, 185, 187, 188, 189, 190], "alpha": [1, 129, 188, 193, 242, 261, 263, 265], "beta": [1, 72, 129, 187, 188, 189, 190, 205, 213, 214, 215, 260], "respect": [1, 2, 4, 97, 129, 177, 196, 203, 205, 212, 213, 214, 215, 271, 278], "togeth": [1, 4, 129, 196], "get": [1, 2, 4, 66, 134, 192, 203, 279], "z": [1, 154], "well": [1, 3, 203, 223, 233, 236], "veri": [1, 3, 236, 279], "easili": 1, "do": [1, 3, 6, 188, 203, 224, 233, 271], "just": [1, 4], "write": [1, 3, 203, 277], "out": [1, 6, 209, 210, 230], "follow": [1, 3, 4, 5, 6, 15, 67, 72, 104, 129, 185, 186, 187, 188, 189, 190, 194, 203, 249, 250, 255, 274, 279], "import": [1, 2, 3, 4, 6, 104, 148, 154, 177, 195, 196, 197, 203, 205, 214, 225, 251, 271, 277, 278], "mx": [1, 2, 3, 4, 104, 148, 154, 177, 203, 205, 214, 218, 225, 240, 251, 255, 264, 271, 273, 274, 277, 278, 279, 280], "def": [1, 2, 3, 4, 154, 177, 203, 271, 277, 279], "simple_axpbi": 1, "float": [1, 13, 15, 57, 95, 96, 104, 130, 131, 136, 139, 140, 185, 186, 187, 188, 189, 190, 193, 194, 199, 205, 208, 209, 210, 213, 214, 215, 218, 239, 241, 245, 246, 247, 252, 254, 260, 261, 267], "return": [1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 37, 50, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 195, 196, 197, 203, 220, 222, 224, 226, 227, 228, 231, 238, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 271, 276, 277, 279], "thi": [1, 3, 4, 6, 12, 13, 14, 15, 22, 23, 24, 25, 77, 101, 104, 111, 113, 114, 115, 117, 118, 127, 128, 132, 154, 157, 158, 159, 166, 168, 178, 203, 208, 209, 210, 219, 220, 222, 223, 226, 227, 228, 231, 233, 234, 235, 236, 238, 246, 249, 250, 257, 267, 271, 276, 277], "perform": [1, 3, 5, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 114, 130, 144, 157, 168, 203, 213, 247, 279], "leav": [1, 196], "differenti": [1, 5], "howev": [1, 203, 212, 213, 274, 277], "vector": [1, 2, 5, 101, 104, 168, 179, 180, 211, 278], "math": [1, 3, 261], "often": [1, 210], "realiz": 1, "axpbi": 1, "routin": 1, "defin": [1, 2, 3, 4, 6, 104, 130, 192, 195, 277], "same": [1, 3, 6, 60, 61, 66, 67, 87, 90, 91, 92, 97, 101, 126, 132, 144, 179, 181, 203, 205, 208, 213, 214, 238, 261, 271, 274, 279], "realli": 1, "part": 1, "doe": [1, 3, 6, 203, 277], "fast": [1, 154, 212, 250, 279], "so": [1, 3, 6, 97, 154, 177, 208, 273, 279], "decid": [1, 196, 222], "want": [1, 3, 279], "reli": 1, "acceler": [1, 205], "framework": [1, 5], "continu": 1, "impos": 1, "our": [1, 3, 4, 185, 186, 187, 189, 190, 243], "assumpt": 1, "also": [1, 3, 4, 5, 11, 73, 74, 83, 86, 89, 92, 98, 99, 102, 103, 111, 116, 119, 121, 129, 165, 184, 192, 203, 222, 234, 236, 238, 242, 244, 248, 265, 266, 268, 273, 277, 278, 280], "assum": [1, 3, 196, 203, 213], "how": [1, 3, 4, 203, 206, 207, 211, 279], "gradient": [1, 2, 4, 97, 164, 177, 184, 185, 187, 188, 189, 190, 194, 203, 223, 234, 238, 257, 271, 273, 277, 278], "ins": 1, "what": [1, 3, 196], "coincid": 1, "right": [1, 129, 212, 249, 250, 254, 261], "place": [1, 3, 144, 277], "cours": 1, "The": [1, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 35, 44, 50, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 147, 152, 153, 155, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 199, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 216, 219, 225, 234, 235, 236, 238, 239, 241, 243, 245, 246, 247, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 267, 271, 273, 277, 278, 279, 280], "structur": [1, 77], "from": [1, 3, 4, 5, 72, 88, 89, 91, 92, 96, 104, 106, 114, 125, 129, 131, 132, 133, 134, 136, 139, 148, 162, 164, 165, 168, 169, 181, 183, 195, 196, 197, 203, 216, 223, 225, 236, 260, 276, 277, 278, 279], "frontend": 1, "api": 1, "redirect": 1, "when": [1, 3, 5, 6, 104, 206, 207, 255, 260, 271, 274, 279], "appropri": 1, "fallback": 1, "metal": 1, "vjp": [1, 278], "jvp": [1, 278], "In": [1, 3, 4, 114, 129, 185, 186, 187, 189, 190, 196, 203, 209, 213, 271, 276, 279], "one": [1, 3, 6, 57, 63, 66, 79, 80, 104, 109, 114, 130, 132, 162, 165, 233, 279], "sentenc": 1, "comput": [1, 2, 3, 4, 5, 6, 72, 97, 101, 104, 111, 117, 129, 154, 157, 164, 172, 177, 178, 179, 184, 185, 187, 188, 189, 190, 203, 205, 213, 214, 215, 223, 234, 238, 239, 241, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 273, 278, 279], "graph": [1, 3, 4, 5, 77, 146, 147, 154], "rule": 1, "evalu": [1, 3, 4, 77, 101, 146, 147, 179, 203, 221, 230, 271, 273, 278], "said": [1, 3], "start": [1, 2, 3, 5, 6, 15, 105, 159, 279], "discuss": 1, "more": [1, 4, 8, 57, 114, 147, 203, 205, 209, 241, 245, 274, 279], "detail": [1, 8, 185, 186, 187, 189, 190, 203, 209, 241, 245], "thei": [1, 2, 3, 67, 190, 243, 253, 271, 276, 278, 279], "c": [1, 3, 104, 199, 205, 206, 207, 209, 210, 214, 277, 278, 279], "scalar": [1, 11, 13, 26, 37, 57, 60, 61, 63, 73, 74, 95, 96, 97, 98, 99, 102, 103, 104, 105, 111, 112, 114, 116, 119, 121, 126, 136, 139, 140, 165, 177, 181, 184, 261, 278], "sum": [1, 2, 11, 104, 113, 157, 172, 203, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 277], "element": [1, 10, 11, 16, 17, 18, 19, 20, 21, 24, 52, 62, 68, 69, 72, 73, 74, 75, 76, 78, 80, 94, 95, 98, 99, 102, 103, 107, 108, 109, 110, 111, 112, 116, 119, 121, 122, 127, 129, 130, 141, 142, 145, 152, 153, 155, 156, 160, 161, 165, 168, 170, 171, 177, 181, 208, 209, 210, 217, 237, 241, 244, 262, 263, 266], "wise": [1, 10, 11, 16, 17, 18, 19, 20, 21, 62, 68, 69, 73, 74, 75, 76, 78, 94, 95, 98, 99, 102, 103, 107, 108, 109, 110, 111, 112, 116, 119, 121, 122, 141, 145, 152, 153, 155, 156, 160, 161, 165, 170, 171, 209, 210, 217, 237, 244, 262, 263, 266], "numpi": [1, 3, 4, 5, 11, 13, 15, 61, 73, 74, 98, 99, 102, 103, 111, 114, 116, 119, 121, 165, 278], "style": [1, 11, 13, 73, 74, 98, 99, 102, 103, 111, 114, 116, 119, 121, 165], "broadcast": [1, 11, 13, 61, 63, 73, 74, 96, 98, 99, 102, 103, 111, 114, 116, 119, 121, 131, 132, 139, 140, 165, 169, 181, 236], "between": [1, 5, 63, 247, 253, 254, 257, 279], "input": [1, 2, 3, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101, 102, 103, 104, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 138, 141, 142, 143, 144, 145, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 180, 181, 183, 205, 206, 207, 209, 210, 211, 213, 214, 215, 216, 236, 238, 239, 241, 246, 247, 251, 253, 254, 255, 257, 259, 261, 267, 278], "upcast": 1, "const": 1, "factor": [1, 252], "streamordevic": 1, "stream": [1, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 151, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 178, 181, 182, 183, 279], "schedul": [1, 279], "itself": 1, "call": [1, 3, 4, 27, 95, 203, 211, 223, 233, 243, 271, 273], "other": [1, 3, 5, 104, 190, 203, 224, 271, 278], "within": [1, 24], "simplest": [1, 203], "wai": [1, 3, 6, 203], "about": [1, 3, 4, 279], "term": [1, 185, 186, 187, 188, 189, 193], "exist": [1, 3, 223, 233], "auto": [1, 6], "ax": [1, 12, 14, 22, 23, 58, 79, 82, 83, 85, 86, 88, 89, 91, 92, 104, 113, 115, 117, 118, 126, 128, 157, 162, 166, 167, 172, 173, 178], "multipli": [1, 129, 130, 208, 245], "earlier": 1, "goal": 1, "themselv": 1, "contain": [1, 3, 50, 77, 87, 88, 89, 104, 112, 129, 159, 181, 203, 222, 224, 225, 247, 271], "act": [1, 257], "data": [1, 4, 5, 8, 15, 80, 90, 91, 96, 100, 105, 124, 139, 174, 182, 210, 277], "nor": [1, 97, 177], "rather": [1, 279], "easi": [1, 203], "interfac": 1, "block": [1, 3, 247], "A": [1, 3, 5, 6, 50, 60, 97, 101, 104, 106, 113, 114, 129, 131, 132, 133, 135, 136, 139, 140, 159, 163, 177, 179, 180, 184, 187, 189, 195, 196, 197, 203, 205, 209, 213, 214, 215, 217, 222, 226, 227, 234, 235, 239, 243, 245, 247, 250, 261, 262, 271, 273, 277], "It": [1, 3, 6, 97, 177, 189, 191, 203, 235, 238, 277], "creat": [1, 3, 6, 80, 100, 203, 271, 273, 277], "output": [1, 3, 6, 12, 13, 14, 15, 22, 23, 24, 61, 80, 87, 90, 91, 92, 96, 97, 100, 104, 105, 113, 115, 117, 118, 124, 125, 127, 128, 131, 132, 133, 135, 136, 139, 140, 148, 149, 157, 162, 166, 169, 174, 177, 178, 179, 180, 181, 182, 183, 205, 206, 207, 214, 216, 236, 238, 246, 247, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 267, 277, 278, 279], "given": [1, 12, 14, 24, 61, 63, 64, 72, 77, 79, 81, 82, 83, 84, 85, 86, 90, 91, 92, 96, 104, 113, 115, 117, 118, 128, 136, 144, 157, 159, 166, 174, 175, 176, 178, 208, 222, 236], "set": [1, 3, 4, 6, 192, 212, 216, 221, 223, 230, 233, 234, 238, 241, 246, 261, 267, 271, 274], "further": [1, 6], "class": [1, 3, 4, 7, 8, 9, 26, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 271], "under": [1, 104], "These": [1, 169, 279], "word": 1, "bit": [1, 72, 129, 130, 199, 218, 238], "abstract": 1, "back": [1, 3, 277], "give": [1, 3, 4, 24], "ourselv": 1, "concret": [1, 216, 279], "imag": [1, 207, 209, 210], "public": [1, 203], "explicit": [1, 274, 277], "alpha_": 1, "beta_": 1, "must": [1, 6, 63, 77, 96, 104, 131, 132, 136, 139, 140, 181, 277], "know": [1, 3], "popul": 1, "To": [1, 2, 3, 4, 6, 203, 278], "avoid": 1, "unnecessari": [1, 3], "alloc": [1, 271], "respons": 1, "space": [1, 105, 259], "void": 1, "eval_cpu": 1, "std": 1, "overrid": 1, "eval_gpu": 1, "jacobian": [1, 101, 179, 278], "product": [1, 101, 114, 128, 172, 179, 236, 278], "primal": [1, 101, 179], "tangent": [1, 20, 21, 101, 170, 171], "int": [1, 3, 4, 7, 9, 12, 14, 15, 22, 23, 24, 25, 29, 30, 31, 32, 40, 41, 42, 43, 45, 48, 50, 53, 56, 57, 59, 61, 64, 65, 66, 72, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 97, 100, 104, 105, 113, 115, 117, 118, 120, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 157, 158, 159, 162, 163, 166, 167, 168, 169, 172, 173, 174, 175, 176, 177, 178, 180, 182, 203, 205, 206, 207, 211, 213, 214, 215, 216, 236, 238, 239, 241, 245, 247, 252, 255, 259, 261, 271], "argnum": [1, 97, 177], "cotan": 1, "across": [1, 213], "pair": [1, 126, 225, 241], "repres": [1, 3, 261, 277], "axi": [1, 3, 4, 12, 14, 22, 23, 24, 25, 29, 30, 31, 32, 40, 41, 42, 43, 45, 53, 56, 59, 64, 79, 81, 84, 87, 88, 89, 90, 91, 92, 104, 113, 115, 117, 118, 120, 126, 127, 128, 132, 142, 157, 158, 159, 162, 163, 166, 167, 168, 169, 173, 178, 180, 252, 255, 259, 261], "correspond": [1, 12, 14, 57, 63, 72, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 113, 115, 118, 128, 166, 172, 180, 196], "dimens": [1, 3, 12, 14, 22, 23, 44, 50, 57, 66, 79, 88, 89, 91, 92, 93, 104, 113, 114, 115, 117, 118, 128, 129, 132, 138, 166, 169, 172, 173, 178, 205, 206, 207, 209, 210, 213, 214, 215, 236, 239, 241, 247], "vmap": [1, 278], "print": [1, 2, 3, 4, 6, 195, 196, 197, 203, 274, 277, 278], "ostream": 1, "os": [1, 6], "equival": [1, 27, 47, 58, 95, 168, 212, 235, 237, 238], "check": [1, 6, 60, 225], "bool": [1, 12, 14, 22, 23, 29, 30, 31, 32, 40, 41, 42, 43, 45, 56, 57, 59, 60, 77, 104, 113, 115, 117, 118, 128, 130, 131, 136, 139, 140, 146, 147, 166, 178, 194, 205, 206, 207, 213, 214, 215, 216, 218, 222, 223, 225, 230, 233, 236, 238, 241, 245, 247], "is_equival": 1, "privat": 1, "fall": 1, "eval": [1, 2, 3, 4, 154, 203, 271, 273, 278], "deriv": 1, "base": [1, 77, 104, 108, 110, 189, 191, 241, 247, 271, 273, 274], "abov": [1, 3, 6, 129, 175, 188, 203, 279], "demonstr": [1, 277], "treat": [1, 60, 88, 89, 91, 92, 168], "paramet": [1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 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