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150, 151, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 200, 201, 202, 203, 204, 205, 207, 209, 210, 211, 212, 213, 214, 215, 216, 217, 227, 230, 231, 232, 233, 234, 235, 236, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 259, 260, 262, 263, 264, 265, 266, 267, 268, 269, 270, 272, 273, 274, 275, 276, 278, 279, 281, 305, 307, 308, 311, 312], "return": [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 29, 42, 60, 69, 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, 103, 104, 105, 106, 109, 110, 111, 113, 114, 115, 116, 118, 119, 120, 122, 123, 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, 150, 151, 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, 185, 186, 187, 188, 189, 190, 192, 196, 197, 200, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 299, 304, 305, 306, 307, 308, 309, 310, 312, 313], "scalar": [5, 6, 8, 22, 42, 69, 73, 78, 79, 80, 81, 82, 84, 113, 114, 118, 146, 147, 150, 151, 152, 153, 156, 163, 164, 165, 169, 173, 179, 180, 181, 182, 184, 186, 201, 203, 204, 207, 211, 213, 218, 225, 228, 229, 231, 234, 238, 258, 274, 276, 279, 283, 307, 309, 311], "b": [5, 6, 8, 16, 73, 78, 79, 80, 81, 113, 114, 118, 128, 146, 148, 151, 152, 155, 156, 163, 164, 165, 169, 179, 180, 182, 184, 186, 201, 203, 207, 210, 213, 215, 222, 231, 234, 258, 266, 274, 287, 288, 307, 308, 309, 310, 311, 312, 313], "addit": [5, 6, 127, 129, 131, 174, 307], "two": [5, 6, 8, 16, 73, 76, 78, 79, 80, 81, 106, 113, 118, 133, 136, 142, 148, 149, 151, 152, 156, 164, 165, 166, 167, 168, 170, 171, 172, 179, 184, 186, 201, 203, 207, 210, 260, 288, 305, 306, 307, 308, 313], "style": [5, 8, 78, 79, 80, 113, 114, 118, 151, 152, 156, 163, 164, 165, 179, 184, 186, 201, 203, 207, 213, 231, 234, 258], "broadcast": [5, 8, 78, 79, 80, 82, 84, 113, 114, 118, 147, 151, 152, 156, 163, 164, 165, 179, 184, 186, 201, 203, 207, 213, 218, 219, 223, 228, 229, 231, 234, 258, 263, 279], "semant": [5, 78, 79, 80, 82, 113, 114, 118, 151, 152, 163, 164, 165, 179, 184, 186, 201, 203, 207, 213, 231, 234, 258, 313], "either": [5, 57, 69, 70, 78, 79, 80, 84, 113, 114, 118, 146, 151, 152, 163, 164, 165, 169, 179, 184, 186, 201, 203, 207, 213, 231, 234, 258, 274, 310], "both": [5, 78, 79, 80, 113, 114, 118, 151, 152, 161, 163, 164, 165, 169, 179, 186, 201, 203, 207, 213, 219, 231, 234, 258, 282, 301, 305, 306, 307, 311, 313], "sum": [5, 99, 110, 155, 169, 183, 248, 266, 269, 299, 306, 308, 310], "c": [6, 169, 310, 311, 313], "alpha": [6, 215], "1": [6, 10, 20, 21, 30, 38, 41, 89, 90, 91, 92, 105, 106, 124, 128, 131, 132, 133, 135, 136, 138, 139, 140, 141, 142, 143, 144, 153, 155, 161, 167, 169, 170, 184, 188, 197, 210, 212, 215, 219, 222, 223, 224, 229, 244, 249, 262, 268, 269, 274, 284, 287, 288, 292, 299, 301, 305, 306, 307, 308, 310, 311, 312, 313], "beta": [6, 104, 126, 215, 301], "matrix": [6, 37, 81, 104, 105, 125, 126, 148, 149, 153, 154, 166, 167, 168, 169, 170, 171, 172, 184, 188, 215, 216, 223], "multipl": [6, 81, 127, 129, 148, 149, 184, 203, 215, 216, 305, 309, 312], "option": [6, 7, 9, 10, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 81, 85, 86, 89, 90, 91, 92, 93, 96, 97, 98, 99, 100, 104, 105, 106, 111, 125, 126, 127, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 153, 154, 159, 160, 166, 167, 168, 169, 170, 171, 172, 173, 174, 183, 185, 187, 188, 197, 200, 204, 208, 211, 212, 214, 215, 216, 218, 219, 220, 222, 223, 224, 225, 227, 228, 229, 232, 233, 248, 249, 250, 253, 254, 255, 259, 261, 262, 266, 268, 269, 270, 271, 272, 273, 274, 275, 278, 280, 282, 285, 286, 287, 288, 302, 305, 312, 314], "scale": [6, 104, 126, 127, 129, 130, 131, 149, 153, 215, 216, 222, 224, 284], "possibli": [6, 81, 148, 184, 284], "batch": [6, 81, 148, 149, 184, 223, 309], "add": [6, 30, 123, 179, 211, 215, 307, 313], "result": [6, 10, 30, 69, 74, 85, 127, 129, 149, 169, 184, 216, 223, 232, 254, 286, 287, 288, 305, 307, 310], "factor": [6, 153, 166, 167, 170], "product": [6, 74, 98, 155, 162, 184, 210, 214, 266, 277, 311], "default": [6, 7, 8, 9, 10, 18, 19, 20, 21, 73, 74, 81, 85, 86, 89, 90, 91, 92, 100, 101, 102, 104, 105, 106, 109, 110, 111, 125, 126, 128, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 148, 149, 150, 153, 154, 156, 166, 167, 168, 169, 170, 171, 172, 173, 174, 183, 185, 187, 188, 196, 197, 200, 204, 208, 211, 212, 214, 215, 216, 218, 219, 220, 222, 223, 224, 225, 227, 228, 229, 232, 233, 235, 242, 243, 249, 250, 253, 254, 255, 257, 259, 261, 266, 268, 269, 270, 271, 272, 273, 274, 275, 278, 280, 282, 292, 302, 304, 305, 307, 310, 312, 314], "axi": [7, 9, 18, 19, 20, 21, 25, 26, 27, 28, 33, 34, 35, 36, 48, 49, 50, 51, 55, 63, 66, 67, 71, 86, 96, 97, 98, 99, 106, 109, 123, 127, 129, 132, 135, 138, 139, 140, 141, 142, 143, 144, 153, 169, 183, 185, 187, 200, 202, 211, 212, 214, 219, 232, 248, 249, 250, 253, 254, 255, 259, 260, 262, 263, 267, 268, 269, 270, 275, 276, 278, 308], "sequenc": [7, 9, 25, 26, 48, 49, 50, 51, 55, 63, 66, 67, 71, 74, 82, 92, 123, 133, 134, 136, 137, 139, 140, 142, 143, 147, 183, 185, 187, 200, 208, 214, 218, 219, 220, 222, 223, 224, 225, 228, 229, 233, 248, 250, 253, 255, 259, 266, 267, 270, 275, 280, 302, 313], "keepdim": [7, 9, 18, 19, 25, 26, 27, 28, 48, 49, 50, 51, 55, 67, 71, 169, 183, 185, 187, 200, 214, 248, 255, 259, 275], "bool": [7, 8, 9, 18, 19, 25, 26, 27, 28, 33, 34, 35, 36, 48, 49, 50, 51, 55, 67, 69, 71, 73, 85, 92, 96, 97, 98, 99, 111, 112, 128, 130, 149, 156, 161, 166, 167, 169, 172, 174, 183, 185, 187, 188, 194, 197, 200, 214, 216, 255, 259, 275], "fals": [7, 8, 9, 18, 19, 25, 26, 27, 28, 33, 34, 35, 36, 48, 49, 50, 51, 55, 67, 71, 73, 85, 92, 96, 97, 98, 99, 111, 156, 161, 166, 167, 169, 172, 174, 183, 185, 187, 188, 197, 200, 214, 255, 259, 275, 279, 282, 285, 286, 287, 288, 292, 310], "reduct": [7, 9, 110, 183, 185, 200, 214, 288, 306], "over": [7, 9, 18, 19, 20, 21, 89, 90, 91, 92, 96, 97, 98, 99, 134, 137, 140, 143, 155, 169, 171, 173, 183, 185, 187, 200, 212, 214, 236, 248, 249, 255, 259, 266, 268, 275, 306, 307], "given": [7, 9, 20, 30, 74, 82, 84, 86, 96, 97, 98, 99, 104, 106, 116, 121, 123, 126, 132, 133, 134, 135, 136, 137, 141, 142, 143, 147, 148, 169, 183, 185, 187, 196, 200, 204, 206, 214, 223, 225, 235, 243, 248, 250, 255, 259, 261, 267, 268, 269, 271, 272, 273, 275, 290], "ax": [7, 9, 18, 19, 70, 100, 123, 133, 134, 136, 137, 139, 140, 142, 143, 144, 155, 169, 183, 185, 187, 200, 211, 214, 248, 253, 255, 259, 260, 266, 270, 275, 307], "reduc": [7, 9, 18, 19, 110, 183, 185, 187, 200, 214, 255, 259, 275, 288], "If": [7, 8, 9, 10, 18, 19, 20, 21, 69, 73, 74, 84, 86, 93, 96, 97, 98, 99, 105, 106, 109, 110, 111, 121, 127, 130, 141, 142, 143, 146, 147, 150, 156, 166, 167, 169, 174, 183, 184, 185, 187, 188, 196, 197, 200, 204, 208, 211, 212, 214, 219, 223, 232, 248, 249, 250, 255, 259, 261, 262, 263, 266, 268, 269, 274, 275, 278, 280, 282, 286, 288, 305, 306, 307, 309, 312, 313, 314], "unspecifi": [7, 9, 10, 18, 19, 20, 21, 86, 96, 97, 98, 99, 147, 183, 185, 187, 200, 208, 212, 214, 232, 248, 249, 255, 259, 262, 268, 269, 275, 280, 314], "thi": [7, 8, 9, 10, 18, 19, 20, 21, 74, 100, 117, 128, 148, 149, 153, 156, 162, 166, 167, 168, 169, 170, 171, 172, 179, 183, 184, 185, 187, 189, 191, 200, 212, 214, 219, 243, 248, 249, 250, 255, 259, 262, 268, 275, 284, 287, 288, 299, 304, 305, 306, 307, 309, 310, 312], "entir": [7, 9, 18, 19, 183, 185, 187, 200, 214, 255, 259, 275], "keep": [7, 9, 18, 19, 183, 185, 187, 200, 214, 255, 259, 275, 299, 307, 309], "singleton": [7, 9, 18, 19, 111, 183, 184, 185, 187, 200, 214, 255, 259, 275], "dimens": [7, 9, 18, 19, 54, 60, 69, 75, 76, 77, 85, 90, 91, 92, 106, 123, 130, 139, 140, 142, 143, 144, 148, 149, 155, 166, 167, 168, 169, 170, 171, 172, 183, 184, 185, 187, 200, 214, 215, 219, 227, 255, 259, 263, 266, 270, 275, 305, 307], "output": [7, 8, 9, 10, 20, 74, 81, 82, 85, 87, 88, 96, 97, 98, 99, 100, 115, 125, 127, 128, 129, 130, 131, 138, 141, 142, 143, 147, 148, 150, 153, 154, 156, 169, 173, 183, 185, 187, 188, 200, 204, 208, 209, 212, 214, 218, 219, 220, 222, 223, 224, 225, 228, 229, 240, 241, 248, 253, 255, 259, 263, 269, 271, 274, 275, 276, 277, 278, 279, 280, 281, 305, 306, 307, 308, 309, 310, 311, 312, 313], "correspond": [7, 9, 69, 84, 104, 106, 126, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 183, 185, 200, 214, 259, 266, 278, 286, 307], "rtol": [8, 156], "1e": [8, 156, 301], "05": [8, 156], "atol": [8, 156], "08": [8, 156], "equal_nan": [8, 73, 156], "approxim": 8, "comparison": [8, 118, 151, 152, 164, 165, 207], "infinit": [8, 156], "consid": [8, 73, 156, 285, 286, 287, 304], "equal": [8, 20, 73, 125, 152, 156, 165, 207, 212, 225, 250], "thei": [8, 93, 149, 156, 304, 305, 306, 309, 311, 312, 313], "have": [8, 73, 75, 76, 77, 81, 109, 139, 140, 142, 143, 149, 156, 184, 198, 219, 276, 285, 304, 305, 306, 308, 309, 313], "same": [8, 30, 73, 82, 85, 90, 91, 92, 93, 109, 127, 129, 138, 141, 142, 143, 149, 150, 156, 162, 211, 219, 235, 276, 277, 279, 287, 299, 302, 305, 306, 308, 313], "sign": [8, 156, 292], "nan": [8, 73, 156, 158, 204], "unless": [8, 156, 169], "true": [8, 33, 34, 35, 36, 73, 85, 96, 97, 98, 99, 128, 130, 149, 156, 161, 166, 167, 169, 174, 188, 197, 216, 248, 279, 282, 285, 286, 287, 288, 292, 299], "all": [8, 20, 30, 75, 76, 77, 85, 90, 91, 92, 100, 109, 110, 111, 125, 134, 137, 140, 143, 148, 149, 171, 184, 211, 212, 253, 282, 299, 302, 305, 308, 309, 311, 314], "ab": [8, 156, 169, 274, 305], "note": [8, 74, 81, 85, 91, 100, 131, 139, 140, 149, 156, 169, 191, 215, 219, 276, 282, 299, 301, 310, 312], "unlik": [8, 156], "array_equ": [8, 156], "rel": [8, 156, 305], "toler": [8, 156], "boolean": [8, 73, 156, 157, 158, 159, 160, 161, 180, 181, 182, 292, 308], "indic": [8, 18, 19, 20, 21, 30, 148, 149, 150, 156, 157, 158, 159, 160, 161, 171, 250, 262, 263, 274, 308], "stop": [10, 173, 199, 256, 307, 308], "step": [10, 299, 305, 306], "rang": [10, 144, 148, 173, 301, 302, 305, 307, 309, 313], "half": [10, 225, 229, 309], "open": [10, 225, 229], "interv": [10, 173, 225, 229], "increment": 10, "specifi": [10, 29, 90, 91, 92, 106, 139, 140, 147, 150, 169, 173, 202, 208, 219, 232, 260, 262, 263, 266, 269, 270, 274, 278, 280, 306, 307, 313], "otherwis": [10, 92, 111, 197, 282, 285, 286, 287, 288, 309, 310], "convent": [10, 93, 115, 116], "actual": [10, 309], "lead": [10, 74, 305], "unexpect": 10, "exampl": [10, 30, 100, 144, 161, 169, 170, 257, 262, 284, 287, 288, 299, 301, 302, 307, 308, 309, 310, 311, 312], "fraction": 10, "integr": [10, 262, 309], "invers": [11, 12, 13, 14, 15, 16, 17, 120, 135, 136, 137, 138, 139, 140, 167, 168, 172], "cosin": [11, 12, 94, 95, 307], "hyperbol": [12, 14, 17, 95, 247, 265], "sine": [13, 14, 246, 247, 307], "tangent": [15, 16, 17, 100, 162, 264, 265], "ratio": 16, "maximum": [18, 30, 84, 96, 193, 197, 284, 299, 309], "along": [18, 19, 85, 86, 96, 97, 98, 99, 109, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 148, 149, 153, 169, 232, 248, 250, 254, 262, 263, 266, 267, 268, 269, 276, 299], "minimum": [19, 30, 84, 97], "kth": [20, 212], "partit": 20, "order": [20, 74, 92, 116, 169, 212, 215, 268, 299, 305, 307], "within": [20, 156], "undefin": [20, 100, 166, 167, 212, 223, 308], "posit": [20, 106, 130, 144, 150, 160, 166, 167, 202, 204, 212, 223, 269, 274, 286, 299], "give": [20, 305], "sort": [20, 21, 212, 268], "befor": [20, 128, 212, 306, 308, 309], "less": [20, 165, 212], "after": [20, 144, 146, 149, 189, 212, 215, 305, 313], "greater": [20, 124, 152, 212, 284], "flatten": [20, 21, 96, 97, 98, 99, 169, 210, 212, 232, 249, 262, 263, 268, 285], "contain": [20, 21, 60, 85, 106, 116, 138, 139, 140, 148, 149, 169, 180, 181, 182, 215, 250, 279, 284, 299, 305, 306, 307], "last": [21, 69, 127, 129, 134, 137, 139, 140, 142, 143, 144, 148, 149, 155, 166, 167, 168, 170, 171, 172, 184, 193, 219, 249, 266, 276, 310], "n": [22, 81, 89, 90, 91, 92, 125, 132, 134, 135, 137, 138, 141, 143, 153, 154, 223, 255, 271, 275, 306], "dimension": [22, 127, 129, 132, 133, 134, 135, 136, 137, 141, 142, 143, 308, 310], "val": [22, 147], "tupl": [22, 57, 60, 70, 86, 90, 91, 92, 114, 116, 121, 123, 162, 169, 170, 171, 211, 215, 233, 253, 274, 277, 285, 286, 287, 288, 289, 304, 307], "ndarrai": [22, 308, 309, 311], "properti": [23, 30, 39, 43, 53, 54, 60, 62, 307], "equival": [23, 57, 70, 114, 146, 149, 153, 262], "call": [23, 128, 146, 189, 193, 299, 301, 305, 306, 307, 309], "transpos": [23, 149, 216], "argument": [23, 57, 70, 85, 121, 150, 274, 286, 287, 288, 299, 302, 306, 307, 312, 313, 314], "union": [24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 75, 76, 77, 81, 115, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 153, 159, 160, 161, 190, 227, 228, 238, 257, 269], "cast": [29, 141, 142, 143, 174, 310], "appli": [30, 130, 131, 148, 171, 286, 287, 288, 299, 305, 306], "updat": [30, 85, 282, 286, 288, 301, 305, 306, 309], "regular": [30, 305, 308], "place": [30, 235, 282, 306, 309, 310], "map": [30, 174, 286], "assign": 30, "For": [30, 131, 148, 161, 169, 215, 289, 299, 301, 302, 305, 306, 307, 308, 309, 310, 311, 312, 313], "instanc": [30, 100, 215, 289, 299, 310], "x": [30, 81, 100, 109, 110, 119, 124, 127, 128, 129, 149, 153, 154, 169, 216, 220, 235, 240, 244, 272, 273, 279, 286, 288, 299, 301, 305, 306, 307, 308, 309, 310, 311, 313], "idx": [30, 308], "y": [30, 100, 153, 279, 299, 301, 305, 306, 307, 309, 310], "As": [30, 262, 299, 305], "ignor": [30, 84, 85, 121], "one": [30, 69, 75, 84, 90, 91, 92, 123, 125, 127, 129, 130, 169, 177, 184, 216, 219, 253, 258, 292, 306, 313], "correctli": 30, "syntax": [30, 308], "In": [30, 184, 215, 286, 299, 304, 305, 306, 307, 309, 312, 313], "subtract": 30, "multipli": [30, 149, 215, 216], "divid": [30, 146, 215, 231, 306], "mx": [30, 87, 88, 100, 111, 128, 144, 161, 169, 170, 174, 240, 274, 284, 299, 301, 302, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314], "2": [30, 90, 105, 106, 119, 133, 136, 138, 139, 140, 141, 142, 143, 144, 153, 161, 166, 167, 168, 169, 170, 171, 172, 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