diff --git a/_sources/domains/sparse_linear_algebra.rst b/_sources/domains/sparse_linear_algebra.rst index 53e4024d3..eb39bd3f1 100644 --- a/_sources/domains/sparse_linear_algebra.rst +++ b/_sources/domains/sparse_linear_algebra.rst @@ -6,7 +6,8 @@ Sparse Linear Algebra See the latest specification for the sparse domain `here `_. -This page documents implementation specific or backend specific details. +This page documents implementation specific or backend specific details of the +sparse domain. OneMKL Intel CPU and GPU backends --------------------------------- @@ -15,6 +16,7 @@ Known limitations as of Intel oneMKL product release 2024.1: - All operations' algorithms except ``no_optimize_alg`` map to the default algorithm. +- The required external workspace size is always 0 bytes. - ``oneapi::mkl::sparse::set_csr_data`` and ``oneapi::mkl::sparse::set_coo_data`` functions cannot be used on a handle that has already been used for an operation or its optimize function. Doing so diff --git a/domains/sparse_linear_algebra.html b/domains/sparse_linear_algebra.html index 6c2f72f98..80b4caa6e 100644 --- a/domains/sparse_linear_algebra.html +++ b/domains/sparse_linear_algebra.html @@ -536,13 +536,15 @@

Contents

Sparse Linear Algebra#

See the latest specification for the sparse domain here.

-

This page documents implementation specific or backend specific details.

+

This page documents implementation specific or backend specific details of the +sparse domain.

OneMKL Intel CPU and GPU backends#

Known limitations as of Intel oneMKL product release 2024.1:

  • All operations’ algorithms except no_optimize_alg map to the default algorithm.

    • +

  • The required external workspace size is always 0 bytes.

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57, 65, 150], "j4": 1, "job": [76, 77, 90, 91, 92, 93, 126, 127, 128, 129], "jobu": [76, 77], "jobvt": [76, 77], "jobz": [90, 91, 92, 93, 126, 127, 128, 129], "k": [9, 13, 18, 19, 20, 21, 27, 32, 33, 44, 55, 56, 57, 58, 59, 61, 66, 79, 96, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 132, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 149, 150], "k_g": [105, 106, 139, 140], "kahan": [90, 126], "kaufman": [96, 98, 100, 132], "kernel": [10, 98, 99, 152], "kg": 106, "kl": [17, 150], "known": 151, "ku": [17, 150], "l": [78, 92, 96, 116, 122, 125, 128, 132, 154], "l_i": [79, 117, 123, 124], "l_il_i": [117, 123, 124], "lambda": [90, 92, 93, 126, 128, 129], "lambda_i": [90, 126], "lapack": [0, 67, 68, 69, 70, 71, 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, 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, 134, 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59, 60, 61, 62, 63, 64, 65, 66, 67, 151, 155], "optim": 151, "option": [1, 76, 77, 90, 92, 98, 101, 126, 128], "order": [76, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 108, 109, 110, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 142, 143, 144, 146, 148, 154], "orgbr": [68, 98, 101, 103], "orgbr_scratchpad_s": [98, 101, 102], "orgqr": [98, 100, 107], "orgqr_batch": [98, 99, 106], "orgqr_batch_scratchpad_s": [98, 99, 105], "orgqr_scratchpad_s": [98, 100, 104], "orgtr": [98, 101, 109], "orgtr_scratchpad_s": [98, 101, 108], "origin": [102, 103, 136, 137], "ormqr": [98, 100, 111], "ormqr_scratchpad_s": [98, 100, 110], "ormrq": [98, 100, 113], "ormrq_scratchpad_s": [98, 100, 112], "ormtr": [98, 101, 115], "ormtr_scratchpad_s": [98, 101, 114], "orthogon": [68, 70, 71, 74, 76, 94, 98, 99, 100, 101, 102, 104, 105, 108, 110, 112, 114, 126, 130, 138, 139], "orthonorm": [104, 105, 138, 139], "other": [0, 1, 42, 43, 50, 90, 126, 150], "otherwis": [13, 23, 41], "output": [1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 74, 76, 78, 79, 82, 83, 86, 87, 90, 92, 94, 96, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148, 154], "over": [110, 112, 144, 146], "overlap": 98, "overlin": 15, "overwrit": [110, 112, 114, 144, 146, 148], "overwritevec": [76, 77], "overwritten": [5, 12, 13, 18, 19, 20, 21, 23, 28, 32, 33, 51, 55, 56, 57, 62, 64, 65, 68, 70, 74, 76, 77, 78, 82, 86, 90, 92, 94, 96, 102, 104, 108, 110, 112, 114, 116, 120, 122, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148], "p": [68, 78, 98, 101, 102, 103, 104, 105, 136, 137, 138, 139], "p_": 68, "p_i": 79, "p_il_iu_i": 79, "pack": [8, 34, 35, 36, 47, 48, 49, 60, 61, 150], "packag": [0, 98], "page": 151, "pal": [90, 126], "parallel": [1, 153, 154], "param": [42, 43], "paramet": [0, 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 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, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149], "parent": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 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, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154], "part": [1, 2, 10, 21, 30, 31, 33, 34, 35, 36, 48, 49, 53, 54, 76, 77, 90, 91, 92, 93, 94, 95, 96, 97, 102, 104, 105, 116, 117, 118, 119, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 136, 138, 139, 150], "parti": 152, "partial": [78, 79], "pass": [69, 72, 73, 75, 77, 80, 81, 84, 85, 88, 89, 91, 93, 95, 97, 103, 106, 107, 109, 111, 113, 115, 118, 119, 121, 124, 125, 127, 129, 131, 133, 135, 137, 140, 141, 143, 145, 147, 149], "path": [0, 1], "path_suffix": 1, "path_to_clang": 0, "path_to_clang_compil": 0, "path_to_icpx_compil": 0, "path_to_icx_compil": 0, "path_to_install_dir": 0, "perform": [0, 5, 7, 8, 9, 12, 13, 14, 15, 16, 19, 23, 32, 33, 36, 40, 42, 46, 48, 55, 56, 57, 65, 67, 69, 70, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 93, 95, 97, 98, 101, 103, 105, 106, 107, 109, 111, 113, 115, 117, 118, 119, 121, 123, 124, 125, 127, 129, 131, 133, 135, 137, 139, 140, 141, 143, 145, 147, 149, 154], "permut": [78, 79, 96, 132], "phantom": 40, "pivot": [70, 71, 74, 78, 79, 96, 132], "plane": [7, 40, 42], "pleas": 1, "plu": 78, "pmatrix": 68, "point": [1, 7, 40, 41, 42, 68, 70, 71, 74, 76, 78, 79, 82, 83, 86, 87, 90, 92, 94, 96, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148], "pointer": [1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 76, 78, 79, 82, 86, 87, 90, 92, 94, 96, 102, 104, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 142, 144, 146, 148], "portfft_registers_per_wi": 0, "posit": [13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 37, 38, 44, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 92, 98, 99, 100, 116, 117, 120, 122, 123, 128, 150], "possibl": 0, "post": 1, "potr": [98, 100, 125], "potrf": [98, 100, 119, 120, 122], "potrf_batch": [98, 99, 118, 123], "potrf_batch_scratchpad_s": [98, 99, 117], "potrf_scratchpad_s": [98, 100, 116], "potri": [98, 100, 121], "potri_scratchpad_s": [98, 100, 120], "potrs_batch": [98, 99, 124], "potrs_batch_scratchpad_s": [98, 99, 123], "potrs_scratchpad_s": [98, 100, 122], "pre": 1, "precis": [2, 3, 4, 5, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 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, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149], "predic": 1, "prefer": 0, "prefix": 0, "previou": 150, "previous": [1, 105, 139], "pro": 0, "problem": [67, 68, 69, 71, 72, 76, 77, 79, 80, 83, 84, 87, 88, 90, 91, 92, 93, 94, 95, 100, 102, 103, 105, 106, 108, 109, 114, 115, 117, 118, 123, 124, 126, 127, 128, 129, 130, 131, 136, 137, 139, 140, 142, 143, 148, 149], "product": [3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 40, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 57, 58, 60, 62, 63, 66, 68, 70, 71, 74, 94, 96, 104, 105, 106, 107, 110, 111, 112, 113, 114, 130, 132, 138, 139, 140, 141, 144, 145, 146, 147, 148, 149, 151], "program": 150, "project": 152, "propag": 1, "proper": 1, "properti": [1, 151], "provid": [0, 1, 6, 10, 67, 68, 70, 71, 74, 79, 83, 87, 94, 98, 99, 117, 118, 123, 124, 130], "public": 1, "push_back": 1, "py": 1, "python": 1, "q": [1, 68, 70, 74, 94, 98, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 112, 113, 114, 115, 130, 136, 137, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149], "q_": 68, "q_1b_1p_1": 68, "q_1b_1p_h": 68, "q_i": [71, 98, 99, 105, 106, 139, 140], "q_ir_i": 71, "qbp": 68, "qc": [110, 112, 114, 144, 146, 148], "ql": [90, 126], "qr": [70, 71, 90, 98, 99, 100, 104, 105, 110, 126, 138, 139, 144], "qtq": [94, 108, 114, 130, 142, 148], "quad": 150, "queri": 1, "queue": [1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 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, 102, 103, 104, 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148, 149], "relat": [0, 67, 98, 101], "releas": 151, "remain": 74, "replac": [0, 42, 50], "repositori": [0, 155], "repres": [68, 70, 71, 72, 74, 94, 130, 150], "represent": [68, 70, 71, 74, 94, 130], "request": [90, 126], "requir": [0, 1, 42, 43, 69, 72, 73, 75, 77, 80, 81, 84, 85, 88, 89, 90, 91, 93, 95, 97, 103, 106, 107, 109, 111, 113, 115, 118, 119, 121, 124, 125, 126, 127, 129, 131, 133, 135, 137, 140, 141, 143, 145, 147, 149, 155], "required_var": 1, "respect": [42, 43, 150], "result": [1, 2, 4, 10, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 37, 38, 39, 43, 44, 46, 47, 48, 51, 52, 53, 54, 68, 70, 71, 74, 76, 78, 79, 82, 83, 86, 87, 90, 92, 94, 96, 98, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148], "retain": 0, "retriev": 0, "return": [2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 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, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149], "rhs_g": 124, "riangular": 154, "right": [13, 28, 40, 50, 51, 61, 62, 64, 65, 66, 76, 86, 87, 88, 89, 98, 99, 100, 110, 111, 112, 113, 114, 115, 122, 123, 124, 125, 134, 135, 144, 145, 146, 147, 148, 149, 150, 154], "rng": 0, "rocbla": 0, "rocfft": 0, "rocminfo": 0, "rocrand": 0, "rocsolv": 0, "root": 0, "rot": 7, "rotat": [7, 40, 41, 42, 43], "rotg": 7, "rotm": 7, "rotmg": 7, "routin": [2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 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, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152], "row": [0, 1, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 44, 47, 48, 49, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 88, 89, 96, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 132, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 149, 150, 154], "row_major": [2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], "rowwis": 76, "rq": [74, 98, 100, 110, 112, 144, 146], "run": 1, "runtime_error": 1, "rx": 0, "safe": 154, "sai": 154, "same": [0, 1, 37, 38, 108, 109, 114, 115, 142, 143, 148, 149, 150, 154], "sb": 46, "sbmv": 8, "scal": 7, "scalar": [2, 3, 4, 5, 7, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 62, 64, 65, 68, 70, 71, 74, 94, 102, 130], "scale": [3, 5, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 43, 44, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 62, 64, 65], "scope": 0, "scratchpad": [68, 69, 70, 71, 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, 123, 124, 125, 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147, 148, 149, 150, 154], "column_major": [2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], "columnwis": 76, "combin": [102, 136], "come": 154, "command": [0, 1], "compil": [0, 1, 152], "complet": [0, 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 74, 76, 78, 79, 82, 83, 86, 87, 90, 92, 94, 96, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148], "complex": [2, 3, 4, 5, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 45, 50, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 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150], "least": [2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88, 90, 92, 94, 96, 98, 100, 102, 105, 106, 108, 110, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126, 128, 130, 132, 134, 136, 139, 140, 142, 144, 146, 148, 150], "left": [13, 28, 40, 50, 51, 62, 64, 65, 76, 77, 110, 111, 112, 113, 114, 115, 144, 145, 146, 147, 148, 149, 150, 154], "left_right": [13, 28, 51, 62, 64, 65], "leftarrow": [3, 4, 11, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 62, 63], "len": [13, 17, 22, 23], "length": [17, 22, 24, 25, 26, 27, 29, 30, 31, 34, 35, 36, 44, 47, 48, 49, 52, 53, 54, 58, 59, 60, 61, 63, 66], "less": [68, 70, 71, 74, 76, 78, 79, 82, 83, 86, 87, 90, 92, 94, 96, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 122, 123, 126, 128, 130, 132, 134, 136, 138, 139, 142, 144, 146, 148], "level": [1, 2, 4, 6, 11, 14, 15, 16, 17, 18, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66], "level1": 6, "level2": 6, "level3": 6, "lib": 1, "lib_nam": 1, "lib_obj": 1, "libnewlib": 1, "libonemkl": 1, "libonemkl_blas_mklcpu": 1, "libonemkl_blas_newlib": 1, "librari": [0, 10, 98, 99, 152, 153], "like": [3, 5, 6, 12, 13, 19, 20, 21, 23, 57, 65, 71, 72, 79, 80, 83, 84, 87, 88, 105, 106, 117, 118, 123, 124, 139, 140, 154], "limit": 151, "linear": [6, 8, 59, 61, 65, 66, 70, 73, 74, 75, 78, 81, 82, 85, 86, 87, 89, 96, 97, 99, 104, 107, 110, 111, 112, 113, 116, 119, 120, 121, 122, 123, 125, 132, 133, 134, 135, 138, 141, 144, 145, 146, 147, 152], "link": 1, "linux": [0, 155], "list": [0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 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135, 144, 145, 146, 147, 148, 149, 154], "nonunit": [134, 135, 154], "norm": [7, 39], "normal": [92, 128], "note": [0, 1, 14, 18, 19, 20, 21, 28, 37, 38, 51, 62, 64, 65, 98, 102, 136], "novec": [76, 77, 90, 91, 92, 93, 126, 127, 128, 129], "now": 1, "nrh": [86, 87, 88, 89, 122, 123, 124, 125, 134, 135], "nrhsg": 88, "nrm2": 7, "number": [2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 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, 101, 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, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149], "nvidia": [0, 155], "nvidia_gpu": 0, "nvptx64": 0, 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44, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 151, 155], "optim": 151, "option": [1, 76, 77, 90, 92, 98, 101, 126, 128], "order": [76, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 108, 109, 110, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 142, 143, 144, 146, 148, 154], "orgbr": [68, 98, 101, 103], "orgbr_scratchpad_s": [98, 101, 102], "orgqr": [98, 100, 107], "orgqr_batch": [98, 99, 106], "orgqr_batch_scratchpad_s": [98, 99, 105], "orgqr_scratchpad_s": [98, 100, 104], "orgtr": [98, 101, 109], "orgtr_scratchpad_s": [98, 101, 108], "origin": [102, 103, 136, 137], "ormqr": [98, 100, 111], "ormqr_scratchpad_s": [98, 100, 110], "ormrq": [98, 100, 113], "ormrq_scratchpad_s": [98, 100, 112], "ormtr": [98, 101, 115], "ormtr_scratchpad_s": [98, 101, 114], "orthogon": [68, 70, 71, 74, 76, 94, 98, 99, 100, 101, 102, 104, 105, 108, 110, 112, 114, 126, 130, 138, 139], 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