{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "",
              "annotation": "ValueError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If the last dimension of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not the same size as the second-to-last dimension of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "output",
              "annotation": "ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Returns the dot product of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ".  If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "out"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is given, then it is returned."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Dot product of two arrays. Specifically,"
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "a",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "First argument."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "b",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Second argument."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "out",
              "annotation": "ndarray, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "dot(a,b)",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "BulletList",
          "__tag": 4053,
          "ordered": false,
          "start": 1,
          "children": [
            {
              "__type": "ListItem",
              "__tag": 4054,
              "children": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If both "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " are 1-D arrays, it is inner product of vectors   (without complex conjugation)."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "ListItem",
              "__tag": 4054,
              "children": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If both "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " are 2-D arrays, it is matrix multiplication,   but using "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "matmul",
                      "domain": null,
                      "role": "func",
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " or "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "a @ b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is preferred."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "ListItem",
              "__tag": 4054,
              "children": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If either "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " or "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is 0-D (scalar), it is equivalent to   "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "multiply",
                      "domain": null,
                      "role": "func",
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and using "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "numpy.multiply(a, b)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " or "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "a * b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is   preferred."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "ListItem",
              "__tag": 4054,
              "children": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is an N-D array and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is a 1-D array, it is a sum product over   the last axis of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "ListItem",
              "__tag": 4054,
              "children": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is an N-D array and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is an M-D array (where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "M>=2"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "), it is a   sum product over the last axis of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and the second-to-last axis of   "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ":      "
                    }
                  ]
                },
                {
                  "__type": "Code",
                  "__tag": 4050,
                  "value": "dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])",
                  "execution_status": null
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "It uses an optimized BLAS library when possible (see "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "numpy.linalg",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.linalg"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ")."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": null,
  "item_line": null,
  "item_type": "_ArrayFunctionDispatcher",
  "aliases": [
    "numpy.dot"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.dot(3, 4)\n",
        "execution_status": "failure"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nNeither argument is complex-conjugated:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.dot([2j, 3j], [2j, 3j])\n",
        "execution_status": "failure"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nFor 2-D arrays it is the matrix product:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "a = [[1, 0], [0, 1]]\nb = [[4, 1], [2, 2]]\nnp.dot(a, b)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "a = np.arange(3*4*5*6).reshape((3,4,5,6))\nb = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.dot(a, b)[2,3,2,1,2,2]\nsum(a[2,3,2,:] * b[1,2,:,2])\n",
        "execution_status": "failure"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "einsum",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "einsum"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Einstein summation convention."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "linalg.multi_dot",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "linalg.multi_dot"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Chained dot product."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "matmul",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "matmul"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "'@' operator as method with out parameter."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "tensordot",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "tensordot"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Sum products over arbitrary axes."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "vdot",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "vdot"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Complex-conjugating dot product."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "vecdot",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "vecdot"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Vector dot product of two arrays."
            }
          ]
        }
      ],
      "type": null
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "b",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "out",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "dot"
  },
  "references": null,
  "qa": "numpy:dot",
  "arbitrary": [],
  "local_refs": [
    "a",
    "b",
    "out",
    "output"
  ]
}