Compute the condition number of a matrix. This function is capable of returning the condition number using one of seven different norms, depending on the value of `p` (see Parameters below). Parameters ---------- x : (..., M, N) array_like The matrix whose cond
(x, p=None)
| 1912 | |
| 1913 | @array_function_dispatch(_cond_dispatcher) |
| 1914 | def cond(x, p=None): |
| 1915 | """ |
| 1916 | Compute the condition number of a matrix. |
| 1917 | |
| 1918 | This function is capable of returning the condition number using |
| 1919 | one of seven different norms, depending on the value of `p` (see |
| 1920 | Parameters below). |
| 1921 | |
| 1922 | Parameters |
| 1923 | ---------- |
| 1924 | x : (..., M, N) array_like |
| 1925 | The matrix whose condition number is sought. |
| 1926 | p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional |
| 1927 | Order of the norm used in the condition number computation: |
| 1928 | |
| 1929 | ===== ============================ |
| 1930 | p norm for matrices |
| 1931 | ===== ============================ |
| 1932 | None 2-norm, computed directly using the ``SVD`` |
| 1933 | 'fro' Frobenius norm |
| 1934 | inf max(sum(abs(x), axis=1)) |
| 1935 | -inf min(sum(abs(x), axis=1)) |
| 1936 | 1 max(sum(abs(x), axis=0)) |
| 1937 | -1 min(sum(abs(x), axis=0)) |
| 1938 | 2 2-norm (largest sing. value) |
| 1939 | -2 smallest singular value |
| 1940 | ===== ============================ |
| 1941 | |
| 1942 | inf means the `numpy.inf` object, and the Frobenius norm is |
| 1943 | the root-of-sum-of-squares norm. |
| 1944 | |
| 1945 | Returns |
| 1946 | ------- |
| 1947 | c : {float, inf} |
| 1948 | The condition number of the matrix. May be infinite. |
| 1949 | |
| 1950 | See Also |
| 1951 | -------- |
| 1952 | numpy.linalg.norm |
| 1953 | |
| 1954 | Notes |
| 1955 | ----- |
| 1956 | The condition number of `x` is defined as the norm of `x` times the |
| 1957 | norm of the inverse of `x` [1]_; the norm can be the usual L2-norm |
| 1958 | (root-of-sum-of-squares) or one of a number of other matrix norms. |
| 1959 | |
| 1960 | References |
| 1961 | ---------- |
| 1962 | .. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL, |
| 1963 | Academic Press, Inc., 1980, pg. 285. |
| 1964 | |
| 1965 | Examples |
| 1966 | -------- |
| 1967 | >>> import numpy as np |
| 1968 | >>> from numpy import linalg as LA |
| 1969 | >>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]]) |
| 1970 | >>> a |
| 1971 | array([[ 1, 0, -1], |
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