matlab中的eps 1-eps

发布网友 发布时间：2022-04-27 00:51

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热心网友 时间：2022-06-21 23:39

浮点数的精度

>> help eps
EPS Spacing of floating point numbers.
D = EPS(X), is the positive distance from ABS(X) to the next larger in
magnitude floating point number of the same precision as X.
X may be either double precision or single precision.
For all X, EPS(X) is equal to EPS(ABS(X)).

EPS, with no arguments, is the distance from 1.0 to the next larger double
precision number, that is EPS with no arguments returns 2^(-52).

EPS('double') is the same as EPS, or EPS(1.0).
EPS('single') is the same as EPS(single(1.0)), or single(2^-23).

Except for numbers whose absolute value is smaller than REALMIN,
if 2^E <= ABS(X) < 2^(E+1), then
EPS(X) returns 2^(E-23) if ISA(X,'single')
EPS(X) returns 2^(E-52) if ISA(X,'double')

For all X of class double such that ABS(X) <= REALMIN, EPS(X)
returns 2^(-1074). Similarly, for all X of class single such that
ABS(X) <= REALMIN('single'), EPS(X) returns 2^(-149).

Replace expressions of the form
if Y < EPS * ABS(X)
with
if Y < EPS(X)

Example return values from calling EPS with various inputs are
presented in the table below:

Expression Return Value
===========================================
eps(1/2) 2^(-53)
eps(1) 2^(-52)
eps(2) 2^(-51)
eps(realmax) 2^971
eps(0) 2^(-1074)
eps(realmin/2) 2^(-1074)
eps(realmin/16) 2^(-1074)
eps(Inf) NaN
eps(NaN) NaN
-------------------------------------------
eps(single(1/2)) 2^(-24)
eps(single(1)) 2^(-23)
eps(single(2)) 2^(-22)
eps(realmax('single')) 2^104
eps(single(0)) 2^(-149)
eps(realmin('single')/2) 2^(-149)
eps(realmin('single')/16) 2^(-149)
eps(single(Inf)) single(NaN)
eps(single(NaN)) single(NaN)

See also realmax, realmin.

Overloaded methods:
codistributed/eps
qfft/eps

Reference page in Help browser
doc eps

热心网友 时间：2022-06-21 23:40

1-eps是一个无限接近于1的一个数，但是又不是1

热心网友 时间：2022-06-21 23:40

机器浮点运算误差上限，PC上默认值为2.2204e-016 。若某个值的绝对值小于此值，则可以认为这个量为0。如果想看详细的，可在matlab 主窗口下输入help eps