(cherry picked from commit 5dda994)

Alternative based on #29187

Tests from rforquet's PR linked above.

(cherry picked from commit 16516b5)

Ref. https://discourse.julialang.org/t/error-undefvarerror-eigvecs-not-defined/14923/2?u=stillyslalom

(cherry picked from commit 2c15430)

(cherry picked from commit 157a6d1)

(cherry picked from commit abe38f1)

The example used identifier `x` for two different purposes. While this isn't a problem for Julia, it makes humans have to read much more carefully. For examples I think it is much clearer to use different identifiers for different purposes.

(cherry picked from commit 6354405)

Minor language fixes. Two more significant changes are:
* it is recommended to use `===` to compare to `nothing`
* `=` is not a binary operator

(cherry picked from commit 27de698)

(cherry picked from commit b777030)

(cherry picked from commit ce64546)

I spotted a typo when reviewing the merge.

(cherry picked from commit 338cf0d)

(cherry picked from commit 60e6794)

…29322)

(cherry picked from commit a854139)

The R function is called is.na, and automatically works element-wise.

(cherry picked from commit 8484f97)

Fixes #29297, see discussion there.

(cherry picked from commit 64a4f18)

(cherry picked from commit 0b5e21c)

(cherry picked from commit c37f4aa)

…routines (#29352)

(cherry picked from commit 993e7d7)

(cherry picked from commit 94aa39b)

* gemm_wrapper! -> mul! (#29224)

* testing for #29224

* code review update: More tests

* Complex times real reinterpret trick fix for vectors and transposed matrices

(cherry picked from commit 82503cd)

#29346)

(cherry picked from commit 48f5bb3)

…29258)

This implements the suggestion in
#27857 (comment)

(cherry picked from commit 8d6c1ce)

(cherry picked from commit 493068b)

(cherry picked from commit 47668c8)

(cherry picked from commit ba41f69)

(cherry picked from commit bc34c64)

also fixes #29357

(cherry picked from commit 6794778)

(cherry picked from commit e1f42b1)

__ldexp_exp(f) requires the second argument to be an Int32, so we might as well hard-code that here. It also seems that the old specification is actually not valid, or might have unexpected results, so we should just go with Int32, see #29400 .

(cherry picked from commit 75f798f)

(cherry picked from commit f42f7b7)

Move whereas clause into subordinate position to avoid sentence fragment.

(cherry picked from commit 8907aff)

(cherry picked from commit f474f75)

(cherry picked from commit e7d15d4)

(cherry picked from commit 8d5c109)

(cherry picked from commit 4020729)

Fix #28820

(cherry picked from commit 2460b57)

Improved English and egs

The examples starting around line 80 showing how to create arrays with dimensions are unhelpful because in every case the dimensions are 2x2 so people don't get any sense of which dimension is which. So I've changed them all to 2x3 which doesn't take up any more vertical space but makes it much clearer which dimension is which.

I don't like the Comprehensions example because the expression is much too complicated: the idea is to show comprehensions, so I think the expression should be a lot simpler.

I changed the `searchsorted` eg to make the searched for number different from all the others to improve clarity.

(cherry picked from commit 29b780e)

Changed `String` to `BitSet` as a `mutable struct` example.

(cherry picked from commit dee7d77)

C and Julia code were inside the same code block

(cherry picked from commit 39117c9)

(cherry picked from commit 37dc16e)

…9487)

(cherry picked from commit ea16391)

…dex(s) (#29465)

(cherry picked from commit a984ad0)

(cherry picked from commit 7cc9209)

(cherry picked from commit 7dd1e4c)

(cherry picked from commit 5bc3de4)

(cherry picked from commit 55c3c29)

(cherry picked from commit 9280bfc)

(cherry picked from commit f9b9d85)

The i-search prompt becomes for example: `(failed forward-i-search)`.

(cherry picked from commit 37ab710)

fix #29510

(cherry picked from commit 601ef78)

(cherry picked from commit 3cc4b80)

My apologies if this small edit is somewhere else waiting to be merged. I couldn't find it...

(cherry picked from commit 62e9ba4)

(cherry picked from commit cfc967b)

(cherry picked from commit 99e0b3b)

…29192)

This code was assuming that character values only have bit-patterns
that decoding a string can produce, but of course `reinterpret` can
produce any bit pattern in a `Char` whatsoever. The fix doesn't use
that assumption and only uses the cache for actual ASCII characters.

(cherry picked from commit 88f74b7)

We use this setting for linking curl, which itself needs to find libssh2
and mbedtls. However, while curl will indeed eventually be in the same
directory as these two libraries, it is not during linking, causing link
failures (unless we happen to have global copies of the same libraries
that the linker can pick up). Add an rpath-link command with the absolute
path to our library directory to make sure the dependent libraries get
picked up at link time.

(cherry picked from commit 59b6645)

These fail to build if mbedtls is not available in the global
linker search path. Add a simple flag to disable them, since
we don't use them.

(cherry picked from commit 4412dd4)

(cherry picked from commit 15843d5)

(cherry picked from commit 38612e0)

(cherry picked from commit 9616406)

* Fix abs for Rational{<:Unsigned}

* Add tests for abs(x::Rational)

(cherry picked from commit 4eb1a93)

(cherry picked from commit f034533)

An errant space was causing the online documentation to render the docstring incorrectly: https://docs.julialang.org/en/v1/stdlib/Statistics/index.html#Statistics.quantile

(cherry picked from commit 367aab3)

(cherry picked from commit e20d1ee)

(cherry picked from commit b7a7002)

(cherry picked from commit 9fd9962)

| subarray: Test Failed at /usr/share/julia/test/subarray.jl:611
|  Expression: #= /usr/share/julia/test/subarray.jl:611 =# @inferred(sum(Base.unaliascopy(V))) == sum(V) == sum(A[2:5, :, 2:5, 1:2:5])
|   Evaluated: 121.8579669083425 == 121.8579669083425 == 121.85796690834263

A = rand(5,5,5,5)
V = view(A, 2:5, :, 2:5, 1:2:5)
@code_typed sum(V)  # calls mapfoldl
@code_typed sum(A[2:5, :, 2:5, 1:2:5])  # calls mapreduce

mapreduce doesn't guarantee the associativity, which is likely
the cause of this precision issue in random sum.

(cherry picked from commit 518f548)

(cherry picked from commit 57a0347)

* fix #29644: getfield of Tridiagonal{SparseVector}

* Fix tests.

(cherry picked from commit 0902d58)

(cherry picked from commit 84b9577)

* Use a stable inverse for Tridiagonal and SymTridiagonal

Fixes #29630

* Fix ldlt in the complex case

(cherry picked from commit 00bb4f2)

Work around for #29675.

(cherry picked from commit 2a9271a)

(cherry picked from commit f51816b)

(cherry picked from commit 0d050ac)

(cherry picked from commit 806d7c2)

(cherry picked from commit dcf0eae)

fix a typo

(cherry picked from commit 1b030b2)

(cherry picked from commit a897365)

(cherry picked from commit 3b7be23)

* Uniform scaling cat with zero dimensions

* Missing type assertion in test

(cherry picked from commit 4093dbf)

…Julia docs as well. (#29731)

(cherry picked from commit 44dd917)

Make nullspace work for Adjoint

Fixes #28846

(cherry picked from commit 2e2b14c)

(cherry picked from commit 53563cd)

(cherry picked from commit 1db6047)

fix two punctuation errors

(cherry picked from commit 2a01598)

(cherry picked from commit 70be5f2)

(cherry picked from commit ee08fd6)

(cherry picked from commit a8cd3a1)

* clarify pinv documentation

The `pinv` documentation falsely implied that it discarded singular values `σ > tol`, when in fact it discards `σ > tol max(σ)`.  This PR corrects the docstring.

(`σ > tol max(σ)` is a good behavior!  `tol` should be a dimensionless quantity that doesn't depend on the overall scaling/units of the matrix.)

* rename tol -> rtol

(cherry picked from commit 2996521)

(cherry picked from commit 679c5b5)

(cherry picked from commit be4b5c9)

(cherry picked from commit ffaf849)

(cherry picked from commit be1ae20)

(cherry picked from commit 82c4fce)