I have a matrix such that

```
julia> svdvals(AA)
1000-element Array{Float64,1}:
31.962791231191257
31.607090491558335
31.255070632248668
22.374974612534174
⋮
22.342788128226456
22.328813384016993
0.01373845014731832
```

but `svd(AA)`

fails with the exception

```
julia> svd(AA)
ERROR: LAPACKException(1)
Stacktrace:
[1] chklapackerror at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.2/LinearAlgebra/src/lapack.jl:38 [inlined]
[2] gesdd!(::Char, ::Array{Float64,2}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.2/LinearAlgebra/src/lapack.jl:1602
[3] #svd!#73(::Bool, ::typeof(svd!), ::Array{Float64,2}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.2/LinearAlgebra/src/svd.jl:63
[4] #svd#74 at ./none:0 [inlined]
[5] svd(::Array{Float64,2}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.2/LinearAlgebra/src/svd.jl:106
[6] top-level scope at none:0
```

Is it possible to tweak `svd`

to use a more robust algorithm for this seemingly difficult problem?

Background: `AA`

is a matrix of mostly Fourier basis functions that are orthogonal to each other, with the exception of one column which is a signal to be decomposed by the Fourier basis in a total least-squares fashion.

Code to generate `AA`

is below

```
T = 1000
t = 0:T-1
f = LinRange(0,0.5-1/length(t)/2,length(t)÷2)
y = sin.(t)
function check_freq(f)
zerofreq = findfirst(iszero, f)
zerofreq !== nothing && zerofreq != 1 && throw(ArgumentError("If zero frequency is included it must be the first frequency"))
zerofreq
end
function get_fourier_regressor(t,f)
zerofreq = check_freq(f)
N = length(t)
Nf = length(f)
Nreg = zerofreq === nothing ? 2Nf : 2Nf-1
N >= Nreg || throw(ArgumentError("Too many frequency components $Nreg > $N"))
A = zeros(N,Nreg)
sinoffset = Nf
for fn=1:Nf
if fn == zerofreq
sinoffset = Nf-1
end
for n = 1:N
phi = 2π*f[fn]*t[n]
A[n,fn] = cos(phi)
if fn != zerofreq
A[n,fn+sinoffset] = -sin(phi)
end
end
end
A, zerofreq
end
A,z = get_fourier_regressor(t,f)
AA = [A y]
```