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thenumbernine
thenumbernine
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Lua, 462 455 431431 427 bytes

There is no built-in complex math in Lua. No vector operations either. All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=wx=math.sqrt z=print i=a-g j=b-h
k=(i^2-j^2)/2+2*(c*e-d*f)m=x(k^2+(i*j+2*(c*f+d*e))^2)n=x(m+k)o=x(m-k)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0

Lua, 462 455 431 bytes

There is no built-in complex math in Lua. No vector operations either. All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=(i^2-j^2)/2+2*(c*e-d*f)m=x(k^2+(i*j+2*(c*f+d*e))^2)n=x(m+k)o=x(m-k)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0

Lua, 462 455 431 427 bytes

There is no built-in complex math in Lua. No vector operations either. All had to be rolled by hand.

a,b,c,d,e,f,g,h=...x=math.sqrt z=print i=a-g j=b-h
k=(i^2-j^2)/2+2*(c*e-d*f)m=x(k^2+(i*j+2*(c*f+d*e))^2)n=x(m+k)o=x(m-k)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0
haven't seen the sgn() matter so I'm taking it out, someone offer a proof that it gets squared/divided away?
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thenumbernine
thenumbernine
  • 381
  • 2
  • 4

Lua, 462 455455 431 bytes

There is no built-in complex math in Lua. No vector operations either. There's not even a sgn() function (as is required to calculate the complex square root). All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=i^2k=(i^2-j^2+4*j^2)/2+2*(c*e-d*f)l=2*i*j+4*(c*f+d*e)m=x(k^2+l^2)n=xk^2+(i*j+2*(m+kc*f+d*e)/2)o=(l<0 and-1 or 1^2)*xn=x(m+k)o=x(m-k)/2)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0

Lua, 462 455 bytes

There is no built-in complex math in Lua. No vector operations either. There's not even a sgn() function (as is required to calculate the complex square root). All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=i^2-j^2+4*(c*e-d*f)l=2*i*j+4*(c*f+d*e)m=x(k^2+l^2)n=x((m+k)/2)o=(l<0 and-1 or 1)*x((m-k)/2)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0

Lua, 462 455 431 bytes

There is no built-in complex math in Lua. No vector operations either. All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=(i^2-j^2)/2+2*(c*e-d*f)m=x(k^2+(i*j+2*(c*f+d*e))^2)n=x(m+k)o=x(m-k)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0
replaced atan2 with short circuit step function (and subsequently fixed a sign error)
Source Link
thenumbernine
thenumbernine
  • 381
  • 2
  • 4

Lua, 462462 455 bytes

There is no built-in complex math in Lua. No vector operations either. There's not even a sgn() function (as is required to calculate the complex square root). All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=i^2-j^2+4*(c*e-d*f)l=2*i*j+4*(c*f+d*e)m=x(k^2+l^2)n=x((m+k)/2)o=(w.atan2(0,l)/w.pi*2l<0 and-1 or 1)*x((m-k)/2)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913    0   -0.52573111211913    0   0.85065080835204    0

Lua, 462 bytes

There is no built-in complex math in Lua. No vector operations either. There's not even a sgn() function (as is required to calculate the complex square root). All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=i^2-j^2+4*(c*e-d*f)l=2*i*j+4*(c*f+d*e)m=x(k^2+l^2)n=x((m+k)/2)o=(w.atan2(0,l)/w.pi*2-1)*x((m-k)/2)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   0.52573111211913    0   -0.52573111211913   0   0.85065080835204    0

Lua, 462 455 bytes

There is no built-in complex math in Lua. No vector operations either. There's not even a sgn() function (as is required to calculate the complex square root). All had to be rolled by hand.

a,b,c,d,e,f,g,h=...w=math x=w.sqrt z=print i=a-g j=b-h
k=i^2-j^2+4*(c*e-d*f)l=2*i*j+4*(c*f+d*e)m=x(k^2+l^2)n=x((m+k)/2)o=(l<0 and-1 or 1)*x((m-k)/2)i=(a+g+n)/2
j=(b+h+o)/2 k=(a+g-n)/2 l=(b+h-o)/2 z(i,j,k,l)q=c^2+d^2 r=e^2+f^2 s=q+r if s==0
then z(1,0,0,0,0,0,1,0)else if r==0 then m,n,o,p=c,d,c,d c,d=i-a,j-b e,f=k-a,l-b
u=x(q+c^2+d^2)v=x(q+e^2+f^2)else m,n=i-g,j-h o,p=k-g,l-h c,d=e,f
u=x(r+m^2+n^2)v=x(r+o^2+p^2)end z(m/u,n/u,o/v,p/v,c/u,d/u,e/v,f/v)end

Run from the command-line with the following arguments:

lua eigen.lua Re(a) Im(a) Re(b) Im(b) Re(c) Im(c) Re(d) Im(d)

Produces the following output:

Re(lambda1) Im(lambda1) Re(lambda2) Im(lambda2)
Re(v11) Im(v11) Re(v12) Im(v12) Re(v21) Im(v21) Re(v22) Im(v22)

...for a,b,c,d the 4 components of the input matrix, lambda1 and lambda2 the two eigenvalues, v11,v21 the first unit eigenvector, and v12,v22 the second unit eigenvector. For example,

lua eigen.lua 1 0  1 0  1 0  0 0

...produces...

1.6180339887499 0   -0.61803398874989   0
0.85065080835204    0   -0.52573111211913   0   0.52573111211913    0   0.85065080835204    0
Source Link
thenumbernine
thenumbernine
  • 381
  • 2
  • 4