Conjugate transpose: Difference between revisions
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(Updated second D entry) |
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// alias CM(T) = Complex!T[][]; // Not yet useful. |
// alias CM(T) = Complex!T[][]; // Not yet useful. |
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auto conjugateTranspose(T)(in Complex!T[][] m) /* |
auto conjugateTranspose(T)(in Complex!T[][] m) pure nothrow /*@safe*/ |
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if (!hasIndirections!T) { |
if (!hasIndirections!T) { |
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return iota(m[0].length) |
return iota(m[0].length) |
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} |
} |
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T[][] matMul(T)(immutable T[][] A, immutable T[][] B) pure nothrow { |
T[][] matMul(T)(immutable T[][] A, immutable T[][] B) pure nothrow /*@safe*/ { |
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immutable Bt = B[0].length.iota.map!(i=> B.transversal(i).array) |
immutable Bt = B[0].length.iota.map!(i=> B.transversal(i).array) |
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.array; |
.array; |
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/// some bits of mantissa. |
/// some bits of mantissa. |
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bool areEqual(T)(in Complex!T[][][] matrices, in size_t nBits=20) |
bool areEqual(T)(in Complex!T[][][] matrices, in size_t nBits=20) |
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pure nothrow { |
pure nothrow /*@safe*/ { |
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static bool allSame(U)(in U[] v) pure nothrow @nogc { |
static bool allSame(U)(in U[] v) pure nothrow @nogc @safe { |
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return v[1 .. $].all!(c => c == v[0]); |
return v[1 .. $].all!(c => c == v[0]); |
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} |
} |
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bool allNearSame(in Complex!T[] v) pure nothrow @nogc { |
bool allNearSame(in Complex!T[] v) pure nothrow @nogc @safe { |
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auto v0 = v[0].Complex!T; // To avoid another cast. |
auto v0 = v[0].Complex!T; // To avoid another cast. |
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return v[1 .. $].all!(c=> feqrel(v0.re, cast()c.re) >= nBits && |
return v[1 .. $].all!(c=> feqrel(v0.re, cast()c.re) >= nBits && |
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bool isHermitian(T)(in Complex!T[][] m, in Complex!T[][] ct) |
bool isHermitian(T)(in Complex!T[][] m, in Complex!T[][] ct) |
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pure nothrow { |
pure nothrow /*@safe*/ { |
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return [m, ct].areEqual; |
return [m, ct].areEqual; |
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} |
} |
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bool isNormal(T)(immutable Complex!T[][] m, immutable Complex!T[][] ct) |
bool isNormal(T)(immutable Complex!T[][] m, immutable Complex!T[][] ct) |
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pure nothrow { |
pure nothrow /*@safe*/ { |
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return [matMul(m, ct), matMul(ct, m)].areEqual; |
return [matMul(m, ct), matMul(ct, m)].areEqual; |
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} |
} |
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auto complexIdentitymatrix(in size_t side) pure nothrow { |
auto complexIdentitymatrix(in size_t side) pure nothrow /*@safe*/ { |
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return side.iota |
return side.iota |
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.map!((in r) => side.iota.map!(c => complex(r == c)).array) |
.map!((in r) => side.iota.map!(c => complex(r == c)).array) |
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bool isUnitary(T)(immutable Complex!T[][] m, immutable Complex!T[][] ct) |
bool isUnitary(T)(immutable Complex!T[][] m, immutable Complex!T[][] ct) |
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pure nothrow { |
pure nothrow /*@safe*/ { |
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immutable mct = matMul(m, ct); |
immutable mct = matMul(m, ct); |
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immutable ident = mct.length.complexIdentitymatrix; |
immutable ident = mct.length.complexIdentitymatrix; |
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