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blas,lapack: clean up docs and comments

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Apply (with manual curation after the fact):
* s/^T/U+1d40/g
* s/^H/U+1d34/g
* s/, {2,3}if / $1/g

Some additional manual editing of odd formatting.
This commit is contained in:
Dan Kortschak
2019-09-03 13:46:38 +09:30
parent 2065cbd6b4
commit 17ea55aedb
164 changed files with 949 additions and 949 deletions
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16
lapack/testlapack/general.go
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@@ -510,7 +510,7 @@ func constructH(tau []float64, v blas64.General, store lapack.StoreV, direct lap
for i := 0; i < m; i++ {
hi.Data[i*m+i] = 1
}
// hi = I - tau * v * v^T
// hi = I - tau * v * vᵀ
blas64.Ger(-tau[i], vec, vec, hi)
hcopy := blas64.General{
@@ -613,7 +613,7 @@ func constructQK(kind string, m, n, k int, a []float64, lda int, tau []float64)
// decomposition) is input in aCopy.
//
// checkBidiagonal constructs the V and U matrices, and from them constructs Q
// and P. Using these constructions, it checks that Q^T * A * P and checks that
// and P. Using these constructions, it checks that Qᵀ * A * P and checks that
// the result is bidiagonal.
func checkBidiagonal(t *testing.T, m, n, nb int, a []float64, lda int, d, e, tauP, tauQ, aCopy []float64) {
// Check the answer.
@@ -621,7 +621,7 @@ func checkBidiagonal(t *testing.T, m, n, nb int, a []float64, lda int, d, e, tau
qMat := constructQPBidiagonal(lapack.ApplyQ, m, n, nb, a, lda, tauQ)
pMat := constructQPBidiagonal(lapack.ApplyP, m, n, nb, a, lda, tauP)
// Compute Q^T * A * P.
// Compute Qᵀ * A * P.
aMat := blas64.General{
Rows: m,
Cols: n,
@@ -1052,7 +1052,7 @@ func randSymBand(uplo blas.Uplo, n, kd, ldab int, rnd *rand.Rand) []float64 {
ab[i*ldab+kd] = float64(n) + rnd.Float64()
}
}
// Compute U^T*U or L*L^T. The resulting (symmetric) matrix A will be
// Compute Uᵀ*U or L*Lᵀ. The resulting (symmetric) matrix A will be
// positive definite and well-conditioned.
dsbmm(uplo, n, kd, ab, ldab)
return ab
@@ -1324,9 +1324,9 @@ func isRightEigenvectorOf(a blas64.General, xRe, xIm []float64, lambda complex12
//
// A left eigenvector corresponding to a complex eigenvalue λ is a complex
// non-zero vector y such that
// y^H A = λ y^H,
// yᴴ A = λ yᴴ,
// which is equivalent for real A to
// A^T y = conj(λ) y,
// Aᵀ y = conj(λ) y,
func isLeftEigenvectorOf(a blas64.General, yRe, yIm []float64, lambda complex128, tol float64) bool {
if a.Rows != a.Cols {
panic("matrix not square")
@@ -1340,7 +1340,7 @@ func isLeftEigenvectorOf(a blas64.General, yRe, yIm []float64, lambda complex128
n := a.Rows
// Compute A^T real(y) and store the result into yReAns.
// Compute Aᵀ real(y) and store the result into yReAns.
yReAns := make([]float64, n)
blas64.Gemv(blas.Trans, 1, a, blas64.Vector{Data: yRe, Inc: 1}, 0, blas64.Vector{Data: yReAns, Inc: 1})
@@ -1358,7 +1358,7 @@ func isLeftEigenvectorOf(a blas64.General, yRe, yIm []float64, lambda complex128
// Complex eigenvector, and real or complex eigenvalue.
// Compute A^T imag(y) and store the result into yImAns.
// Compute Aᵀ imag(y) and store the result into yImAns.
yImAns := make([]float64, n)
blas64.Gemv(blas.Trans, 1, a, blas64.Vector{Data: yIm, Inc: 1}, 0, blas64.Vector{Data: yImAns, Inc: 1})