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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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112
blas/cblas64/cblas64.go
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@@ -111,14 +111,14 @@ const negInc = "cblas64: negative vector increment"
// Dotu computes the dot product of the two vectors without
// complex conjugation:
// x^T * y
// xᵀ * y
func Dotu(n int, x, y Vector) complex64 {
return cblas64.Cdotu(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Dotc computes the dot product of the two vectors with
// complex conjugation:
// x^H * y.
// xᴴ * y.
func Dotc(n int, x, y Vector) complex64 {
return cblas64.Cdotc(n, x.Data, x.Inc, y.Data, y.Inc)
}
@@ -206,9 +206,9 @@ func Dscal(n int, alpha float32, x Vector) {
// Level 2
// Gemv computes
// y = alpha * A * x + beta * y, if t == blas.NoTrans,
// y = alpha * A^T * x + beta * y, if t == blas.Trans,
// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
// y = alpha * A * x + beta * y if t == blas.NoTrans,
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
// scalars.
func Gemv(t blas.Transpose, alpha complex64, a General, x Vector, beta complex64, y Vector) {
@@ -216,9 +216,9 @@ func Gemv(t blas.Transpose, alpha complex64, a General, x Vector, beta complex64
}
// Gbmv computes
// y = alpha * A * x + beta * y, if t == blas.NoTrans,
// y = alpha * A^T * x + beta * y, if t == blas.Trans,
// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
// y = alpha * A * x + beta * y if t == blas.NoTrans,
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
// scalars.
func Gbmv(t blas.Transpose, alpha complex64, a Band, x Vector, beta complex64, y Vector) {
@@ -226,36 +226,36 @@ func Gbmv(t blas.Transpose, alpha complex64, a Band, x Vector, beta complex64, y
}
// Trmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// x = A * x if t == blas.NoTrans,
// x = Aᵀ * x if t == blas.Trans,
// x = Aᴴ * x if t == blas.ConjTrans,
// where A is an n×n triangular matrix, and x is a vector.
func Trmv(t blas.Transpose, a Triangular, x Vector) {
cblas64.Ctrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
}
// Tbmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// x = A * x if t == blas.NoTrans,
// x = Aᵀ * x if t == blas.Trans,
// x = Aᴴ * x if t == blas.ConjTrans,
// where A is an n×n triangular band matrix, and x is a vector.
func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
cblas64.Ctbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
}
// Tpmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// x = A * x if t == blas.NoTrans,
// x = Aᵀ * x if t == blas.Trans,
// x = Aᴴ * x if t == blas.ConjTrans,
// where A is an n×n triangular matrix in packed format, and x is a vector.
func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
cblas64.Ctpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
}
// Trsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// A * x = b if t == blas.NoTrans,
// Aᵀ * x = b if t == blas.Trans,
// Aᴴ * x = b if t == blas.ConjTrans,
// where A is an n×n triangular matrix and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
@@ -268,9 +268,9 @@ func Trsv(t blas.Transpose, a Triangular, x Vector) {
}
// Tbsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// A * x = b if t == blas.NoTrans,
// Aᵀ * x = b if t == blas.Trans,
// Aᴴ * x = b if t == blas.ConjTrans,
// where A is an n×n triangular band matrix, and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
@@ -283,9 +283,9 @@ func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
}
// Tpsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// A * x = b if t == blas.NoTrans,
// Aᵀ * x = b if t == blas.Trans,
// Aᴴ * x = b if t == blas.ConjTrans,
// where A is an n×n triangular matrix in packed format and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
@@ -322,28 +322,28 @@ func Hpmv(alpha complex64, a HermitianPacked, x Vector, beta complex64, y Vector
}
// Geru performs a rank-1 update
// A += alpha * x * y^T,
// A += alpha * x * yᵀ,
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
func Geru(alpha complex64, x, y Vector, a General) {
cblas64.Cgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Gerc performs a rank-1 update
// A += alpha * x * y^H,
// A += alpha * x * yᴴ,
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
func Gerc(alpha complex64, x, y Vector, a General) {
cblas64.Cgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Her performs a rank-1 update
// A += alpha * x * y^T,
// A += alpha * x * yᵀ,
// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
func Her(alpha float32, x Vector, a Hermitian) {
cblas64.Cher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
}
// Hpr performs a rank-1 update
// A += alpha * x * x^H,
// A += alpha * x * xᴴ,
// where A is an n×n Hermitian matrix in packed format, x is a vector, and
// alpha is a scalar.
func Hpr(alpha float32, x Vector, a HermitianPacked) {
@@ -351,14 +351,14 @@ func Hpr(alpha float32, x Vector, a HermitianPacked) {
}
// Her2 performs a rank-2 update
// A += alpha * x * y^H + conj(alpha) * y * x^H,
// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
func Her2(alpha complex64, x, y Vector, a Hermitian) {
cblas64.Cher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Hpr2 performs a rank-2 update
// A += alpha * x * y^H + conj(alpha) * y * x^H,
// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
// and alpha is a scalar.
func Hpr2(alpha complex64, x, y Vector, a HermitianPacked) {
@@ -387,8 +387,8 @@ func Gemm(tA, tB blas.Transpose, alpha complex64, a, b General, beta complex64,
}
// Symm performs
// C = alpha * A * B + beta * C, if s == blas.Left,
// C = alpha * B * A + beta * C, if s == blas.Right,
// C = alpha * A * B + beta * C if s == blas.Left,
// C = alpha * B * A + beta * C if s == blas.Right,
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
// alpha and beta are scalars.
func Symm(s blas.Side, alpha complex64, a Symmetric, b General, beta complex64, c General) {
@@ -402,8 +402,8 @@ func Symm(s blas.Side, alpha complex64, a Symmetric, b General, beta complex64,
}
// Syrk performs a symmetric rank-k update
// C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
// C = alpha * A^T * A + beta * C, if t == blas.Trans,
// C = alpha * A * Aᵀ + beta * C if t == blas.NoTrans,
// C = alpha * Aᵀ * A + beta * C if t == blas.Trans,
// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
// and a k×n matrix otherwise, and alpha and beta are scalars.
func Syrk(t blas.Transpose, alpha complex64, a General, beta complex64, c Symmetric) {
@@ -417,8 +417,8 @@ func Syrk(t blas.Transpose, alpha complex64, a General, beta complex64, c Symmet
}
// Syr2k performs a symmetric rank-2k update
// C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
// C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans,
// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if t == blas.NoTrans,
// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if t == blas.Trans,
// where C is an n×n symmetric matrix, A and B are n×k matrices if
// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
func Syr2k(t blas.Transpose, alpha complex64, a, b General, beta complex64, c Symmetric) {
@@ -432,12 +432,12 @@ func Syr2k(t blas.Transpose, alpha complex64, a, b General, beta complex64, c Sy
}
// Trmm performs
// B = alpha * A * B, if tA == blas.NoTrans and s == blas.Left,
// B = alpha * A^T * B, if tA == blas.Trans and s == blas.Left,
// B = alpha * A^H * B, if tA == blas.ConjTrans and s == blas.Left,
// B = alpha * B * A, if tA == blas.NoTrans and s == blas.Right,
// B = alpha * B * A^T, if tA == blas.Trans and s == blas.Right,
// B = alpha * B * A^H, if tA == blas.ConjTrans and s == blas.Right,
// B = alpha * A * B if tA == blas.NoTrans and s == blas.Left,
// B = alpha * Aᵀ * B if tA == blas.Trans and s == blas.Left,
// B = alpha * Aᴴ * B if tA == blas.ConjTrans and s == blas.Left,
// B = alpha * B * A if tA == blas.NoTrans and s == blas.Right,
// B = alpha * B * Aᵀ if tA == blas.Trans and s == blas.Right,
// B = alpha * B * Aᴴ if tA == blas.ConjTrans and s == blas.Right,
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
// a scalar.
func Trmm(s blas.Side, tA blas.Transpose, alpha complex64, a Triangular, b General) {
@@ -445,12 +445,12 @@ func Trmm(s blas.Side, tA blas.Transpose, alpha complex64, a Triangular, b Gener
}
// Trsm solves
// A * X = alpha * B, if tA == blas.NoTrans and s == blas.Left,
// A^T * X = alpha * B, if tA == blas.Trans and s == blas.Left,
// A^H * X = alpha * B, if tA == blas.ConjTrans and s == blas.Left,
// X * A = alpha * B, if tA == blas.NoTrans and s == blas.Right,
// X * A^T = alpha * B, if tA == blas.Trans and s == blas.Right,
// X * A^H = alpha * B, if tA == blas.ConjTrans and s == blas.Right,
// A * X = alpha * B if tA == blas.NoTrans and s == blas.Left,
// Aᵀ * X = alpha * B if tA == blas.Trans and s == blas.Left,
// Aᴴ * X = alpha * B if tA == blas.ConjTrans and s == blas.Left,
// X * A = alpha * B if tA == blas.NoTrans and s == blas.Right,
// X * Aᵀ = alpha * B if tA == blas.Trans and s == blas.Right,
// X * Aᴴ = alpha * B if tA == blas.ConjTrans and s == blas.Right,
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
// alpha is a scalar.
//
@@ -463,8 +463,8 @@ func Trsm(s blas.Side, tA blas.Transpose, alpha complex64, a Triangular, b Gener
}
// Hemm performs
// C = alpha * A * B + beta * C, if s == blas.Left,
// C = alpha * B * A + beta * C, if s == blas.Right,
// C = alpha * A * B + beta * C if s == blas.Left,
// C = alpha * B * A + beta * C if s == blas.Right,
// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
// alpha and beta are scalars.
func Hemm(s blas.Side, alpha complex64, a Hermitian, b General, beta complex64, c General) {
@@ -478,8 +478,8 @@ func Hemm(s blas.Side, alpha complex64, a Hermitian, b General, beta complex64,
}
// Herk performs the Hermitian rank-k update
// C = alpha * A * A^H + beta*C, if t == blas.NoTrans,
// C = alpha * A^H * A + beta*C, if t == blas.ConjTrans,
// C = alpha * A * Aᴴ + beta*C if t == blas.NoTrans,
// C = alpha * Aᴴ * A + beta*C if t == blas.ConjTrans,
// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
// and a k×n matrix otherwise, and alpha and beta are scalars.
func Herk(t blas.Transpose, alpha float32, a General, beta float32, c Hermitian) {
@@ -493,8 +493,8 @@ func Herk(t blas.Transpose, alpha float32, a General, beta float32, c Hermitian)
}
// Her2k performs the Hermitian rank-2k update
// C = alpha * A * B^H + conj(alpha) * B * A^H + beta * C, if t == blas.NoTrans,
// C = alpha * A^H * B + conj(alpha) * B^H * A + beta * C, if t == blas.ConjTrans,
// C = alpha * A * Bᴴ + conj(alpha) * B * Aᴴ + beta * C if t == blas.NoTrans,
// C = alpha * Aᴴ * B + conj(alpha) * Bᴴ * A + beta * C if t == blas.ConjTrans,
// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
// and k×n matrices otherwise, and alpha and beta are scalars.
func Her2k(t blas.Transpose, alpha complex64, a, b General, beta float32, c Hermitian) {