mirror of https://github.com/k3s-io/k3s
473 lines
15 KiB
Go
473 lines
15 KiB
Go
// Copyright ©2015 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package blas64
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/gonum"
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)
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var blas64 blas.Float64 = gonum.Implementation{}
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// Use sets the BLAS float64 implementation to be used by subsequent BLAS calls.
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// The default implementation is
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// gonum.org/v1/gonum/blas/gonum.Implementation.
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func Use(b blas.Float64) {
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blas64 = b
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}
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// Implementation returns the current BLAS float64 implementation.
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//
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// Implementation allows direct calls to the current the BLAS float64 implementation
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// giving finer control of parameters.
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func Implementation() blas.Float64 {
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return blas64
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}
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// Vector represents a vector with an associated element increment.
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type Vector struct {
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N int
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Data []float64
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Inc int
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}
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// General represents a matrix using the conventional storage scheme.
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type General struct {
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Rows, Cols int
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Data []float64
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Stride int
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}
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// Band represents a band matrix using the band storage scheme.
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type Band struct {
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Rows, Cols int
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KL, KU int
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Data []float64
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Stride int
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}
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// Triangular represents a triangular matrix using the conventional storage scheme.
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type Triangular struct {
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Uplo blas.Uplo
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Diag blas.Diag
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N int
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Data []float64
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Stride int
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}
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// TriangularBand represents a triangular matrix using the band storage scheme.
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type TriangularBand struct {
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Uplo blas.Uplo
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Diag blas.Diag
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N, K int
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Data []float64
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Stride int
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}
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// TriangularPacked represents a triangular matrix using the packed storage scheme.
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type TriangularPacked struct {
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Uplo blas.Uplo
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Diag blas.Diag
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N int
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Data []float64
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}
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// Symmetric represents a symmetric matrix using the conventional storage scheme.
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type Symmetric struct {
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Uplo blas.Uplo
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N int
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Data []float64
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Stride int
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}
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// SymmetricBand represents a symmetric matrix using the band storage scheme.
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type SymmetricBand struct {
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Uplo blas.Uplo
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N, K int
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Data []float64
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Stride int
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}
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// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
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type SymmetricPacked struct {
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Uplo blas.Uplo
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N int
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Data []float64
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}
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// Level 1
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const (
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negInc = "blas64: negative vector increment"
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badLength = "blas64: vector length mismatch"
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)
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// Dot computes the dot product of the two vectors:
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// \sum_i x[i]*y[i].
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// Dot will panic if the lengths of x and y do not match.
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func Dot(x, y Vector) float64 {
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if x.N != y.N {
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panic(badLength)
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}
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return blas64.Ddot(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Nrm2 computes the Euclidean norm of the vector x:
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// sqrt(\sum_i x[i]*x[i]).
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//
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// Nrm2 will panic if the vector increment is negative.
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func Nrm2(x Vector) float64 {
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if x.Inc < 0 {
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panic(negInc)
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}
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return blas64.Dnrm2(x.N, x.Data, x.Inc)
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}
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// Asum computes the sum of the absolute values of the elements of x:
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// \sum_i |x[i]|.
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//
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// Asum will panic if the vector increment is negative.
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func Asum(x Vector) float64 {
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if x.Inc < 0 {
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panic(negInc)
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}
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return blas64.Dasum(x.N, x.Data, x.Inc)
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}
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// Iamax returns the index of an element of x with the largest absolute value.
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// If there are multiple such indices the earliest is returned.
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// Iamax returns -1 if n == 0.
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//
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// Iamax will panic if the vector increment is negative.
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func Iamax(x Vector) int {
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if x.Inc < 0 {
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panic(negInc)
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}
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return blas64.Idamax(x.N, x.Data, x.Inc)
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}
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// Swap exchanges the elements of the two vectors:
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// x[i], y[i] = y[i], x[i] for all i.
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// Swap will panic if the lengths of x and y do not match.
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func Swap(x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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blas64.Dswap(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Copy copies the elements of x into the elements of y:
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// y[i] = x[i] for all i.
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// Copy will panic if the lengths of x and y do not match.
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func Copy(x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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blas64.Dcopy(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Axpy adds x scaled by alpha to y:
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// y[i] += alpha*x[i] for all i.
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// Axpy will panic if the lengths of x and y do not match.
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func Axpy(alpha float64, x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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blas64.Daxpy(x.N, alpha, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Rotg computes the parameters of a Givens plane rotation so that
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// ⎡ c s⎤ ⎡a⎤ ⎡r⎤
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// ⎣-s c⎦ * ⎣b⎦ = ⎣0⎦
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// where a and b are the Cartesian coordinates of a given point.
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// c, s, and r are defined as
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// r = ±Sqrt(a^2 + b^2),
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// c = a/r, the cosine of the rotation angle,
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// s = a/r, the sine of the rotation angle,
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// and z is defined such that
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// if |a| > |b|, z = s,
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// otherwise if c != 0, z = 1/c,
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// otherwise z = 1.
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func Rotg(a, b float64) (c, s, r, z float64) {
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return blas64.Drotg(a, b)
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}
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// Rotmg computes the modified Givens rotation. See
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// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
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// for more details.
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func Rotmg(d1, d2, b1, b2 float64) (p blas.DrotmParams, rd1, rd2, rb1 float64) {
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return blas64.Drotmg(d1, d2, b1, b2)
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}
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// Rot applies a plane transformation to n points represented by the vectors x
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// and y:
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// x[i] = c*x[i] + s*y[i],
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// y[i] = -s*x[i] + c*y[i], for all i.
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func Rot(x, y Vector, c, s float64) {
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if x.N != y.N {
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panic(badLength)
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}
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blas64.Drot(x.N, x.Data, x.Inc, y.Data, y.Inc, c, s)
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}
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// Rotm applies the modified Givens rotation to n points represented by the
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// vectors x and y.
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func Rotm(x, y Vector, p blas.DrotmParams) {
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if x.N != y.N {
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panic(badLength)
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}
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blas64.Drotm(x.N, x.Data, x.Inc, y.Data, y.Inc, p)
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}
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// Scal scales the vector x by alpha:
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// x[i] *= alpha for all i.
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//
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// Scal will panic if the vector increment is negative.
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func Scal(alpha float64, x Vector) {
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if x.Inc < 0 {
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panic(negInc)
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}
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blas64.Dscal(x.N, alpha, x.Data, x.Inc)
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}
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// Level 2
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// Gemv computes
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// y = alpha * A * x + beta * y if t == blas.NoTrans,
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// y = alpha * Aᵀ * x + beta * y if t == blas.Trans or blas.ConjTrans,
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// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
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func Gemv(t blas.Transpose, alpha float64, a General, x Vector, beta float64, y Vector) {
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blas64.Dgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Gbmv computes
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// y = alpha * A * x + beta * y if t == blas.NoTrans,
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// y = alpha * Aᵀ * x + beta * y if t == blas.Trans or blas.ConjTrans,
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// where A is an m×n band matrix, x and y are vectors, and alpha and beta are scalars.
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func Gbmv(t blas.Transpose, alpha float64, a Band, x Vector, beta float64, y Vector) {
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blas64.Dgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Trmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular matrix, and x is a vector.
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func Trmv(t blas.Transpose, a Triangular, x Vector) {
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blas64.Dtrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tbmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular band matrix, and x is a vector.
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func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
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blas64.Dtbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tpmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular matrix in packed format, and x is a vector.
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func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
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blas64.Dtpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
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}
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// Trsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular matrix, and x and b are vectors.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in-place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Trsv(t blas.Transpose, a Triangular, x Vector) {
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blas64.Dtrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tbsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular band matrix, and x and b are vectors.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
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blas64.Dtbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tpsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
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// where A is an n×n triangular matrix in packed format, and x and b are
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// vectors.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
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blas64.Dtpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
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}
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// Symv computes
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// y = alpha * A * x + beta * y,
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// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
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// beta are scalars.
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func Symv(alpha float64, a Symmetric, x Vector, beta float64, y Vector) {
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blas64.Dsymv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Sbmv performs
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// y = alpha * A * x + beta * y,
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// where A is an n×n symmetric band matrix, x and y are vectors, and alpha
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// and beta are scalars.
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func Sbmv(alpha float64, a SymmetricBand, x Vector, beta float64, y Vector) {
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blas64.Dsbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Spmv performs
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// y = alpha * A * x + beta * y,
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// where A is an n×n symmetric matrix in packed format, x and y are vectors,
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// and alpha and beta are scalars.
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func Spmv(alpha float64, a SymmetricPacked, x Vector, beta float64, y Vector) {
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blas64.Dspmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Ger performs a rank-1 update
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// A += alpha * x * yᵀ,
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// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
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func Ger(alpha float64, x, y Vector, a General) {
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blas64.Dger(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
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}
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// Syr performs a rank-1 update
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// A += alpha * x * xᵀ,
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// where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.
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func Syr(alpha float64, x Vector, a Symmetric) {
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blas64.Dsyr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
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}
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// Spr performs the rank-1 update
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// A += alpha * x * xᵀ,
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// where A is an n×n symmetric matrix in packed format, x is a vector, and
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// alpha is a scalar.
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func Spr(alpha float64, x Vector, a SymmetricPacked) {
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blas64.Dspr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
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}
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// Syr2 performs a rank-2 update
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// A += alpha * x * yᵀ + alpha * y * xᵀ,
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// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
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func Syr2(alpha float64, x, y Vector, a Symmetric) {
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blas64.Dsyr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
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}
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// Spr2 performs a rank-2 update
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// A += alpha * x * yᵀ + alpha * y * xᵀ,
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// where A is an n×n symmetric matrix in packed format, x and y are vectors,
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// and alpha is a scalar.
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func Spr2(alpha float64, x, y Vector, a SymmetricPacked) {
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blas64.Dspr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
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}
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// Level 3
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// Gemm computes
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// C = alpha * A * B + beta * C,
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// where A, B, and C are dense matrices, and alpha and beta are scalars.
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// tA and tB specify whether A or B are transposed.
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func Gemm(tA, tB blas.Transpose, alpha float64, a, b General, beta float64, c General) {
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var m, n, k int
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if tA == blas.NoTrans {
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m, k = a.Rows, a.Cols
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} else {
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m, k = a.Cols, a.Rows
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}
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if tB == blas.NoTrans {
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n = b.Cols
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} else {
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n = b.Rows
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}
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blas64.Dgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
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}
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// Symm performs
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// C = alpha * A * B + beta * C if s == blas.Left,
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// C = alpha * B * A + beta * C if s == blas.Right,
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// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
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// alpha is a scalar.
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func Symm(s blas.Side, alpha float64, a Symmetric, b General, beta float64, c General) {
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var m, n int
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if s == blas.Left {
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m, n = a.N, b.Cols
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} else {
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m, n = b.Rows, a.N
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}
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blas64.Dsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
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}
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// Syrk performs a symmetric rank-k update
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// C = alpha * A * Aᵀ + beta * C if t == blas.NoTrans,
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// C = alpha * Aᵀ * A + beta * C if t == blas.Trans or blas.ConjTrans,
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// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans and
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// a k×n matrix otherwise, and alpha and beta are scalars.
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func Syrk(t blas.Transpose, alpha float64, a General, beta float64, c Symmetric) {
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var n, k int
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if t == blas.NoTrans {
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n, k = a.Rows, a.Cols
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} else {
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n, k = a.Cols, a.Rows
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}
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blas64.Dsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
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}
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// Syr2k performs a symmetric rank-2k update
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// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if t == blas.NoTrans,
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// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if t == blas.Trans or blas.ConjTrans,
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// where C is an n×n symmetric matrix, A and B are n×k matrices if t == NoTrans
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// and k×n matrices otherwise, and alpha and beta are scalars.
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func Syr2k(t blas.Transpose, alpha float64, a, b General, beta float64, c Symmetric) {
|
||
var n, k int
|
||
if t == blas.NoTrans {
|
||
n, k = a.Rows, a.Cols
|
||
} else {
|
||
n, k = a.Cols, a.Rows
|
||
}
|
||
blas64.Dsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||
}
|
||
|
||
// Trmm performs
|
||
// B = alpha * A * B if tA == blas.NoTrans and s == blas.Left,
|
||
// B = alpha * Aᵀ * B if tA == blas.Trans or 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 or 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 float64, a Triangular, b General) {
|
||
blas64.Dtrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||
}
|
||
|
||
// Trsm solves
|
||
// A * X = alpha * B if tA == blas.NoTrans and s == blas.Left,
|
||
// Aᵀ * X = alpha * B if tA == blas.Trans or 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 or 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.
|
||
//
|
||
// At entry to the function, X contains the values of B, and the result is
|
||
// stored in-place into X.
|
||
//
|
||
// No check is made that A is invertible.
|
||
func Trsm(s blas.Side, tA blas.Transpose, alpha float64, a Triangular, b General) {
|
||
blas64.Dtrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||
}
|