cublas

package
v0.9.4 Latest Latest
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 Go to latest Published: Aug 2, 2021 License: Apache-2.0 Imports: 6 Imported by: 6

README

cublas

Package cublas implements a Go API for CUDA's cuBLAS. It matches the gonum/blas interface.

How To Use

To install: go get -u gorgonia.org/cu

The CUDA Toolkit 8.0 is required. LDFlags and CFlags may not be quite accurate. File an issue if you find one, thank you.

Bear in mind that cublas only supports FORTRAN ordered matrices. Most Go matrices are created with the C ordering (gonum/matrix, gorgonia/tensor), therefore care must be applied.

For example, here's how to use Dgemm:

func main() {
	dev := cu.Device(0)
	ctx, err := dev.MakeContext(cu.SchedAuto)
	if err != nil {
		log.Fatal(err)
	}
	defer cu.DestroyContext(&ctx)

	dt := tensor.Float64
	s0 := tensor.Shape{5, 10}
	s1 := tensor.Shape{10, 12}
	s2 := tensor.Shape{5, 12}

	memsize0 := calcMemsize(dt, s0)
	mem0, err := cu.MemAllocManaged(memsize0, cu.AttachGlobal)
	if err != nil {
		log.Fatal(err)
	}
	mat0 := tensor.New(tensor.Of(dt), tensor.WithShape(s0...), tensor.FromMemory(uintptr(mem0), uintptr(memsize0)))
	d0 := mat0.Data().([]float64)
	for i := range d0 {
		d0[i] = float64(i + 1)
	}
	fmt.Printf("A: \n%#v\n", mat0)

	memsize1 := calcMemsize(dt, s1)
	mem1, err := cu.MemAllocManaged(memsize1, cu.AttachGlobal)
	if err != nil {
		log.Fatal(err)
	}
	mat1 := tensor.New(tensor.Of(dt), tensor.WithShape(s1...), tensor.FromMemory(uintptr(mem1), uintptr(memsize1)))
	d1 := mat1.Data().([]float64)
	for i := range d1 {
		d1[i] = float64(i + 1)
	}
	fmt.Printf("B: \n%#v\n", mat1)

	memsize2 := calcMemsize(dt, s2)
	mem2, err := cu.MemAllocManaged(memsize2, cu.AttachGlobal)
	if err != nil {
		log.Fatal(err)
	}
	mat2 := tensor.New(tensor.Of(dt), tensor.WithShape(s2...), tensor.FromMemory(uintptr(mem2), uintptr(memsize2)))
	d2 := mat2.Data().([]float64)
	fmt.Printf("C: \n%#v\n", mat2)

	impl := cublas.NewImplementation()

	m := s0[0]
	k := s0[1]
	n := s1[1]
	lda := mat0.Strides()[0]
	ldb := mat1.Strides()[0]
	ldc := mat2.Strides()[0]
	alpha := 1.0
	beta := 0.0
	impl.Dgemm(blas.NoTrans, blas.NoTrans, n, m, k, alpha, d1, ldn, d0, lda, beta, d2, ldc)
	if err := cu.Synchronize(); err != nil {
		log.Fatal(err)
	}
	fmt.Printf("C: \n%#v\n", mat2)
	cu.MemFree(mem0)
	cu.MemFree(mem1)
	cu.MemFree(mem2)
}

These are things to note: To do a A×B, you need to essentially do Bᵀ×Aᵀ.

How This Package Is Developed

The majority of the CUDA interface was generated with the cublasgen program. The cublasgen program was adapted from the cgo generator from the gonum/blas package.

The cudagen.h file was generated based off the propietary header from nvidia, then further edited (several variable names were renamed) to match the cblas interface in order to quickly generate the API.

Documentation

Overview

Example 
package main

import (
	"reflect"
	"runtime"
	"unsafe"

	"github.com/pkg/errors"
	"gonum.org/v1/gonum/blas"
	"gorgonia.org/cu"
	cublas "gorgonia.org/cu/blas"
	"gorgonia.org/tensor"
)

type Engine struct {
	tensor.StdEng
	ctx cu.Context
	*cublas.Standard
}

func newEngine() *Engine {
	ctx := cu.NewContext(cu.Device(0), cu.SchedAuto)
	blas := cublas.New(cublas.WithContext(ctx))
	return &Engine{
		ctx:      ctx,
		Standard: blas,
	}
}

func (e *Engine) AllocAccessible() bool { return true }

func (e *Engine) Alloc(size int64) (tensor.Memory, error) {
	return e.ctx.MemAllocManaged(size, cu.AttachGlobal)
}

func (e *Engine) AllocFlags() (tensor.MemoryFlag, tensor.DataOrder) {
	return tensor.MakeMemoryFlag(tensor.ManuallyManaged), tensor.ColMajor
}

func (e *Engine) Free(mem tensor.Memory, size int64) error {
	e.ctx.MemFree(mem.(cu.DevicePtr))
	return nil
}

func (e *Engine) Memset(mem tensor.Memory, val interface{}) error {
	panic("not implemented")
}

func (e *Engine) Memclr(mem tensor.Memory) {
	panic("not implemented")
}

func (e *Engine) Memcpy(dst tensor.Memory, src tensor.Memory) error {
	panic("not implemented")
}

func (e *Engine) Accessible(mem tensor.Memory) (tensor.Memory, error) {
	// panic("not implemented")
	size := mem.MemSize()
	retVal := make([]byte, int(size))
	e.ctx.MemcpyDtoH(unsafe.Pointer(&retVal[0]), cu.DevicePtr(mem.Uintptr()), int64(size))
	l := int(size / 8)
	foo2 := &reflect.SliceHeader{
		Data: uintptr(unsafe.Pointer(&retVal[0])),
		Len:  l,
		Cap:  l,
	}
	return *(*foomem)(unsafe.Pointer(foo2)), e.ctx.Error()

}

func (e *Engine) WorksWith(order tensor.DataOrder) bool { return true }

func (e *Engine) NonStdAlloc() {}

func (e *Engine) ContextErr() error { return e.ctx.Error() }

type foomem []float64

func (m foomem) Uintptr() uintptr { return uintptr(unsafe.Pointer(&m[0])) }
func (m foomem) MemSize() uintptr { return uintptr(len(m) * 8) }

func (e *Engine) checkThreeFloat(a, b, ret tensor.Tensor) (ad, bd, retVal *tensor.Dense, err error) {
	if /*a.IsNativelyAccessible() &&*/ !a.IsManuallyManaged() {
		return nil, nil, nil, errors.New("CUDA Engine only takes non-natively accessible memory (memory on graphics cards). a isn't.")
	}

	if /* b.IsNativelyAccessible() && */ !b.IsManuallyManaged() {
		return nil, nil, nil, errors.New("CUDA Engine only takes non-natively accessible memory (memory on graphics cards). b isn't")
	}

	if /* ret.IsNativelyAccessible() && */ !ret.IsManuallyManaged() {
		return nil, nil, nil, errors.New("CUDA Engine only takes non-natively accessible memory (memory on graphics cards). ret isn't")
	}

	if a.Dtype() != b.Dtype() || b.Dtype() != ret.Dtype() {
		return nil, nil, nil, errors.New("Expected a and b and retVal all to have the same Dtype")
	}
	var ok bool
	if ad, ok = a.(*tensor.Dense); !ok {
		return nil, nil, nil, errors.New("Expected a to be a *tensor.Dense")
	}
	if bd, ok = b.(*tensor.Dense); !ok {
		return nil, nil, nil, errors.New("Expected b to be a *tensor.Dense")
	}
	if retVal, ok = ret.(*tensor.Dense); !ok {
		return nil, nil, nil, errors.New("Expected ret to be a *tensor.Dense")
	}
	return
}

func (e *Engine) MatVecMul(a, b, prealloc tensor.Tensor) (err error) {
	var ad, bd, pd *tensor.Dense
	if ad, bd, pd, err = e.checkThreeFloat(a, b, prealloc); err != nil {
		return errors.Wrapf(err, "MatVecMul failed pre check")
	}

	tA := blas.Trans
	do := a.DataOrder()
	z := do.IsTransposed()

	m := a.Shape()[0]
	n := a.Shape()[1]

	var lda int
	switch {
	case do.IsRowMajor() && z:
		tA = blas.NoTrans
		lda = m
	case do.IsRowMajor() && !z:
		lda = n
		m, n = n, m
	case do.IsColMajor() && z:
		tA = blas.Trans
		lda = n
		m, n = n, m
	case do.IsColMajor() && !z:
		lda = m
		tA = blas.NoTrans
	}

	incX, incY := 1, 1 // step size

	// ASPIRATIONAL TODO: different incX and incY
	// TECHNICAL DEBT. TECHDEBT. TECH DEBT
	// Example use case:
	// log.Printf("a %v %v", ad.Strides(), ad.ostrides())
	// log.Printf("b %v", b.Strides())
	// incX := a.Strides()[0]
	// incY = b.Strides()[0]

	switch ad.Dtype() {
	case tensor.Float64:
		A := ad.Float64s()
		X := bd.Float64s()
		Y := pd.Float64s()
		alpha, beta := float64(1), float64(0)
		e.Standard.Dgemv(tA, m, n, alpha, A, lda, X, incX, beta, Y, incY)
	case tensor.Float32:
		A := ad.Float32s()
		X := bd.Float32s()
		Y := pd.Float32s()
		alpha, beta := float32(1), float32(0)
		e.Standard.Sgemv(tA, m, n, alpha, A, lda, X, incX, beta, Y, incY)
	default:
		return errors.New("Unsupported Dtype")
	}
	return e.Standard.Err()
}

func (e *Engine) MatMul(a, b, prealloc tensor.Tensor) (err error) {
	var ad, bd, pd *tensor.Dense
	if ad, bd, pd, err = e.checkThreeFloat(a, b, prealloc); err != nil {
		return errors.Wrapf(err, "MatVecMul failed pre check")
	}

	ado := a.DataOrder()
	bdo := b.DataOrder()
	if !ado.HasSameOrder(bdo) {
		return errors.Errorf("a does not have the same data order as b. a is %v. b is %v", a.DataOrder(), b.DataOrder())
	}

	// get result shapes. k is the shared dimension
	// a is (m, k)
	// b is (k, n)
	// c is (m, n)
	var m, n, k int
	m = ad.Shape()[0]
	k = ad.Shape()[1]
	n = bd.Shape()[1]

	// // wrt the strides, we use the original strides, because that's what BLAS needs, instead of calling .Strides()
	// // lda in colmajor = number of rows;
	// // lda in row major = number of cols
	var lda, ldb, ldc int
	tA, tB := blas.Trans, blas.Trans
	za := ado.IsTransposed()
	zb := bdo.IsTransposed()

	// swapping around the operands if they are row major (a becomes b, and b becomes a)
	switch {
	case ado.IsColMajor() && bdo.IsColMajor() && !za && !zb:
		lda = m
		ldb = k
		ldc = prealloc.Shape()[0]
		tA, tB = blas.NoTrans, blas.NoTrans
	case ado.IsColMajor() && bdo.IsColMajor() && za && !zb:
		lda = k
		ldb = k
		ldc = prealloc.Shape()[0]
		tA, tB = blas.Trans, blas.NoTrans
	case ado.IsColMajor() && bdo.IsColMajor() && za && zb:
		lda = k
		ldb = n
		ldc = prealloc.Shape()[0]
		tA, tB = blas.Trans, blas.Trans
	case ado.IsColMajor() && bdo.IsColMajor() && !za && zb:
		lda = m
		ldb = n
		ldc = prealloc.Shape()[0]
		tA, tB = blas.NoTrans, blas.Trans
	case ado.IsRowMajor() && bdo.IsRowMajor() && !za && !zb:
		lda = k
		ldb = n
		ldc = prealloc.Shape()[1]
		tA, tB = blas.NoTrans, blas.NoTrans

		// magic swappy thingy
		m, n = n, m
		lda, ldb = ldb, lda
		ad, bd = bd, ad
	case ado.IsRowMajor() && bdo.IsRowMajor() && za && !zb:
		lda = m
		ldb = n
		ldc = prealloc.Shape()[1]
		tA, tB = blas.Trans, blas.NoTrans

		// magic swappy thingy
		m, n = n, m
		lda, ldb = ldb, lda
		tA, tB = tB, tA
		ad, bd = bd, ad
	case ado.IsRowMajor() && bdo.IsRowMajor() && za && zb:
		lda = m
		ldb = k
		ldc = prealloc.Shape()[1]
		tA, tB = blas.Trans, blas.Trans

		// magic swappy thingy
		m, n = n, m
		lda, ldb = ldb, lda
		ad, bd = bd, ad
	case ado.IsRowMajor() && bdo.IsRowMajor() && !za && zb:
		lda = k
		ldb = k
		ldc = prealloc.Shape()[1]
		tA, tB = blas.NoTrans, blas.Trans

		// magic swappy thingy
		m, n = n, m
		lda, ldb = ldb, lda
		tA, tB = tB, tA
		ad, bd = bd, ad

	default:
		panic("Unreachable")
	}

	switch ad.Dtype() {
	case tensor.Float64:
		A := ad.Float64s()
		B := bd.Float64s()
		C := pd.Float64s()
		alpha, beta := float64(1), float64(0)
		e.Standard.Dgemm(tA, tB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc)

	case tensor.Float32:
		A := ad.Float32s()
		B := bd.Float32s()
		C := pd.Float32s()
		alpha, beta := float32(1), float32(0)
		e.Standard.Sgemm(tA, tB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc)
	default:
		return errors.Errorf("Unsupported Dtype %v", ad.Dtype())
	}
	return e.Standard.Err()
}

func (e *Engine) Outer(a, b, prealloc tensor.Tensor) (err error) {
	var ad, bd, pd *tensor.Dense
	if ad, bd, pd, err = e.checkThreeFloat(a, b, prealloc); err != nil {
		return errors.Wrapf(err, "MatVecMul failed pre check")
	}
	m := ad.Size()
	n := bd.Size()
	pdo := pd.DataOrder()

	var lda int
	switch {
	case pdo.IsColMajor():
		lda = pd.Shape()[0]
	case pdo.IsRowMajor():
		aShape := a.Shape().Clone()
		bShape := b.Shape().Clone()
		if err = a.Reshape(aShape[0], 1); err != nil {
			return err
		}
		if err = b.Reshape(1, bShape[0]); err != nil {
			return err
		}

		if err = e.MatMul(a, b, prealloc); err != nil {
			return err
		}

		if err = b.Reshape(bShape...); err != nil {
			return
		}
		if err = a.Reshape(aShape...); err != nil {
			return
		}
		return nil
	}
	incX, incY := 1, 1
	switch ad.Dtype() {
	case tensor.Float64:
		x := ad.Float64s()
		y := bd.Float64s()
		A := pd.Float64s()
		alpha := float64(1)
		e.Standard.Dger(m, n, alpha, x, incX, y, incY, A, lda)
	case tensor.Float32:
		x := ad.Float32s()
		y := bd.Float32s()
		A := pd.Float32s()
		alpha := float32(1)
		e.Standard.Sger(m, n, alpha, x, incX, y, incY, A, lda)
	}
	return e.Standard.Err()
}
func main() {
	// debug.SetGCPercent(-1)
	runtime.LockOSThread()
	defer runtime.UnlockOSThread()

	matVecMulColmajorNonTransposed()
	matVecMulColmajorTransposed()
	matVecMulRowMajorNonTransposed()
	matVecMulRowMajorTransposed()

	matMulColmajorNTNT()
	matMulColmajorTNT()
	matMulColmajorTT()
	matMulColmajorNTT()

	matMulRowmajorNTNT()
	matMulRowmajorTNT()
	matMulRowmajorTT()
	matMulRowmajorNTT()

	outerColMajor()
	outerRowMajor()

}

Output:

ColMajor Non Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:[1  2  3]
C:[1000  1000]
C:
[14 32]
==========
ColMajor Transposed
A:
⎡1  4⎤
⎢2  5⎥
⎣3  6⎦

B:[1  2]
C[1000  1000  1000]
C:
[9 12 15]
==========
RowMajor Non Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:[1  2  3]
C[1000  1000]
C:
[14 32]
==========
RowMajor Transposed
A:
⎡1  4⎤
⎢2  5⎥
⎣3  6⎦

B:[1  2]
C[1000  1000  1000]
C:
[9 12 15]
==========
ColMajor Non Transposed Non Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:
⎡ 0   1   2   3⎤
⎢ 4   5   6   7⎥
⎣ 8   9  10  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[32 68 38 83 44 98 50 113]
==========
ColMajor Transposed Non Transposed
A:
⎡1  4⎤
⎢2  5⎥
⎣3  6⎦

B:
⎡0  1  2  3⎤
⎣4  5  6  7⎦

C:
⎡1000  1000  1000  1000⎤
⎢1000  1000  1000  1000⎥
⎣1000  1000  1000  1000⎦

C:
[16 20 24 21 27 33 26 34 42 31 41 51]
==========
ColMajor Transposed Transposed
A:
⎡1  4⎤
⎢2  5⎥
⎣3  6⎦

B:
⎡0  2  4  6⎤
⎣1  3  5  7⎦

C:
⎡1000  1000  1000  1000⎤
⎢1000  1000  1000  1000⎥
⎣1000  1000  1000  1000⎦

C:
[4 5 6 14 19 24 24 33 42 34 47 60]
==========
ColMajor Non Transposed Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:
⎡ 0   3   6   9⎤
⎢ 1   4   7  10⎥
⎣ 2   5   8  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[8 17 26 62 44 107 62 152]
==========
RowMajor Non Transposed Non Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:
⎡ 0   1   2   3⎤
⎢ 4   5   6   7⎥
⎣ 8   9  10  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[32 38 44 50 68 83 98 113]
==========
RowMajor Transposed Non Transposed
A:
⎡1  3  5⎤
⎣2  4  6⎦

B:
⎡ 0   1   2   3⎤
⎢ 4   5   6   7⎥
⎣ 8   9  10  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[52 61 70 79 64 76 88 100]
==========
RowMajor Transposed Non Transposed
A:
⎡1  3  5⎤
⎣2  4  6⎦

B:
⎡ 0   3   6   9⎤
⎢ 1   4   7  10⎥
⎣ 2   5   8  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[13 40 67 94 16 52 88 124]
==========
RowMajor Transposed Non Transposed
A:
⎡1  2  3⎤
⎣4  5  6⎦

B:
⎡ 0   3   6   9⎤
⎢ 1   4   7  10⎥
⎣ 2   5   8  11⎦

C:
⎡1000  1000  1000  1000⎤
⎣1000  1000  1000  1000⎦

C:
[8 26 44 62 17 62 107 152]
==========
RowMajor Non Transposed
A:
[1  2  3]
B:[0  1]
C
⎡1000  1000⎤
⎢1000  1000⎥
⎣1000  1000⎦

C:
[0 0 0 1 2 3]
==========
RowMajor Non Transposed
A:
[1  2  3]
B:[0  1]
C
⎡1000  1000⎤
⎢1000  1000⎥
⎣1000  1000⎦

C:
[0 1 0 2 0 3]
==========

Index

Examples

Constants

View Source 
const (
	NoTrans   = C.CUBLAS_OP_N // NoTrans represents the no-transpose operation
	Trans     = C.CUBLAS_OP_T // Trans represents the transpose operation
	ConjTrans = C.CUBLAS_OP_C // ConjTrans represents the conjugate transpose operation

	Upper = C.CUBLAS_FILL_MODE_UPPER // Upper is used to specify that the matrix is an upper triangular matrix
	Lower = C.CUBLAS_FILL_MODE_LOWER // Lower is used to specify that the matrix is an lower triangular matrix

	NonUnit = C.CUBLAS_DIAG_NON_UNIT // NonUnit is used to specify that the matrix is not a unit triangular matrix
	Unit    = C.CUBLAS_DIAG_UNIT     // Unit is used to specify that the matrix is a unit triangular matrix

	Left  = C.CUBLAS_SIDE_LEFT  // Left is used to specify a multiplication op is performed from the left
	Right = C.CUBLAS_SIDE_RIGHT // Right is used to specify a multiplication op is performed from the right
)

Variables

This section is empty.

Functions

This section is empty.

Types

type BLAS 

type BLAS interface {
	cu.Context
	blas.Float32
	blas.Float64
	blas.Complex64
	blas.Complex128
}

BLAS is the interface for all cuBLAS implementaions

type ConsOpt added in v0.9.1 

type ConsOpt func(impl *Standard)

func WithContext added in v0.9.1 

func WithContext(ctx cu.Context) ConsOpt

func WithNativeData added in v0.9.1 

func WithNativeData() ConsOpt

type Order 

type Order byte

Order is used to specify the matrix storage format. We still interact with an API that allows client calls to specify order, so this is here to document that fact. 

const (
	RowMajor Order = iota // Row Major
	ColMajor              // Column Major (cublas assumes all matrices be stored in this order)
)

type PointerMode 

type PointerMode byte

PointerMode 

const (
	Host PointerMode = iota
	Device
)

type Standard 

type Standard struct {
	cu.Context

	sync.Mutex
	// contains filtered or unexported fields
}

Standard is the standard cuBLAS handler. By default it assumes that the data is in RowMajor, DESPITE the fact that cuBLAS takes ColMajor only. This is done for the ease of use of developers writing in Go.

Use New to create a new BLAS handler. Use the various ConsOpts to set the options

func New added in v0.9.1 

func New(opts ...ConsOpt) *Standard

func (*Standard) Caxpy 

func (impl *Standard) Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int)

func (*Standard) Ccopy 

func (impl *Standard) Ccopy(n int, x []complex64, incX int, y []complex64, incY int)

func (*Standard) Cdgmm 

func (impl *Standard) Cdgmm(mode blas.Side, m, n int, a []complex64, lda int, x []complex64, incX int, c []complex64, ldc int)

func (*Standard) Cdotc 

func (impl *Standard) Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64)

func (*Standard) Cdotu 

func (impl *Standard) Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64)

func (*Standard) Cgbmv 

func (impl *Standard) Cgbmv(tA blas.Transpose, m, n, kl, ku int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Cgeam 

func (impl *Standard) Cgeam(tA, tB blas.Transpose, m, n int, alpha complex64, a []complex64, lda int, beta complex64, b []complex64, ldb int, c []complex64, ldc int)

func (*Standard) Cgemm 

func (impl *Standard) Cgemm(tA, tB blas.Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Cgemm3m 

func (impl *Standard) Cgemm3m(tA, tB blas.Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Cgemv 

func (impl *Standard) Cgemv(tA blas.Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Cgerc 

func (impl *Standard) Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

func (*Standard) Cgeru 

func (impl *Standard) Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

func (*Standard) Chbmv 

func (impl *Standard) Chbmv(ul blas.Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Chemm 

func (impl *Standard) Chemm(s blas.Side, ul blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Chemv 

func (impl *Standard) Chemv(ul blas.Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Cher 

func (impl *Standard) Cher(ul blas.Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int)

func (*Standard) Cher2 

func (impl *Standard) Cher2(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

func (*Standard) Cher2k 

func (impl *Standard) Cher2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)

func (*Standard) Cherk 

func (impl *Standard) Cherk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int)

func (*Standard) Cherkx 

func (impl *Standard) Cherkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)

func (*Standard) Chpmv 

func (impl *Standard) Chpmv(ul blas.Uplo, n int, alpha complex64, aP, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Chpr 

func (impl *Standard) Chpr(ul blas.Uplo, n int, alpha float32, x []complex64, incX int, aP []complex64)

func (*Standard) Chpr2 

func (impl *Standard) Chpr2(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, aP []complex64)

func (*Standard) Close added in v0.9.1 

func (impl *Standard) Close() error

func (*Standard) Crot 

func (impl *Standard) Crot(n int, x []complex64, incX int, y []complex64, incY int, cScalar float32, sScalar []complex64)

func (*Standard) Cscal 

func (impl *Standard) Cscal(n int, alpha complex64, x []complex64, incX int)

func (*Standard) Csscal 

func (impl *Standard) Csscal(n int, alpha float32, x []complex64, incX int)

func (*Standard) Cswap 

func (impl *Standard) Cswap(n int, x []complex64, incX int, y []complex64, incY int)

func (*Standard) Csymm 

func (impl *Standard) Csymm(s blas.Side, ul blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Csymv 

func (impl *Standard) Csymv(ul blas.Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

func (*Standard) Csyr 

func (impl *Standard) Csyr(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, a []complex64, lda int)

func (*Standard) Csyr2 

func (impl *Standard) Csyr2(ul blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

func (*Standard) Csyr2k 

func (impl *Standard) Csyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Csyrk 

func (impl *Standard) Csyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int)

func (*Standard) Csyrkx 

func (impl *Standard) Csyrkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

func (*Standard) Ctbmv 

func (impl *Standard) Ctbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int)

func (*Standard) Ctbsv 

func (impl *Standard) Ctbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int)

func (*Standard) Ctpmv 

func (impl *Standard) Ctpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []complex64, incX int)

func (*Standard) Ctpsv 

func (impl *Standard) Ctpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []complex64, incX int)

func (*Standard) Ctpttr 

func (impl *Standard) Ctpttr(ul blas.Uplo, n int, aP, a []complex64, lda int)

func (*Standard) Ctrmm 

func (impl *Standard) Ctrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)

func (*Standard) Ctrmv 

func (impl *Standard) Ctrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex64, lda int, x []complex64, incX int)

func (*Standard) Ctrsm 

func (impl *Standard) Ctrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)

func (*Standard) Ctrsv 

func (impl *Standard) Ctrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex64, lda int, x []complex64, incX int)

func (*Standard) Ctrttp 

func (impl *Standard) Ctrttp(ul blas.Uplo, n int, a []complex64, lda int, aP []complex64)

func (*Standard) Dasum 

func (impl *Standard) Dasum(n int, x []float64, incX int) (retVal float64)

Dasum computes the sum of the absolute values of the elements of x. 

\sum_i |x[i]|

Dasum returns 0 if incX is negative.

func (*Standard) Daxpy 

func (impl *Standard) Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)

Daxpy adds alpha times x to y 

y[i] += alpha * x[i] for all i

func (*Standard) Dcopy 

func (impl *Standard) Dcopy(n int, x []float64, incX int, y []float64, incY int)

Dcopy copies the elements of x into the elements of y. 

y[i] = x[i] for all i

func (*Standard) Ddgmm 

func (impl *Standard) Ddgmm(mode blas.Side, m, n int, a []float64, lda int, x []float64, incX int, c []float64, ldc int)

func (*Standard) Ddot 

func (impl *Standard) Ddot(n int, x []float64, incX int, y []float64, incY int) (retVal float64)

Ddot computes the dot product of the two vectors 

\sum_i x[i]*y[i]

func (*Standard) Dgbmv 

func (impl *Standard) Dgbmv(tA blas.Transpose, m, n, kl, ku int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dgbmv computes 

y = alpha * A * x + beta * y if tA == blas.NoTrans
y = alpha * A^T * x + beta * y if tA == blas.Trans or blas.ConjTrans

where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and m and n refer to the size of the full dense matrix it represents. x and y are vectors, and alpha and beta are scalars.

func (*Standard) Dgeam 

func (impl *Standard) Dgeam(tA, tB blas.Transpose, m, n int, alpha float64, a []float64, lda int, beta float64, b []float64, ldb int, c []float64, ldc int)

func (*Standard) Dgemm 

func (impl *Standard) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dgemm computes 

C = beta * C + alpha * A * B,

where A, B, and C are dense matrices, and alpha and beta are scalars. tA and tB specify whether A or B are transposed.

func (*Standard) Dgemv 

func (impl *Standard) Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dgemv computes 

y = alpha * a * x + beta * y if tA = blas.NoTrans
y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Dger 

func (impl *Standard) Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)

Dger performs the rank-one operation 

A += alpha * x * y^T

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Dnrm2 

func (impl *Standard) Dnrm2(n int, x []float64, incX int) (retVal float64)

Dnrm2 computes the Euclidean norm of a vector, 

sqrt(\sum_i x[i] * x[i]).

This function returns 0 if incX is negative.

func (*Standard) Drot 

func (impl *Standard) Drot(n int, x []float64, incX int, y []float64, incY int, cScalar, sScalar float64)

Drot applies a plane transformation. 

x[i] = c * x[i] + s * y[i]
y[i] = c * y[i] - s * x[i]

func (*Standard) Drotg 

func (impl *Standard) Drotg(a float64, b float64) (c float64, s float64, r float64, z float64)

func (*Standard) Drotm 

func (impl *Standard) Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams)

func (*Standard) Drotmg 

func (impl *Standard) Drotmg(d1 float64, d2 float64, b1 float64, b2 float64) (p blas.DrotmParams, rd1 float64, rd2 float64, rb1 float64)

func (*Standard) Dsbmv 

func (impl *Standard) Dsbmv(ul blas.Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dsbmv performs 

y = alpha * A * x + beta * y

where A is an n×n symmetric banded matrix, x and y are vectors, and alpha and beta are scalars.

func (*Standard) Dscal 

func (impl *Standard) Dscal(n int, alpha float64, x []float64, incX int)

Dscal scales x by alpha. 

x[i] *= alpha

Dscal has no effect if incX < 0.

func (*Standard) Dsdot 

func (impl *Standard) Dsdot(n int, x []float32, incX int, y []float32, incY int) float64

func (*Standard) Dspmv 

func (impl *Standard) Dspmv(ul blas.Uplo, n int, alpha float64, aP, x []float64, incX int, beta float64, y []float64, incY int)

Dspmv performs 

y = alpha * A * x + beta * y,

where A is an n×n symmetric matrix in packed format, x and y are vectors and alpha and beta are scalars.

func (*Standard) Dspr 

func (impl *Standard) Dspr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, aP []float64)

Dspr computes the rank-one operation 

a += alpha * x * x^T

where a is an n×n symmetric matrix in packed format, x is a vector, and alpha is a scalar.

func (*Standard) Dspr2 

func (impl *Standard) Dspr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, aP []float64)

Dspr2 performs the symmetric rank-2 update 

A += alpha * x * y^T + alpha * y * x^T,

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha is a scalar.

func (*Standard) Dswap 

func (impl *Standard) Dswap(n int, x []float64, incX int, y []float64, incY int)

Dswap exchanges the elements of two vectors. 

x[i], y[i] = y[i], x[i] for all i

func (*Standard) Dsymm 

func (impl *Standard) Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dsymm performs one of 

C = alpha * A * B + beta * C, if side == blas.Left,
C = alpha * B * A + beta * C, if side == blas.Right,

where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha is a scalar.

func (*Standard) Dsymv 

func (impl *Standard) Dsymv(ul blas.Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dsymv computes 

y = alpha * A * x + beta * y,

where a is an n×n symmetric matrix, x and y are vectors, and alpha and beta are scalars.

func (*Standard) Dsyr 

func (impl *Standard) Dsyr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)

Dsyr performs the rank-one update 

a += alpha * x * x^T

where a is an n×n symmetric matrix, and x is a vector.

func (*Standard) Dsyr2 

func (impl *Standard) Dsyr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)

Dsyr2 performs the symmetric rank-two update 

A += alpha * x * y^T + alpha * y * x^T

where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Dsyr2k 

func (impl *Standard) Dsyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dsyr2k performs the symmetric rank 2k operation 

C = alpha * A * B^T + alpha * B * A^T + beta * C

where C is an n×n symmetric matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. alpha and beta are scalars.

func (*Standard) Dsyrk 

func (impl *Standard) Dsyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)

Dsyrk performs the symmetric rank-k operation 

C = alpha * A * A^T + beta*C

C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. alpha and beta are scalars.

func (*Standard) Dsyrkx 

func (impl *Standard) Dsyrkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

func (*Standard) Dtbmv 

func (impl *Standard) Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)

Dtbmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular banded matrix with k diagonals, and x is a vector.

func (*Standard) Dtbsv 

func (impl *Standard) Dtbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)

Dtbsv solves 

A * x = b

where A is an n×n triangular banded matrix with k diagonals in packed format, and x is a vector. At entry to the function, x contains the values of b, and the result is stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Dtpmv 

func (impl *Standard) Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []float64, incX int)

Dtpmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

where A is an n×n unit triangular matrix in packed format, and x is a vector.

func (*Standard) Dtpsv 

func (impl *Standard) Dtpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []float64, incX int)

Dtpsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or 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 stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Dtpttr 

func (impl *Standard) Dtpttr(ul blas.Uplo, n int, aP, a []float64, lda int)

func (*Standard) Dtrmm 

func (impl *Standard) Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)

func (*Standard) Dtrmv 

func (impl *Standard) Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)

Dtrmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

A is an n×n Triangular matrix and x is a vector.

func (*Standard) Dtrsm 

func (impl *Standard) Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)

Dtrsm solves 

A * X = alpha * B,   if tA == blas.NoTrans side == blas.Left,
A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
X * A = alpha * B,   if tA == blas.NoTrans side == blas.Right,
X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,

where A is an n×n or m×m triangular matrix, X is an m×n matrix, 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 (*Standard) Dtrsv 

func (impl *Standard) Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)

Dtrsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or blas.ConjTrans

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 stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Dtrttp 

func (impl *Standard) Dtrttp(ul blas.Uplo, n int, a []float64, lda int, aP []float64)

func (*Standard) Dzasum 

func (impl *Standard) Dzasum(n int, x []complex128, incX int) (retVal float64)

func (*Standard) Dznrm2 

func (impl *Standard) Dznrm2(n int, x []complex128, incX int) (retVal float64)

func (*Standard) Err 

func (impl *Standard) Err() error

func (*Standard) Icamax 

func (impl *Standard) Icamax(n int, x []complex64, incX int) (retVal int)

func (*Standard) Icamin 

func (impl *Standard) Icamin(n int, x []complex64, incX int) (retVal int)

func (*Standard) Idamax 

func (impl *Standard) Idamax(n int, x []float64, incX int) (retVal int)

Idamax returns the index of an element of x with the largest absolute value. If there are multiple such indices the earliest is returned. Idamax returns -1 if n == 0.

func (*Standard) Idamin 

func (impl *Standard) Idamin(n int, x []float64, incX int) (retVal int)

func (*Standard) Init added in v0.9.1 

func (impl *Standard) Init(opts ...ConsOpt) error

func (*Standard) Isamax 

func (impl *Standard) Isamax(n int, x []float32, incX int) (retVal int)

Isamax returns the index of an element of x with the largest absolute value. If there are multiple such indices the earliest is returned. Isamax returns -1 if n == 0.

func (*Standard) Isamin 

func (impl *Standard) Isamin(n int, x []float32, incX int) (retVal int)

func (*Standard) Izamax 

func (impl *Standard) Izamax(n int, x []complex128, incX int) (retVal int)

func (*Standard) Izamin 

func (impl *Standard) Izamin(n int, x []complex128, incX int) (retVal int)

func (*Standard) Sasum 

func (impl *Standard) Sasum(n int, x []float32, incX int) (retVal float32)

Sasum computes the sum of the absolute values of the elements of x. 

\sum_i |x[i]|

Sasum returns 0 if incX is negative.

func (*Standard) Saxpy 

func (impl *Standard) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int)

Saxpy adds alpha times x to y 

y[i] += alpha * x[i] for all i

func (*Standard) Scasum 

func (impl *Standard) Scasum(n int, x []complex64, incX int) (retVal float32)

func (*Standard) Scnrm2 

func (impl *Standard) Scnrm2(n int, x []complex64, incX int) (retVal float32)

func (*Standard) Scopy 

func (impl *Standard) Scopy(n int, x []float32, incX int, y []float32, incY int)

Scopy copies the elements of x into the elements of y. 

y[i] = x[i] for all i

func (*Standard) Sdgmm 

func (impl *Standard) Sdgmm(mode blas.Side, m, n int, a []float32, lda int, x []float32, incX int, c []float32, ldc int)

func (*Standard) Sdot 

func (impl *Standard) Sdot(n int, x []float32, incX int, y []float32, incY int) (retVal float32)

Sdot computes the dot product of the two vectors 

\sum_i x[i]*y[i]

func (*Standard) Sdsdot 

func (impl *Standard) Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32

func (*Standard) Sgbmv 

func (impl *Standard) Sgbmv(tA blas.Transpose, m, n, kl, ku int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Sgbmv computes 

y = alpha * A * x + beta * y if tA == blas.NoTrans
y = alpha * A^T * x + beta * y if tA == blas.Trans or blas.ConjTrans

where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and m and n refer to the size of the full dense matrix it represents. x and y are vectors, and alpha and beta are scalars.

func (*Standard) Sgeam 

func (impl *Standard) Sgeam(tA, tB blas.Transpose, m, n int, alpha float32, a []float32, lda int, beta float32, b []float32, ldb int, c []float32, ldc int)

func (*Standard) Sgemm 

func (impl *Standard) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Sgemm computes 

C = beta * C + alpha * A * B,

where A, B, and C are dense matrices, and alpha and beta are scalars. tA and tB specify whether A or B are transposed.

func (*Standard) Sgemv 

func (impl *Standard) Sgemv(tA blas.Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Sgemv computes 

y = alpha * a * x + beta * y if tA = blas.NoTrans
y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Sger 

func (impl *Standard) Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)

Sger performs the rank-one operation 

A += alpha * x * y^T

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Snrm2 

func (impl *Standard) Snrm2(n int, x []float32, incX int) (retVal float32)

Snrm2 computes the Euclidean norm of a vector, 

sqrt(\sum_i x[i] * x[i]).

This function returns 0 if incX is negative.

func (*Standard) Srot 

func (impl *Standard) Srot(n int, x []float32, incX int, y []float32, incY int, cScalar, sScalar float32)

Srot applies a plane transformation. 

x[i] = c * x[i] + s * y[i]
y[i] = c * y[i] - s * x[i]

func (*Standard) Srotg 

func (impl *Standard) Srotg(a float32, b float32) (c float32, s float32, r float32, z float32)

func (*Standard) Srotm 

func (impl *Standard) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams)

func (*Standard) Srotmg 

func (impl *Standard) Srotmg(d1 float32, d2 float32, b1 float32, b2 float32) (p blas.SrotmParams, rd1 float32, rd2 float32, rb1 float32)

func (*Standard) Ssbmv 

func (impl *Standard) Ssbmv(ul blas.Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Ssbmv performs 

y = alpha * A * x + beta * y

where A is an n×n symmetric banded matrix, x and y are vectors, and alpha and beta are scalars.

func (*Standard) Sscal 

func (impl *Standard) Sscal(n int, alpha float32, x []float32, incX int)

Sscal scales x by alpha. 

x[i] *= alpha

Sscal has no effect if incX < 0.

func (*Standard) Sspmv 

func (impl *Standard) Sspmv(ul blas.Uplo, n int, alpha float32, aP, x []float32, incX int, beta float32, y []float32, incY int)

Sspmv performs 

y = alpha * A * x + beta * y,

where A is an n×n symmetric matrix in packed format, x and y are vectors and alpha and beta are scalars.

func (*Standard) Sspr 

func (impl *Standard) Sspr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, aP []float32)

Sspr computes the rank-one operation 

a += alpha * x * x^T

where a is an n×n symmetric matrix in packed format, x is a vector, and alpha is a scalar.

func (*Standard) Sspr2 

func (impl *Standard) Sspr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, aP []float32)

Sspr2 performs the symmetric rank-2 update 

A += alpha * x * y^T + alpha * y * x^T,

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha is a scalar.

func (*Standard) Sswap 

func (impl *Standard) Sswap(n int, x []float32, incX int, y []float32, incY int)

Sswap exchanges the elements of two vectors. 

x[i], y[i] = y[i], x[i] for all i

func (*Standard) Ssymm 

func (impl *Standard) Ssymm(s blas.Side, ul blas.Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Ssymm performs one of 

C = alpha * A * B + beta * C, if side == blas.Left,
C = alpha * B * A + beta * C, if side == blas.Right,

where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha is a scalar.

func (*Standard) Ssymv 

func (impl *Standard) Ssymv(ul blas.Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Ssymv computes 

y = alpha * A * x + beta * y,

where a is an n×n symmetric matrix, x and y are vectors, and alpha and beta are scalars.

func (*Standard) Ssyr 

func (impl *Standard) Ssyr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int)

Ssyr performs the rank-one update 

a += alpha * x * x^T

where a is an n×n symmetric matrix, and x is a vector.

func (*Standard) Ssyr2 

func (impl *Standard) Ssyr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)

Ssyr2 performs the symmetric rank-two update 

A += alpha * x * y^T + alpha * y * x^T

where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.

func (*Standard) Ssyr2k 

func (impl *Standard) Ssyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Ssyr2k performs the symmetric rank 2k operation 

C = alpha * A * B^T + alpha * B * A^T + beta * C

where C is an n×n symmetric matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. alpha and beta are scalars.

func (*Standard) Ssyrk 

func (impl *Standard) Ssyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int)

Ssyrk performs the symmetric rank-k operation 

C = alpha * A * A^T + beta*C

C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. alpha and beta are scalars.

func (*Standard) Ssyrkx 

func (impl *Standard) Ssyrkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

func (*Standard) Stbmv 

func (impl *Standard) Stbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int)

Stbmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular banded matrix with k diagonals, and x is a vector.

func (*Standard) Stbsv 

func (impl *Standard) Stbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int)

Stbsv solves 

A * x = b

where A is an n×n triangular banded matrix with k diagonals in packed format, and x is a vector. At entry to the function, x contains the values of b, and the result is stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Stpmv 

func (impl *Standard) Stpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []float32, incX int)

Stpmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

where A is an n×n unit triangular matrix in packed format, and x is a vector.

func (*Standard) Stpsv 

func (impl *Standard) Stpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []float32, incX int)

Stpsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or 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 stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Stpttr 

func (impl *Standard) Stpttr(ul blas.Uplo, n int, aP, a []float32, lda int)

func (*Standard) Strmm 

func (impl *Standard) Strmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)

func (*Standard) Strmv 

func (impl *Standard) Strmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int)

Strmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans or blas.ConjTrans

A is an n×n Triangular matrix and x is a vector.

func (*Standard) Strsm 

func (impl *Standard) Strsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)

Strsm solves 

A * X = alpha * B,   if tA == blas.NoTrans side == blas.Left,
A^T * X = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Left,
X * A = alpha * B,   if tA == blas.NoTrans side == blas.Right,
X * A^T = alpha * B, if tA == blas.Trans or blas.ConjTrans, and side == blas.Right,

where A is an n×n or m×m triangular matrix, X is an m×n matrix, 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 (*Standard) Strsv 

func (impl *Standard) Strsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int)

Strsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or blas.ConjTrans

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 stored in place into x.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

func (*Standard) Strttp 

func (impl *Standard) Strttp(ul blas.Uplo, n int, a []float32, lda int, aP []float32)

func (*Standard) Zaxpy 

func (impl *Standard) Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)

func (*Standard) Zcopy 

func (impl *Standard) Zcopy(n int, x []complex128, incX int, y []complex128, incY int)

func (*Standard) Zdgmm 

func (impl *Standard) Zdgmm(mode blas.Side, m, n int, a []complex128, lda int, x []complex128, incX int, c []complex128, ldc int)

func (*Standard) Zdotc 

func (impl *Standard) Zdotc(n int, x []complex128, incX int, y []complex128, incY int) (dotc complex128)

func (*Standard) Zdotu 

func (impl *Standard) Zdotu(n int, x []complex128, incX int, y []complex128, incY int) (dotu complex128)

func (*Standard) Zdscal 

func (impl *Standard) Zdscal(n int, alpha float64, x []complex128, incX int)

func (*Standard) Zgbmv 

func (impl *Standard) Zgbmv(tA blas.Transpose, m, n, kl, ku int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zgeam 

func (impl *Standard) Zgeam(tA, tB blas.Transpose, m, n int, alpha complex128, a []complex128, lda int, beta complex128, b []complex128, ldb int, c []complex128, ldc int)

func (*Standard) Zgemm 

func (impl *Standard) Zgemm(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Zgemm3m 

func (impl *Standard) Zgemm3m(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Zgemv 

func (impl *Standard) Zgemv(tA blas.Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zgerc 

func (impl *Standard) Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

func (*Standard) Zgeru 

func (impl *Standard) Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

func (*Standard) Zhbmv 

func (impl *Standard) Zhbmv(ul blas.Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zhemm 

func (impl *Standard) Zhemm(s blas.Side, ul blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Zhemv 

func (impl *Standard) Zhemv(ul blas.Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zher 

func (impl *Standard) Zher(ul blas.Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)

func (*Standard) Zher2 

func (impl *Standard) Zher2(ul blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

func (*Standard) Zher2k 

func (impl *Standard) Zher2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)

func (*Standard) Zherk 

func (impl *Standard) Zherk(ul blas.Uplo, t blas.Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int)

func (*Standard) Zherkx 

func (impl *Standard) Zherkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)

func (*Standard) Zhpmv 

func (impl *Standard) Zhpmv(ul blas.Uplo, n int, alpha complex128, aP, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zhpr 

func (impl *Standard) Zhpr(ul blas.Uplo, n int, alpha float64, x []complex128, incX int, aP []complex128)

func (*Standard) Zhpr2 

func (impl *Standard) Zhpr2(ul blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, aP []complex128)

func (*Standard) Zrot 

func (impl *Standard) Zrot(n int, x []complex128, incX int, y []complex128, incY int, cScalar float64, sScalar complex128)

func (*Standard) Zscal 

func (impl *Standard) Zscal(n int, alpha complex128, x []complex128, incX int)

func (*Standard) Zswap 

func (impl *Standard) Zswap(n int, x []complex128, incX int, y []complex128, incY int)

func (*Standard) Zsymm 

func (impl *Standard) Zsymm(s blas.Side, ul blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Zsymv 

func (impl *Standard) Zsymv(ul blas.Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

func (*Standard) Zsyr 

func (impl *Standard) Zsyr(ul blas.Uplo, n int, alpha complex128, x []complex128, incX int, a []complex128, lda int)

func (*Standard) Zsyr2 

func (impl *Standard) Zsyr2(ul blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

func (*Standard) Zsyr2k 

func (impl *Standard) Zsyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Zsyrk 

func (impl *Standard) Zsyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)

func (*Standard) Zsyrkx 

func (impl *Standard) Zsyrkx(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

func (*Standard) Ztbmv 

func (impl *Standard) Ztbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int)

func (*Standard) Ztbsv 

func (impl *Standard) Ztbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int)

func (*Standard) Ztpmv 

func (impl *Standard) Ztpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []complex128, incX int)

func (*Standard) Ztpsv 

func (impl *Standard) Ztpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, aP, x []complex128, incX int)

func (*Standard) Ztpttr 

func (impl *Standard) Ztpttr(ul blas.Uplo, n int, aP, a []complex128, lda int)

func (*Standard) Ztrmm 

func (impl *Standard) Ztrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)

func (*Standard) Ztrmv 

func (impl *Standard) Ztrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex128, lda int, x []complex128, incX int)

func (*Standard) Ztrsm 

func (impl *Standard) Ztrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)

func (*Standard) Ztrsv 

func (impl *Standard) Ztrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []complex128, lda int, x []complex128, incX int)

func (*Standard) Ztrttp 

func (impl *Standard) Ztrttp(ul blas.Uplo, n int, a []complex128, lda int, aP []complex128)

type Status 

type Status int

Status is the cublas status. 

const (
	Success        Status = C.CUBLAS_STATUS_SUCCESS          // The operation completed successfully.
	NotInitialized Status = C.CUBLAS_STATUS_NOT_INITIALIZED  // The cuBLAS library was not initialized. This is usually caused by the lack of a prior cublasCreate() call,
	AllocFailed    Status = C.CUBLAS_STATUS_ALLOC_FAILED     // Resource allocation failed inside the cuBLAS library.
	InvalidValue   Status = C.CUBLAS_STATUS_INVALID_VALUE    // An unsupported value or parameter was passed to the function (a negative vector size, for example).
	ArchMismatch   Status = C.CUBLAS_STATUS_ARCH_MISMATCH    // The function requires a feature absent from the device architecture; usually caused by the lack of support for double precision.
	MappingError   Status = C.CUBLAS_STATUS_MAPPING_ERROR    // An access to GPU memory space failed, which is usually caused by a failure to bind a texture.
	ExecFailed     Status = C.CUBLAS_STATUS_EXECUTION_FAILED // The GPU program failed to execute. This is often caused by a launch failure of the kernel on the GPU, which can be caused by multiple reasons.
	InternalError  Status = C.CUBLAS_STATUS_INTERNAL_ERROR   // An internal cuBLAS operation failed. This error is usually caused by a cudaMemcpyAsync() failure.
	Unsupported    Status = C.CUBLAS_STATUS_NOT_SUPPORTED    // The functionnality requested is not supported
	LicenceError   Status = C.CUBLAS_STATUS_LICENSE_ERROR    // The functionnality requested requires some license and an error was detected when trying to check the current licensing.
)

func (Status) Error 

func (err Status) Error() string

func (Status) String 

func (err Status) String() string

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