// Sdot computes the dot product of the two vectors
// \sum_i x[i]*y[i]
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Sdot(n int, x []float32, incX int, y []float32, incY int) float32 {
if n < 0 {
panic(negativeN)
}
if incX == 0 {
panic(zeroIncX)
}
if incY == 0 {
panic(zeroIncY)
}
if incX == 1 && incY == 1 {
if len(x) < n {
panic(badLenX)
}
if len(y) < n {
panic(badLenY)
}
return asm.SdotUnitary(x[:n], y)
}
var ix, iy int
if incX < 0 {
ix = (-n + 1) * incX
}
if incY < 0 {
iy = (-n + 1) * incY
}
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
panic(badLenX)
}
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
panic(badLenY)
}
return asm.SdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
}
// sgemmSerial where neither a is not transposed and b is
func sgemmSerialNotTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
// This style is used instead of the literal [i*stride +j]) is used because
// approximately 5 times faster as of go 1.3.
for i := 0; i < m; i++ {
atmp := a[i*lda : i*lda+k]
ctmp := c[i*ldc : i*ldc+n]
for j := 0; j < n; j++ {
ctmp[j] += alpha * asm.SdotUnitary(atmp, b[j*ldb:j*ldb+k])
}
}
}
// sgemmSerial where neither a is not transposed and b is
func sgemmSerialNotTrans(a, b, c general32, alpha float32) {
if debug {
if a.cols != b.cols {
panic("inner dimension mismatch")
}
if a.rows != c.rows {
panic("outer dimension mismatch")
}
if b.rows != c.cols {
panic("outer dimension mismatch")
}
}
// This style is used instead of the literal [i*stride +j]) is used because
// approximately 5 times faster as of go 1.3.
for i := 0; i < a.rows; i++ {
atmp := a.data[i*a.stride : i*a.stride+a.cols]
ctmp := c.data[i*c.stride : i*c.stride+c.cols]
for j := 0; j < b.rows; j++ {
ctmp[j] += alpha * asm.SdotUnitary(atmp, b.data[j*b.stride:j*b.stride+b.cols])
}
}
}
// 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.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Sgemv(tA blas.Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
panic(badTranspose)
}
if m < 0 {
panic(mLT0)
}
if n < 0 {
panic(nLT0)
}
if lda < max(1, n) {
panic(badLdA)
}
if incX == 0 {
panic(zeroIncX)
}
if incY == 0 {
panic(zeroIncY)
}
// Set up indexes
lenX := m
lenY := n
if tA == blas.NoTrans {
lenX = n
lenY = m
}
if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
panic(badX)
}
if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
panic(badY)
}
if lda*(m-1)+n > len(a) || lda < max(1, n) {
panic(badLdA)
}
// Quick return if possible
if m == 0 || n == 0 || (alpha == 0 && beta == 1) {
return
}
var kx, ky int
if incX > 0 {
kx = 0
} else {
kx = -(lenX - 1) * incX
}
if incY > 0 {
ky = 0
} else {
ky = -(lenY - 1) * incY
}
// First form y := beta * y
if incY > 0 {
Implementation{}.Sscal(lenY, beta, y, incY)
} else {
Implementation{}.Sscal(lenY, beta, y, -incY)
}
if alpha == 0 {
return
}
// Form y := alpha * A * x + y
if tA == blas.NoTrans {
if incX == 1 && incY == 1 {
for i := 0; i < m; i++ {
y[i] += alpha * asm.SdotUnitary(a[lda*i:lda*i+n], x)
}
return
}
iy := ky
for i := 0; i < m; i++ {
y[iy] += alpha * asm.SdotInc(x, a[lda*i:lda*i+n], uintptr(n), uintptr(incX), 1, uintptr(kx), 0)
iy += incY
}
return
}
// Cases where a is transposed.
if incX == 1 && incY == 1 {
for i := 0; i < m; i++ {
tmp := alpha * x[i]
if tmp != 0 {
asm.SaxpyUnitaryTo(y, tmp, a[lda*i:lda*i+n], y)
}
}
return
}
ix := kx
for i := 0; i < m; i++ {
tmp := alpha * x[ix]
if tmp != 0 {
asm.SaxpyInc(tmp, a[lda*i:lda*i+n], y, uintptr(n), 1, uintptr(incY), 0, uintptr(ky))
}
ix += incX
}
}
// Strmm performs
// B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
// B = alpha * A^T * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
// B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
// B = alpha * B * A^T if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
// where A is an n×n triangular matrix, and B is an m×n matrix.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) 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) {
if s != blas.Left && s != blas.Right {
panic(badSide)
}
if ul != blas.Lower && ul != blas.Upper {
panic(badUplo)
}
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
panic(badTranspose)
}
if d != blas.NonUnit && d != blas.Unit {
panic(badDiag)
}
if m < 0 {
panic(mLT0)
}
if n < 0 {
panic(nLT0)
}
var k int
if s == blas.Left {
k = m
} else {
k = n
}
if lda*(k-1)+k > len(a) || lda < max(1, k) {
panic(badLdA)
}
if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
panic(badLdB)
}
if alpha == 0 {
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for j := range btmp {
btmp[j] = 0
}
}
return
}
nonUnit := d == blas.NonUnit
if s == blas.Left {
if tA == blas.NoTrans {
if ul == blas.Upper {
for i := 0; i < m; i++ {
tmp := alpha
if nonUnit {
tmp *= a[i*lda+i]
}
btmp := b[i*ldb : i*ldb+n]
for j := range btmp {
btmp[j] *= tmp
}
for ka, va := range a[i*lda+i+1 : i*lda+m] {
k := ka + i + 1
tmp := alpha * va
if tmp != 0 {
asm.SaxpyUnitary(tmp, b[k*ldb:k*ldb+n], btmp, btmp)
}
}
}
return
}
for i := m - 1; i >= 0; i-- {
tmp := alpha
if nonUnit {
tmp *= a[i*lda+i]
}
btmp := b[i*ldb : i*ldb+n]
for j := range btmp {
btmp[j] *= tmp
}
for k, va := range a[i*lda : i*lda+i] {
tmp := alpha * va
if tmp != 0 {
asm.SaxpyUnitary(tmp, b[k*ldb:k*ldb+n], btmp, btmp)
}
}
}
return
}
// Cases where a is transposed.
if ul == blas.Upper {
for k := m - 1; k >= 0; k-- {
btmpk := b[k*ldb : k*ldb+n]
for ia, va := range a[k*lda+k+1 : k*lda+m] {
i := ia + k + 1
btmp := b[i*ldb : i*ldb+n]
tmp := alpha * va
if tmp != 0 {
asm.SaxpyUnitary(tmp, btmpk, btmp, btmp)
}
}
tmp := alpha
if nonUnit {
tmp *= a[k*lda+k]
}
if tmp != 1 {
for j := 0; j < n; j++ {
btmpk[j] *= tmp
}
}
}
return
}
for k := 0; k < m; k++ {
btmpk := b[k*ldb : k*ldb+n]
for i, va := range a[k*lda : k*lda+k] {
btmp := b[i*ldb : i*ldb+n]
tmp := alpha * va
if tmp != 0 {
asm.SaxpyUnitary(tmp, btmpk, btmp, btmp)
}
}
tmp := alpha
if nonUnit {
tmp *= a[k*lda+k]
}
if tmp != 1 {
for j := 0; j < n; j++ {
btmpk[j] *= tmp
}
}
}
return
}
// Cases where a is on the right
if tA == blas.NoTrans {
if ul == blas.Upper {
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for k := n - 1; k >= 0; k-- {
tmp := alpha * btmp[k]
if tmp != 0 {
btmp[k] = tmp
if nonUnit {
btmp[k] *= a[k*lda+k]
}
for ja, v := range a[k*lda+k+1 : k*lda+n] {
j := ja + k + 1
btmp[j] += tmp * v
}
}
}
}
return
}
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for k := 0; k < n; k++ {
tmp := alpha * btmp[k]
if tmp != 0 {
btmp[k] = tmp
if nonUnit {
btmp[k] *= a[k*lda+k]
}
asm.SaxpyUnitary(tmp, a[k*lda:k*lda+k], btmp, btmp)
}
}
}
return
}
// Cases where a is transposed.
if ul == blas.Upper {
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for j, vb := range btmp {
tmp := vb
if nonUnit {
tmp *= a[j*lda+j]
}
tmp += asm.SdotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
btmp[j] = alpha * tmp
}
}
return
}
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for j := n - 1; j >= 0; j-- {
tmp := btmp[j]
if nonUnit {
tmp *= a[j*lda+j]
}
tmp += asm.SdotUnitary(a[j*lda:j*lda+j], btmp[:j])
btmp[j] = alpha * tmp
}
}
}
// 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.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) Ssyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int) {
if ul != blas.Lower && ul != blas.Upper {
panic(badUplo)
}
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
panic(badTranspose)
}
if n < 0 {
panic(nLT0)
}
if k < 0 {
panic(kLT0)
}
if ldc < n {
panic(badLdC)
}
var row, col int
if tA == blas.NoTrans {
row, col = n, k
} else {
row, col = k, n
}
if lda*(row-1)+col > len(a) || lda < max(1, col) {
panic(badLdA)
}
if ldc*(n-1)+n > len(c) || ldc < max(1, n) {
panic(badLdC)
}
if alpha == 0 {
if beta == 0 {
if ul == blas.Upper {
for i := 0; i < n; i++ {
ctmp := c[i*ldc+i : i*ldc+n]
for j := range ctmp {
ctmp[j] = 0
}
}
return
}
for i := 0; i < n; i++ {
ctmp := c[i*ldc : i*ldc+i+1]
for j := range ctmp {
ctmp[j] = 0
}
}
return
}
if ul == blas.Upper {
for i := 0; i < n; i++ {
ctmp := c[i*ldc+i : i*ldc+n]
for j := range ctmp {
ctmp[j] *= beta
}
}
return
}
for i := 0; i < n; i++ {
ctmp := c[i*ldc : i*ldc+i+1]
for j := range ctmp {
ctmp[j] *= beta
}
}
return
}
if tA == blas.NoTrans {
if ul == blas.Upper {
for i := 0; i < n; i++ {
ctmp := c[i*ldc+i : i*ldc+n]
atmp := a[i*lda : i*lda+k]
for jc, vc := range ctmp {
j := jc + i
ctmp[jc] = vc*beta + alpha*asm.SdotUnitary(atmp, a[j*lda:j*lda+k])
}
}
return
}
for i := 0; i < n; i++ {
atmp := a[i*lda : i*lda+k]
for j, vc := range c[i*ldc : i*ldc+i+1] {
c[i*ldc+j] = vc*beta + alpha*asm.SdotUnitary(a[j*lda:j*lda+k], atmp)
}
}
return
}
// Cases where a is transposed.
if ul == blas.Upper {
for i := 0; i < n; i++ {
ctmp := c[i*ldc+i : i*ldc+n]
if beta != 1 {
for j := range ctmp {
ctmp[j] *= beta
}
}
for l := 0; l < k; l++ {
tmp := alpha * a[l*lda+i]
if tmp != 0 {
asm.SaxpyUnitary(tmp, a[l*lda+i:l*lda+n], ctmp, ctmp)
}
}
}
return
}
for i := 0; i < n; i++ {
ctmp := c[i*ldc : i*ldc+i+1]
if beta != 0 {
for j := range ctmp {
ctmp[j] *= beta
}
}
for l := 0; l < k; l++ {
tmp := alpha * a[l*lda+i]
if tmp != 0 {
asm.SaxpyUnitary(tmp, a[l*lda:l*lda+i+1], ctmp, ctmp)
}
}
}
}
// Strsm solves
// A * X = alpha * B if tA == blas.NoTrans and 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 and 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 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.
//
// Float32 implementations are autogenerated and not directly tested.
func (Implementation) 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) {
if s != blas.Left && s != blas.Right {
panic(badSide)
}
if ul != blas.Lower && ul != blas.Upper {
panic(badUplo)
}
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
panic(badTranspose)
}
if d != blas.NonUnit && d != blas.Unit {
panic(badDiag)
}
if m < 0 {
panic(mLT0)
}
if n < 0 {
panic(nLT0)
}
if ldb < n {
panic(badLdB)
}
var k int
if s == blas.Left {
k = m
} else {
k = n
}
if lda*(k-1)+k > len(a) || lda < max(1, k) {
panic(badLdA)
}
if ldb*(m-1)+n > len(b) || ldb < max(1, n) {
panic(badLdB)
}
if m == 0 || n == 0 {
return
}
if alpha == 0 {
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
for j := range btmp {
btmp[j] = 0
}
}
return
}
nonUnit := d == blas.NonUnit
if s == blas.Left {
if tA == blas.NoTrans {
if ul == blas.Upper {
for i := m - 1; i >= 0; i-- {
btmp := b[i*ldb : i*ldb+n]
if alpha != 1 {
for j := range btmp {
btmp[j] *= alpha
}
}
for ka, va := range a[i*lda+i+1 : i*lda+m] {
k := ka + i + 1
if va != 0 {
asm.SaxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp, btmp)
}
}
if nonUnit {
tmp := 1 / a[i*lda+i]
for j := 0; j < n; j++ {
btmp[j] *= tmp
}
}
}
return
}
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
if alpha != 1 {
for j := 0; j < n; j++ {
btmp[j] *= alpha
}
}
for k, va := range a[i*lda : i*lda+i] {
if va != 0 {
asm.SaxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp, btmp)
}
}
if nonUnit {
tmp := 1 / a[i*lda+i]
for j := 0; j < n; j++ {
btmp[j] *= tmp
}
}
}
return
}
// Cases where a is transposed
if ul == blas.Upper {
for k := 0; k < m; k++ {
btmpk := b[k*ldb : k*ldb+n]
if nonUnit {
tmp := 1 / a[k*lda+k]
for j := 0; j < n; j++ {
btmpk[j] *= tmp
}
}
for ia, va := range a[k*lda+k+1 : k*lda+m] {
i := ia + k + 1
if va != 0 {
btmp := b[i*ldb : i*ldb+n]
asm.SaxpyUnitary(-va, btmpk, btmp, btmp)
}
}
if alpha != 1 {
for j := 0; j < n; j++ {
btmpk[j] *= alpha
}
}
}
return
}
for k := m - 1; k >= 0; k-- {
btmpk := b[k*ldb : k*ldb+n]
if nonUnit {
tmp := 1 / a[k*lda+k]
for j := 0; j < n; j++ {
btmpk[j] *= tmp
}
}
for i, va := range a[k*lda : k*lda+k] {
if va != 0 {
btmp := b[i*ldb : i*ldb+n]
asm.SaxpyUnitary(-va, btmpk, btmp, btmp)
}
}
if alpha != 1 {
for j := 0; j < n; j++ {
btmpk[j] *= alpha
}
}
}
return
}
// Cases where a is to the right of X.
if tA == blas.NoTrans {
if ul == blas.Upper {
for i := 0; i < m; i++ {
btmp := b[i*ldb : i*ldb+n]
if alpha != 1 {
for j := 0; j < n; j++ {
btmp[j] *= alpha
}
}
for k, vb := range btmp {
if vb != 0 {
if btmp[k] != 0 {
if nonUnit {
btmp[k] /= a[k*lda+k]
}
btmpk := btmp[k+1 : n]
asm.SaxpyUnitary(-btmp[k], a[k*lda+k+1:k*lda+n], btmpk, btmpk)
}
}
}
}
return
}
for i := 0; i < m; i++ {
btmp := b[i*lda : i*lda+n]
if alpha != 1 {
for j := 0; j < n; j++ {
btmp[j] *= alpha
}
}
for k := n - 1; k >= 0; k-- {
if btmp[k] != 0 {
if nonUnit {
btmp[k] /= a[k*lda+k]
}
asm.SaxpyUnitary(-btmp[k], a[k*lda:k*lda+k], btmp, btmp)
}
}
}
return
}
// Cases where a is transposed.
if ul == blas.Upper {
for i := 0; i < m; i++ {
btmp := b[i*lda : i*lda+n]
for j := n - 1; j >= 0; j-- {
tmp := alpha*btmp[j] - asm.SdotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
if nonUnit {
tmp /= a[j*lda+j]
}
btmp[j] = tmp
}
}
return
}
for i := 0; i < m; i++ {
btmp := b[i*lda : i*lda+n]
for j := 0; j < n; j++ {
tmp := alpha*btmp[j] - asm.SdotUnitary(a[j*lda:j*lda+j], btmp)
if nonUnit {
tmp /= a[j*lda+j]
}
btmp[j] = tmp
}
}
}