gonum.org/v1/gonum@v0.14.0/blas/testblas/common.go

// Copyright ©2014 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package testblas

import (
	"math"
	"math/cmplx"
	"testing"

	"golang.org/x/exp/rand"

	"gonum.org/v1/gonum/blas"
	"gonum.org/v1/gonum/floats/scalar"
)

// throwPanic will throw unexpected panics if true, or will just report them as errors if false
const throwPanic = true

var znan = cmplx.NaN()

func dTolEqual(a, b float64) bool {
	if math.IsNaN(a) && math.IsNaN(b) {
		return true
	}
	if a == b {
		return true
	}
	m := math.Max(math.Abs(a), math.Abs(b))
	if m > 1 {
		a /= m
		b /= m
	}
	if math.Abs(a-b) < 1e-14 {
		return true
	}
	return false
}

func dSliceTolEqual(a, b []float64) bool {
	if len(a) != len(b) {
		return false
	}
	for i := range a {
		if !dTolEqual(a[i], b[i]) {
			return false
		}
	}
	return true
}

func dStridedSliceTolEqual(n int, a []float64, inca int, b []float64, incb int) bool {
	ia := 0
	ib := 0
	if inca <= 0 {
		ia = -(n - 1) * inca
	}
	if incb <= 0 {
		ib = -(n - 1) * incb
	}
	for i := 0; i < n; i++ {
		if !dTolEqual(a[ia], b[ib]) {
			return false
		}
		ia += inca
		ib += incb
	}
	return true
}

func dSliceEqual(a, b []float64) bool {
	if len(a) != len(b) {
		return false
	}
	for i := range a {
		if !dTolEqual(a[i], b[i]) {
			return false
		}
	}
	return true
}

func dCopyTwoTmp(x, xTmp, y, yTmp []float64) {
	if len(x) != len(xTmp) {
		panic("x size mismatch")
	}
	if len(y) != len(yTmp) {
		panic("y size mismatch")
	}
	copy(xTmp, x)
	copy(yTmp, y)
}

// returns true if the function panics
func panics(f func()) (b bool) {
	defer func() {
		err := recover()
		if err != nil {
			b = true
		}
	}()
	f()
	return
}

func testpanics(f func(), name string, t *testing.T) {
	b := panics(f)
	if !b {
		t.Errorf("%v should panic and does not", name)
	}
}

func sliceOfSliceCopy(a [][]float64) [][]float64 {
	n := make([][]float64, len(a))
	for i := range a {
		n[i] = make([]float64, len(a[i]))
		copy(n[i], a[i])
	}
	return n
}

func sliceCopy(a []float64) []float64 {
	n := make([]float64, len(a))
	copy(n, a)
	return n
}

func flatten(a [][]float64) []float64 {
	if len(a) == 0 {
		return nil
	}
	m := len(a)
	n := len(a[0])
	s := make([]float64, m*n)
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			s[i*n+j] = a[i][j]
		}
	}
	return s
}

func unflatten(a []float64, m, n int) [][]float64 {
	s := make([][]float64, m)
	for i := 0; i < m; i++ {
		s[i] = make([]float64, n)
		for j := 0; j < n; j++ {
			s[i][j] = a[i*n+j]
		}
	}
	return s
}

// flattenTriangular turns the upper or lower triangle of a dense slice of slice
// into a single slice with packed storage. a must be a square matrix.
func flattenTriangular(a [][]float64, ul blas.Uplo) []float64 {
	m := len(a)
	aFlat := make([]float64, m*(m+1)/2)
	var k int
	if ul == blas.Upper {
		for i := 0; i < m; i++ {
			k += copy(aFlat[k:], a[i][i:])
		}
		return aFlat
	}
	for i := 0; i < m; i++ {
		k += copy(aFlat[k:], a[i][:i+1])
	}
	return aFlat
}

// flattenBanded turns a dense banded slice of slice into the compact banded matrix format
func flattenBanded(a [][]float64, ku, kl int) []float64 {
	m := len(a)
	n := len(a[0])
	if ku < 0 || kl < 0 {
		panic("testblas: negative band length")
	}
	nRows := m
	nCols := (ku + kl + 1)
	aflat := make([]float64, nRows*nCols)
	for i := range aflat {
		aflat[i] = math.NaN()
	}
	// loop over the rows, and then the bands
	// elements in the ith row stay in the ith row
	// order in bands is kept
	for i := 0; i < nRows; i++ {
		min := -kl
		if i-kl < 0 {
			min = -i
		}
		max := ku
		if i+ku >= n {
			max = n - i - 1
		}
		for j := min; j <= max; j++ {
			col := kl + j
			aflat[i*nCols+col] = a[i][i+j]
		}
	}
	return aflat
}

// makeIncremented takes a float64 slice with inc == 1 and makes an incremented version
// and adds extra values on the end
func makeIncremented(x []float64, inc int, extra int) []float64 {
	if inc == 0 {
		panic("zero inc")
	}
	absinc := inc
	if absinc < 0 {
		absinc = -inc
	}
	xcopy := make([]float64, len(x))
	if inc > 0 {
		copy(xcopy, x)
	} else {
		for i := 0; i < len(x); i++ {
			xcopy[i] = x[len(x)-i-1]
		}
	}

	// don't use NaN because it makes comparison hard
	// Do use a weird unique value for easier debugging
	counter := 100.0
	var xnew []float64
	for i, v := range xcopy {
		xnew = append(xnew, v)
		if i != len(x)-1 {
			for j := 0; j < absinc-1; j++ {
				xnew = append(xnew, counter)
				counter++
			}
		}
	}
	for i := 0; i < extra; i++ {
		xnew = append(xnew, counter)
		counter++
	}
	return xnew
}

// makeIncremented32 takes a float32 slice with inc == 1 and makes an incremented version
// and adds extra values on the end
func makeIncremented32(x []float32, inc int, extra int) []float32 {
	if inc == 0 {
		panic("zero inc")
	}
	absinc := inc
	if absinc < 0 {
		absinc = -inc
	}
	xcopy := make([]float32, len(x))
	if inc > 0 {
		copy(xcopy, x)
	} else {
		for i := 0; i < len(x); i++ {
			xcopy[i] = x[len(x)-i-1]
		}
	}

	// don't use NaN because it makes comparison hard
	// Do use a weird unique value for easier debugging
	var counter float32 = 100.0
	var xnew []float32
	for i, v := range xcopy {
		xnew = append(xnew, v)
		if i != len(x)-1 {
			for j := 0; j < absinc-1; j++ {
				xnew = append(xnew, counter)
				counter++
			}
		}
	}
	for i := 0; i < extra; i++ {
		xnew = append(xnew, counter)
		counter++
	}
	return xnew
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func allPairs(x, y []int) [][2]int {
	var p [][2]int
	for _, v0 := range x {
		for _, v1 := range y {
			p = append(p, [2]int{v0, v1})
		}
	}
	return p
}

func sameFloat64(a, b float64) bool {
	return a == b || math.IsNaN(a) && math.IsNaN(b)
}

func sameComplex128(x, y complex128) bool {
	return sameFloat64(real(x), real(y)) && sameFloat64(imag(x), imag(y))
}

func zsame(x, y []complex128) bool {
	if len(x) != len(y) {
		return false
	}
	for i, v := range x {
		w := y[i]
		if !sameComplex128(v, w) {
			return false
		}
	}
	return true
}

// zSameAtNonstrided returns whether elements at non-stride positions of vectors
// x and y are same.
func zSameAtNonstrided(x, y []complex128, inc int) bool {
	if len(x) != len(y) {
		return false
	}
	if inc < 0 {
		inc = -inc
	}
	for i, v := range x {
		if i%inc == 0 {
			continue
		}
		w := y[i]
		if !sameComplex128(v, w) {
			return false
		}
	}
	return true
}

// zEqualApproxAtStrided returns whether elements at stride positions of vectors
// x and y are approximately equal within tol.
func zEqualApproxAtStrided(x, y []complex128, inc int, tol float64) bool {
	if len(x) != len(y) {
		return false
	}
	if inc < 0 {
		inc = -inc
	}
	for i := 0; i < len(x); i += inc {
		v := x[i]
		w := y[i]
		if !(cmplx.Abs(v-w) <= tol) {
			return false
		}
	}
	return true
}

func makeZVector(data []complex128, inc int) []complex128 {
	if inc == 0 {
		panic("bad test")
	}
	if len(data) == 0 {
		return nil
	}
	inc = abs(inc)
	x := make([]complex128, (len(data)-1)*inc+1)
	for i := range x {
		x[i] = znan
	}
	for i, v := range data {
		x[i*inc] = v
	}
	return x
}

func makeZGeneral(data []complex128, m, n int, ld int) []complex128 {
	if m < 0 || n < 0 {
		panic("bad test")
	}
	if data != nil && len(data) != m*n {
		panic("bad test")
	}
	if ld < max(1, n) {
		panic("bad test")
	}
	if m == 0 || n == 0 {
		return nil
	}
	a := make([]complex128, (m-1)*ld+n)
	for i := range a {
		a[i] = znan
	}
	if data != nil {
		for i := 0; i < m; i++ {
			copy(a[i*ld:i*ld+n], data[i*n:i*n+n])
		}
	}
	return a
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

// zPack returns the uplo triangle of an n×n matrix A in packed format.
func zPack(uplo blas.Uplo, n int, a []complex128, lda int) []complex128 {
	if n == 0 {
		return nil
	}
	ap := make([]complex128, n*(n+1)/2)
	var ii int
	if uplo == blas.Upper {
		for i := 0; i < n; i++ {
			for j := i; j < n; j++ {
				ap[ii] = a[i*lda+j]
				ii++
			}
		}
	} else {
		for i := 0; i < n; i++ {
			for j := 0; j <= i; j++ {
				ap[ii] = a[i*lda+j]
				ii++
			}
		}
	}
	return ap
}

// zUnpackAsHermitian returns an n×n general Hermitian matrix (with stride n)
// whose packed uplo triangle is stored on entry in ap.
func zUnpackAsHermitian(uplo blas.Uplo, n int, ap []complex128) []complex128 {
	if n == 0 {
		return nil
	}
	a := make([]complex128, n*n)
	lda := n
	var ii int
	if uplo == blas.Upper {
		for i := 0; i < n; i++ {
			for j := i; j < n; j++ {
				a[i*lda+j] = ap[ii]
				if i != j {
					a[j*lda+i] = cmplx.Conj(ap[ii])
				}
				ii++
			}
		}
	} else {
		for i := 0; i < n; i++ {
			for j := 0; j <= i; j++ {
				a[i*lda+j] = ap[ii]
				if i != j {
					a[j*lda+i] = cmplx.Conj(ap[ii])
				}
				ii++
			}
		}
	}
	return a
}

// zPackBand returns the (kL+1+kU) band of an m×n general matrix A in band
// matrix format with ldab stride. Out-of-range elements are filled with NaN.
func zPackBand(kL, kU, ldab int, m, n int, a []complex128, lda int) []complex128 {
	if m == 0 || n == 0 {
		return nil
	}
	nRow := min(m, n+kL)
	ab := make([]complex128, (nRow-1)*ldab+kL+1+kU)
	for i := range ab {
		ab[i] = znan
	}
	for i := 0; i < m; i++ {
		off := max(0, kL-i)
		var k int
		for j := max(0, i-kL); j < min(n, i+kU+1); j++ {
			ab[i*ldab+off+k] = a[i*lda+j]
			k++
		}
	}
	return ab
}

// zPackTriBand returns in band matrix format the (k+1) band in the uplo
// triangle of an n×n matrix A. Out-of-range elements are filled with NaN.
func zPackTriBand(k, ldab int, uplo blas.Uplo, n int, a []complex128, lda int) []complex128 {
	if n == 0 {
		return nil
	}
	ab := make([]complex128, (n-1)*ldab+k+1)
	for i := range ab {
		ab[i] = znan
	}
	if uplo == blas.Upper {
		for i := 0; i < n; i++ {
			var k int
			for j := i; j < min(n, i+k+1); j++ {
				ab[i*ldab+k] = a[i*lda+j]
				k++
			}
		}
	} else {
		for i := 0; i < n; i++ {
			off := max(0, k-i)
			var kk int
			for j := max(0, i-k); j <= i; j++ {
				ab[i*ldab+off+kk] = a[i*lda+j]
				kk++
			}
		}
	}
	return ab
}

// zEqualApprox returns whether the slices a and b are approximately equal.
func zEqualApprox(a, b []complex128, tol float64) bool {
	if len(a) != len(b) {
		panic("mismatched slice length")
	}
	for i, ai := range a {
		if !scalar.EqualWithinAbs(cmplx.Abs(ai), cmplx.Abs(b[i]), tol) {
			return false
		}
	}
	return true
}

// rndComplex128 returns a complex128 with random components.
func rndComplex128(rnd *rand.Rand) complex128 {
	return complex(rnd.NormFloat64(), rnd.NormFloat64())
}

// zmm returns the result of one of the matrix-matrix operations
//
//	alpha * op(A) * op(B) + beta * C
//
// where op(X) is one of
//
//	op(X) = X  or  op(X) = Xᵀ  or  op(X) = Xᴴ,
//
// alpha and beta are scalars, and A, B and C are matrices, with op(A) an m×k matrix,
// op(B) a k×n matrix and C an m×n matrix.
//
// The returned slice is newly allocated, has the same length as c and the
// matrix it represents has the stride ldc. Out-of-range elements are equal to
// those of C to ease comparison of results from BLAS Level 3 functions.
func zmm(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) []complex128 {
	r := make([]complex128, len(c))
	copy(r, c)
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			r[i*ldc+j] = 0
		}
	}
	switch tA {
	case blas.NoTrans:
		switch tB {
		case blas.NoTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[i*lda+l] * b[l*ldb+j]
					}
				}
			}
		case blas.Trans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[i*lda+l] * b[j*ldb+l]
					}
				}
			}
		case blas.ConjTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[i*lda+l] * cmplx.Conj(b[j*ldb+l])
					}
				}
			}
		}
	case blas.Trans:
		switch tB {
		case blas.NoTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[l*lda+i] * b[l*ldb+j]
					}
				}
			}
		case blas.Trans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[l*lda+i] * b[j*ldb+l]
					}
				}
			}
		case blas.ConjTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += a[l*lda+i] * cmplx.Conj(b[j*ldb+l])
					}
				}
			}
		}
	case blas.ConjTrans:
		switch tB {
		case blas.NoTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += cmplx.Conj(a[l*lda+i]) * b[l*ldb+j]
					}
				}
			}
		case blas.Trans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += cmplx.Conj(a[l*lda+i]) * b[j*ldb+l]
					}
				}
			}
		case blas.ConjTrans:
			for i := 0; i < m; i++ {
				for j := 0; j < n; j++ {
					for l := 0; l < k; l++ {
						r[i*ldc+j] += cmplx.Conj(a[l*lda+i]) * cmplx.Conj(b[j*ldb+l])
					}
				}
			}
		}
	}
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			r[i*ldc+j] = alpha * r[i*ldc+j]
			if beta != 0 {
				r[i*ldc+j] += beta * c[i*ldc+j]
			}
		}
	}
	return r
}

// transString returns a string representation of blas.Transpose.
func transString(t blas.Transpose) string {
	switch t {
	case blas.NoTrans:
		return "NoTrans"
	case blas.Trans:
		return "Trans"
	case blas.ConjTrans:
		return "ConjTrans"
	}
	return "unknown trans"
}

// uploString returns a string representation of blas.Uplo.
func uploString(uplo blas.Uplo) string {
	switch uplo {
	case blas.Lower:
		return "Lower"
	case blas.Upper:
		return "Upper"
	}
	return "unknown uplo"
}

// sideString returns a string representation of blas.Side.
func sideString(side blas.Side) string {
	switch side {
	case blas.Left:
		return "Left"
	case blas.Right:
		return "Right"
	}
	return "unknown side"
}

// diagString returns a string representation of blas.Diag.
func diagString(diag blas.Diag) string {
	switch diag {
	case blas.Unit:
		return "Unit"
	case blas.NonUnit:
		return "NonUnit"
	}
	return "unknown diag"
}

// zSameLowerTri returns whether n×n matrices A and B are same under the diagonal.
func zSameLowerTri(n int, a []complex128, lda int, b []complex128, ldb int) bool {
	for i := 1; i < n; i++ {
		for j := 0; j < i; j++ {
			aij := a[i*lda+j]
			bij := b[i*ldb+j]
			if !sameComplex128(aij, bij) {
				return false
			}
		}
	}
	return true
}

// zSameUpperTri returns whether n×n matrices A and B are same above the diagonal.
func zSameUpperTri(n int, a []complex128, lda int, b []complex128, ldb int) bool {
	for i := 0; i < n-1; i++ {
		for j := i + 1; j < n; j++ {
			aij := a[i*lda+j]
			bij := b[i*ldb+j]
			if !sameComplex128(aij, bij) {
				return false
			}
		}
	}
	return true
}