// checkPLU checks that the PLU factorization contained in factorize matches
// the original matrix contained in original.
func checkPLU(t *testing.T, ok bool, m, n, lda int, ipiv []int, factorized, original []float64, tol float64, print bool) {
var hasZeroDiagonal bool
for i := 0; i < min(m, n); i++ {
if factorized[i*lda+i] == 0 {
hasZeroDiagonal = true
break
}
}
if hasZeroDiagonal && ok {
t.Error("Has a zero diagonal but returned ok")
}
if !hasZeroDiagonal && !ok {
t.Error("Non-zero diagonal but returned !ok")
}
// Check that the LU decomposition is correct.
mn := min(m, n)
l := make([]float64, m*mn)
ldl := mn
u := make([]float64, mn*n)
ldu := n
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
v := factorized[i*lda+j]
switch {
case i == j:
l[i*ldl+i] = 1
u[i*ldu+i] = v
case i > j:
l[i*ldl+j] = v
case i < j:
u[i*ldu+j] = v
}
}
}
LU := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
U := blas64.General{
Rows: mn,
Cols: n,
Stride: ldu,
Data: u,
}
L := blas64.General{
Rows: m,
Cols: mn,
Stride: ldl,
Data: l,
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, U, 0, LU)
p := make([]float64, m*m)
ldp := m
for i := 0; i < m; i++ {
p[i*ldp+i] = 1
}
for i := len(ipiv) - 1; i >= 0; i-- {
v := ipiv[i]
blas64.Swap(m, blas64.Vector{1, p[i*ldp:]}, blas64.Vector{1, p[v*ldp:]})
}
P := blas64.General{
Rows: m,
Cols: m,
Stride: m,
Data: p,
}
aComp := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
copy(aComp.Data, factorized)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, P, LU, 0, aComp)
if !floats.EqualApprox(aComp.Data, original, tol) {
if print {
t.Errorf("PLU multiplication does not match original matrix.\nWant: %v\nGot: %v", original, aComp.Data)
return
}
t.Error("PLU multiplication does not match original matrix.")
}
}
func testDgebak(t *testing.T, impl Dgebaker, job lapack.Job, side blas.Side, ilo, ihi int, v blas64.General, rnd *rand.Rand) {
const tol = 1e-15
n := v.Rows
m := v.Cols
extra := v.Stride - v.Cols
// Create D and D^{-1} by generating random scales between ilo and ihi.
d := eye(n, n)
dinv := eye(n, n)
scale := nanSlice(n)
if job == lapack.Scale || job == lapack.PermuteScale {
if ilo == ihi {
scale[ilo] = 1
} else {
for i := ilo; i <= ihi; i++ {
scale[i] = 2 * rnd.Float64()
d.Data[i*d.Stride+i] = scale[i]
dinv.Data[i*dinv.Stride+i] = 1 / scale[i]
}
}
}
// Create P by generating random column swaps.
p := eye(n, n)
if job == lapack.Permute || job == lapack.PermuteScale {
// Make up some random permutations.
for i := n - 1; i > ihi; i-- {
scale[i] = float64(rnd.Intn(i + 1))
blas64.Swap(n,
blas64.Vector{p.Stride, p.Data[i:]},
blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
}
for i := 0; i < ilo; i++ {
scale[i] = float64(i + rnd.Intn(ihi-i+1))
blas64.Swap(n,
blas64.Vector{p.Stride, p.Data[i:]},
blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
}
}
got := cloneGeneral(v)
impl.Dgebak(job, side, n, ilo, ihi, scale, m, got.Data, got.Stride)
prefix := fmt.Sprintf("Case job=%v, side=%v, n=%v, ilo=%v, ihi=%v, m=%v, extra=%v",
job, side, n, ilo, ihi, m, extra)
if !generalOutsideAllNaN(got) {
t.Errorf("%v: out-of-range write to V\n%v", prefix, got.Data)
}
// Compute D*V or D^{-1}*V and store into dv.
dv := zeros(n, m, m)
if side == blas.Right {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d, v, 0, dv)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, dinv, v, 0, dv)
}
// Compute P*D*V or P*D^{-1}*V and store into want.
want := zeros(n, m, m)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, dv, 0, want)
if !equalApproxGeneral(want, got, tol) {
t.Errorf("%v: unexpected value of V", prefix)
}
}
func testDgebal(t *testing.T, impl Dgebaler, job lapack.Job, a blas64.General) {
const tol = 1e-14
n := a.Rows
extra := a.Stride - n
var scale []float64
if n > 0 {
scale = nanSlice(n)
}
want := cloneGeneral(a)
ilo, ihi := impl.Dgebal(job, n, a.Data, a.Stride, scale)
prefix := fmt.Sprintf("Case job=%v, n=%v, extra=%v", job, n, extra)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
}
if n == 0 {
if ilo != 0 {
t.Errorf("%v: unexpected ilo when n=0. Want 0, got %v", prefix, n, ilo)
}
if ihi != -1 {
t.Errorf("%v: unexpected ihi when n=0. Want -1, got %v", prefix, n, ihi)
}
return
}
if job == lapack.None {
if ilo != 0 {
t.Errorf("%v: unexpected ilo when job=None. Want 0, got %v", prefix, ilo)
}
if ihi != n-1 {
t.Errorf("%v: unexpected ihi when job=None. Want %v, got %v", prefix, n-1, ihi)
}
k := -1
for i := range scale {
if scale[i] != 1 {
k = i
break
}
}
if k != -1 {
t.Errorf("%v: unexpected scale[%v] when job=None. Want 1, got %v", prefix, k, scale[k])
}
if !equalApproxGeneral(a, want, 0) {
t.Errorf("%v: unexpected modification of A when job=None", prefix)
}
return
}
if ilo < 0 || ihi < ilo || n <= ihi {
t.Errorf("%v: invalid ordering of ilo=%v and ihi=%v", prefix, ilo, ihi)
}
if ilo >= 2 && !isUpperTriangular(blas64.General{ilo - 1, ilo - 1, a.Stride, a.Data}) {
t.Errorf("%v: T1 is not upper triangular", prefix)
}
m := n - ihi - 1 // Order of T2.
k := ihi + 1
if m >= 2 && !isUpperTriangular(blas64.General{m, m, a.Stride, a.Data[k*a.Stride+k:]}) {
t.Errorf("%v: T2 is not upper triangular", prefix)
}
if job == lapack.Permute || job == lapack.PermuteScale {
// Check that all rows in [ilo:ihi+1] have at least one nonzero
// off-diagonal element.
zeroRow := -1
for i := ilo; i <= ihi; i++ {
onlyZeros := true
for j := ilo; j <= ihi; j++ {
if i != j && a.Data[i*a.Stride+j] != 0 {
onlyZeros = false
break
}
}
if onlyZeros {
zeroRow = i
break
}
}
if zeroRow != -1 && ilo != ihi {
t.Errorf("%v: row %v has only zero off-diagonal elements, ilo=%v, ihi=%v", prefix, zeroRow, ilo, ihi)
}
// Check that all columns in [ilo:ihi+1] have at least one nonzero
// off-diagonal element.
zeroCol := -1
for j := ilo; j <= ihi; j++ {
onlyZeros := true
for i := ilo; i <= ihi; i++ {
if i != j && a.Data[i*a.Stride+j] != 0 {
onlyZeros = false
break
}
}
if onlyZeros {
zeroCol = j
break
}
}
if zeroCol != -1 && ilo != ihi {
t.Errorf("%v: column %v has only zero off-diagonal elements, ilo=%v, ihi=%v", prefix, zeroCol, ilo, ihi)
}
// Create the permutation matrix P.
p := eye(n, n)
for j := n - 1; j > ihi; j-- {
blas64.Swap(n,
blas64.Vector{p.Stride, p.Data[j:]},
blas64.Vector{p.Stride, p.Data[int(scale[j]):]})
}
for j := 0; j < ilo; j++ {
blas64.Swap(n,
blas64.Vector{p.Stride, p.Data[j:]},
blas64.Vector{p.Stride, p.Data[int(scale[j]):]})
}
// Compute P^T*A*P and store into want.
ap := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, want, p, 0, ap)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, p, ap, 0, want)
}
if job == lapack.Scale || job == lapack.PermuteScale {
// Modify want by D and D^{-1}.
d := eye(n, n)
dinv := eye(n, n)
for i := ilo; i <= ihi; i++ {
d.Data[i*d.Stride+i] = scale[i]
dinv.Data[i*dinv.Stride+i] = 1 / scale[i]
}
ad := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, want, d, 0, ad)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, dinv, ad, 0, want)
}
if !equalApproxGeneral(want, a, tol) {
t.Errorf("%v: unexpected value of A, ilo=%v, ihi=%v", prefix, ilo, ihi)
}
}