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native: restructure dsterqr.go part 1
Remove gotos.
This commit is contained in:
kortschak
492
native/dsteqr.go
492
native/dsteqr.go
@@ -88,7 +88,6 @@ func (impl Implementation) Dsteqr(compz lapack.EigComp, n int, d, e, z []float64
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// Determine where the matrix splits and choose QL or QR iteration for each
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// block, according to whether top or bottom diagonal element is smaller.
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// TODO(btracey): Reformat the gotos to use structural flow techniques.
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// TODO(btracey): Move these variables closer to actual usage when
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// gotos are removed.
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l1 := 0
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@@ -104,256 +103,268 @@ func (impl Implementation) Dsteqr(compz lapack.EigComp, n int, d, e, z []float64
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)
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var iscale scaletype
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Ten:
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if l1 > n-1 {
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goto OneSixty
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}
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if l1 > 0 {
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e[l1-1] = 0
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}
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if l1 <= nm1 {
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for m = l1; m < nm1; m++ {
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test := math.Abs(e[m])
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if test == 0 {
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goto Thirty
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}
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if test <= (math.Sqrt(math.Abs(d[m]))*math.Sqrt(math.Abs(d[m+1])))*eps {
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e[m] = 0
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goto Thirty
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for {
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if l1 > n-1 {
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// Order eigenvalues and eigenvectors.
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if icompz == 0 {
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impl.Dlasrt(lapack.SortIncreasing, n, d)
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} else {
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// TODO(btracey): Consider replacing this sort with a call to sort.Sort.
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for ii := 1; ii < n; ii++ {
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i := ii - 1
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k := i
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p := d[i]
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for j := ii; j < n; j++ {
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if d[j] < p {
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k = j
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p = d[j]
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}
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}
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if k != i {
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d[k] = d[i]
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d[i] = p
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bi.Dswap(n, z[i:], ldz, z[k:], ldz)
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}
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}
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}
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return true
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}
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}
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m = n - 1
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Thirty:
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l = l1
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lsv = l
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lend = m
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lendsv = lend
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l1 = m + 1
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if lend == l {
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goto Ten
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}
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// Scale submatrix in rows and columns L to Lend
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anorm = impl.Dlanst(lapack.MaxAbs, lend-l+1, d[l:], e[l:])
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switch {
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case anorm == 0:
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goto Ten
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case anorm > ssfmax:
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iscale = down
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// TODO(btracey): Why is lda n?
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l+1, 1, d[l:], n)
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l, 1, e[l:], n)
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case anorm < ssfmin:
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iscale = up
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// TODO(btracey): Why is lda n?
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l+1, 1, d[l:], n)
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l, 1, e[l:], n)
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}
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// Choose between QL and QR.
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if math.Abs(d[lend]) < math.Abs(d[l]) {
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lend = lsv
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l = lendsv
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}
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if lend > l {
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// QL Iteration. Look for small subdiagonal element.
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Fourty:
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if l != lend {
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lendm1 := lend - 1
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for m = l; m <= lendm1; m++ {
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v := math.Abs(e[m])
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if v*v <= (eps2*math.Abs(d[m]))*math.Abs(d[m+1])+safmin {
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goto Sixty
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if l1 > 0 {
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e[l1-1] = 0
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}
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if l1 <= nm1 {
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for m = l1; m < nm1; m++ {
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test := math.Abs(e[m])
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if test == 0 {
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break
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}
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if test <= (math.Sqrt(math.Abs(d[m]))*math.Sqrt(math.Abs(d[m+1])))*eps {
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e[m] = 0
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break
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}
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}
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}
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m = lend
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Sixty:
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if m < lend {
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e[m] = 0
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}
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p = d[l]
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if m == l {
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goto Eighty
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l = l1
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lsv = l
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lend = m
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lendsv = lend
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l1 = m + 1
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if lend == l {
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continue
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}
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// If remaining matrix is 2×2, use Dlae2 to compute its eigensystem.
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if m == l+1 {
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if icompz > 0 {
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d[l], d[l+1], work[l], work[n-1+l] = impl.Dlaev2(d[l], e[l], d[l+1])
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
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n, 2, work[l:], work[n-1+l:], z[l:], ldz)
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} else {
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d[l], d[l+1] = impl.Dlae2(d[l], e[l], d[l+1])
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}
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e[l] = 0
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l += 2
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if l <= lend {
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goto Fourty
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}
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goto OneFourty
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// Scale submatrix in rows and columns L to Lend
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anorm = impl.Dlanst(lapack.MaxAbs, lend-l+1, d[l:], e[l:])
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switch {
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case anorm == 0:
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continue
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case anorm > ssfmax:
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iscale = down
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// TODO(btracey): Why is lda n?
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l+1, 1, d[l:], n)
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l, 1, e[l:], n)
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case anorm < ssfmin:
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iscale = up
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// TODO(btracey): Why is lda n?
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l+1, 1, d[l:], n)
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impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l, 1, e[l:], n)
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}
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if jtot == nmaxit {
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goto OneFourty
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// Choose between QL and QR.
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if math.Abs(d[lend]) < math.Abs(d[l]) {
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lend = lsv
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l = lendsv
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}
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jtot++
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// Form shift
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g = (d[l+1] - p) / (2 * e[l])
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r = impl.Dlapy2(g, 1)
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g = d[m] - p + e[l]/(g+math.Copysign(r, g))
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s = 1
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c = 1
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p = 0
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// Inner loop
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for i := m - 1; i >= l; i-- {
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f := s * e[i]
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b := c * e[i]
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c, s, r = impl.Dlartg(g, f)
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if i != m-1 {
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e[i+1] = r
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}
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g = d[i+1] - p
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r = (d[i]-g)*s + 2*c*b
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p = s * r
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d[i+1] = g + p
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g = c*r - b
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// If eigenvectors are desired, then save rotations.
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if icompz > 0 {
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work[i] = c
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work[n-1+i] = -s
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}
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}
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// If eigenvectors are desired, then apply saved rotations.
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if icompz > 0 {
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mm := m - l + 1
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
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n, mm, work[l:], work[n-1+l:], z[l:], ldz)
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}
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d[l] -= p
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e[l] = g
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goto Fourty
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// Eigenvalue found.
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Eighty:
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d[l] = p
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l++
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if l <= lend {
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goto Fourty
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}
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goto OneFourty
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} else {
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// QR Iteration.
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// Look for small superdiagonal element.
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Ninety:
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if l != lend {
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lendp1 := lend + 1
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for m = l; m >= lendp1; m-- {
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v := math.Abs(e[m-1])
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if v*v <= (eps2*math.Abs(d[m])*math.Abs(d[m-1]) + safmin) {
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goto OneTen
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if lend > l {
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// QL Iteration. Look for small subdiagonal element.
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for {
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if l != lend {
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for m = l; m < lend; m++ {
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v := math.Abs(e[m])
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if v*v <= (eps2*math.Abs(d[m]))*math.Abs(d[m+1])+safmin {
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break
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}
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}
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} else {
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m = lend
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}
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if m < lend {
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e[m] = 0
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}
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p = d[l]
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if m == l {
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// Eigenvalue found.
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d[l] = p
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l++
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if l > lend {
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break
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}
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continue
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}
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// If remaining matrix is 2×2, use Dlae2 to compute its eigensystem.
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if m == l+1 {
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if icompz > 0 {
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d[l], d[l+1], work[l], work[n-1+l] = impl.Dlaev2(d[l], e[l], d[l+1])
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
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n, 2, work[l:], work[n-1+l:], z[l:], ldz)
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} else {
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d[l], d[l+1] = impl.Dlae2(d[l], e[l], d[l+1])
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}
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e[l] = 0
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l += 2
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if l > lend {
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break
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}
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continue
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}
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if jtot == nmaxit {
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break
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}
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jtot++
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// Form shift
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g = (d[l+1] - p) / (2 * e[l])
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r = impl.Dlapy2(g, 1)
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g = d[m] - p + e[l]/(g+math.Copysign(r, g))
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s = 1
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c = 1
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p = 0
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// Inner loop
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for i := m - 1; i >= l; i-- {
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f := s * e[i]
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b := c * e[i]
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c, s, r = impl.Dlartg(g, f)
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if i != m-1 {
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e[i+1] = r
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}
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g = d[i+1] - p
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r = (d[i]-g)*s + 2*c*b
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p = s * r
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d[i+1] = g + p
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g = c*r - b
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// If eigenvectors are desired, then save rotations.
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if icompz > 0 {
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work[i] = c
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work[n-1+i] = -s
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}
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}
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// If eigenvectors are desired, then apply saved rotations.
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if icompz > 0 {
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mm := m - l + 1
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Backward,
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n, mm, work[l:], work[n-1+l:], z[l:], ldz)
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}
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d[l] -= p
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e[l] = g
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}
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}
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m = lend
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OneTen:
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if m > lend {
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e[m-1] = 0
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}
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p = d[l]
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if m == l {
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goto OneThirty
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}
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} else {
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// QR Iteration.
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// Look for small superdiagonal element.
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for {
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if l != lend {
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for m = l; m > lend; m-- {
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v := math.Abs(e[m-1])
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if v*v <= (eps2*math.Abs(d[m])*math.Abs(d[m-1]) + safmin) {
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break
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}
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}
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} else {
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m = lend
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}
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if m > lend {
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e[m-1] = 0
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}
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p = d[l]
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if m == l {
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// Eigenvalue found
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d[l] = p
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l--
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if l < lend {
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break
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}
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continue
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}
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// If remaining matrix is 2×2, use Dlae2 to compute its eigenvalues.
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if m == l-1 {
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if icompz > 0 {
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d[l-1], d[l], work[m], work[n-1+m] = impl.Dlaev2(d[l-1], e[l-1], d[l])
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
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n, 2, work[m:], work[n-1+m:], z[l-1:], ldz)
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} else {
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d[l-1], d[l] = impl.Dlae2(d[l-1], e[l-1], d[l])
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}
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e[l-1] = 0
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l -= 2
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if l >= lend {
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goto Ninety
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}
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goto OneFourty
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}
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if jtot == nmaxit {
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goto OneFourty
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}
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jtot++
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// If remaining matrix is 2×2, use Dlae2 to compute its eigenvalues.
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if m == l-1 {
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if icompz > 0 {
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d[l-1], d[l], work[m], work[n-1+m] = impl.Dlaev2(d[l-1], e[l-1], d[l])
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impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
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n, 2, work[m:], work[n-1+m:], z[l-1:], ldz)
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} else {
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d[l-1], d[l] = impl.Dlae2(d[l-1], e[l-1], d[l])
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}
|
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e[l-1] = 0
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l -= 2
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if l < lend {
|
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break
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}
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continue
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}
|
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if jtot == nmaxit {
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break
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}
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jtot++
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|
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// Form shift.
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g = (d[l-1] - p) / (2 * e[l-1])
|
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r = impl.Dlapy2(g, 1)
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g = d[m] - p + (e[l-1])/(g+math.Copysign(r, g))
|
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// Form shift.
|
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g = (d[l-1] - p) / (2 * e[l-1])
|
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r = impl.Dlapy2(g, 1)
|
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g = d[m] - p + (e[l-1])/(g+math.Copysign(r, g))
|
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|
||||
s = 1
|
||||
c = 1
|
||||
p = 0
|
||||
s = 1
|
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c = 1
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p = 0
|
||||
|
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// Inner loop.
|
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for i := m; i < l; i++ {
|
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f := s * e[i]
|
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b := c * e[i]
|
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c, s, r = impl.Dlartg(g, f)
|
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if i != m {
|
||||
e[i-1] = r
|
||||
}
|
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g = d[i] - p
|
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r = (d[i+1]-g)*s + 2*c*b
|
||||
p = s * r
|
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d[i] = g + p
|
||||
g = c*r - b
|
||||
// Inner loop.
|
||||
for i := m; i < l; i++ {
|
||||
f := s * e[i]
|
||||
b := c * e[i]
|
||||
c, s, r = impl.Dlartg(g, f)
|
||||
if i != m {
|
||||
e[i-1] = r
|
||||
}
|
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g = d[i] - p
|
||||
r = (d[i+1]-g)*s + 2*c*b
|
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p = s * r
|
||||
d[i] = g + p
|
||||
g = c*r - b
|
||||
|
||||
// If eigenvectors are desired, then save rotations.
|
||||
if icompz > 0 {
|
||||
work[i] = c
|
||||
work[n-1+i] = s
|
||||
// If eigenvectors are desired, then save rotations.
|
||||
if icompz > 0 {
|
||||
work[i] = c
|
||||
work[n-1+i] = s
|
||||
}
|
||||
}
|
||||
|
||||
// If eigenvectors are desired, then apply saved rotations.
|
||||
if icompz > 0 {
|
||||
mm := l - m + 1
|
||||
impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
|
||||
n, mm, work[m:], work[n-1+m:], z[m:], ldz)
|
||||
}
|
||||
d[l] -= p
|
||||
e[l-1] = g
|
||||
}
|
||||
}
|
||||
|
||||
// If eigenvectors are desired, then apply saved rotations.
|
||||
if icompz > 0 {
|
||||
mm := l - m + 1
|
||||
impl.Dlasr(blas.Right, lapack.Variable, lapack.Forward,
|
||||
n, mm, work[m:], work[n-1+m:], z[m:], ldz)
|
||||
// Undo scaling if necessary.
|
||||
switch iscale {
|
||||
case down:
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, d[lsv:], n)
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv, 1, e[lsv:], n)
|
||||
case up:
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, e[lsv:], n)
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv, 1, e[lsv:], n)
|
||||
}
|
||||
d[l] -= p
|
||||
e[l-1] = g
|
||||
goto Ninety
|
||||
|
||||
// Eigenvalue found
|
||||
OneThirty:
|
||||
d[l] = p
|
||||
l--
|
||||
if l >= lend {
|
||||
goto Ninety
|
||||
// Check for no convergence to an eigenvalue after a total of n*maxit iterations.
|
||||
if jtot >= nmaxit {
|
||||
break
|
||||
}
|
||||
goto OneFourty
|
||||
}
|
||||
|
||||
// Undo scaling if necessary.
|
||||
OneFourty:
|
||||
switch iscale {
|
||||
case down:
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, d[lsv:], n)
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv, 1, e[lsv:], n)
|
||||
case up:
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, e[lsv:], n)
|
||||
impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv, 1, e[lsv:], n)
|
||||
}
|
||||
|
||||
// Check for no convergence to an eigenvalue after a total of n*maxit iterations.
|
||||
if jtot < nmaxit {
|
||||
goto Ten
|
||||
}
|
||||
for i := 0; i < n-1; i++ {
|
||||
if e[i] != 0 {
|
||||
@@ -361,29 +372,4 @@ OneFourty:
|
||||
}
|
||||
}
|
||||
return true
|
||||
|
||||
// Order eigenvalues and eigenvectors.
|
||||
OneSixty:
|
||||
if icompz == 0 {
|
||||
impl.Dlasrt(lapack.SortIncreasing, n, d)
|
||||
} else {
|
||||
// TODO(btracey): Consider replacing this sort with a call to sort.Sort.
|
||||
for ii := 1; ii < n; ii++ {
|
||||
i := ii - 1
|
||||
k := i
|
||||
p := d[i]
|
||||
for j := ii; j < n; j++ {
|
||||
if d[j] < p {
|
||||
k = j
|
||||
p = d[j]
|
||||
}
|
||||
}
|
||||
if k != i {
|
||||
d[k] = d[i]
|
||||
d[i] = p
|
||||
bi.Dswap(n, z[i:], ldz, z[k:], ldz)
|
||||
}
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user