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222 lines
6.2 KiB
Go
222 lines
6.2 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import "gonum.org/v1/gonum/lapack"
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// Dtrexc reorders the real Schur factorization of a n×n real matrix
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// A = Q*T*Q^T
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// so that the diagonal block of T with row index ifst is moved to row ilst.
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//
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// On entry, T must be in Schur canonical form, that is, block upper triangular
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// with 1×1 and 2×2 diagonal blocks; each 2×2 diagonal block has its diagonal
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// elements equal and its off-diagonal elements of opposite sign.
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//
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// On return, T will be reordered by an orthogonal similarity transformation Z
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// as Z^T*T*Z, and will be again in Schur canonical form.
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//
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// If compq is lapack.UpdateSchur, on return the matrix Q of Schur vectors will be
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// updated by postmultiplying it with Z.
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// If compq is lapack.None, the matrix Q is not referenced and will not be
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// updated.
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// For other values of compq Dtrexc will panic.
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//
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// ifst and ilst specify the reordering of the diagonal blocks of T. The block
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// with row index ifst is moved to row ilst, by a sequence of transpositions
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// between adjacent blocks.
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//
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// If ifst points to the second row of a 2×2 block, ifstOut will point to the
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// first row, otherwise it will be equal to ifst.
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//
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// ilstOut will point to the first row of the block in its final position. If ok
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// is true, ilstOut may differ from ilst by +1 or -1.
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//
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// It must hold that
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// 0 <= ifst < n, and 0 <= ilst < n,
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// otherwise Dtrexc will panic.
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//
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// If ok is false, two adjacent blocks were too close to swap because the
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// problem is very ill-conditioned. T may have been partially reordered, and
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// ilstOut will point to the first row of the block at the position to which it
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// has been moved.
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//
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// work must have length at least n, otherwise Dtrexc will panic.
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//
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// Dtrexc is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dtrexc(compq lapack.EVComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool) {
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checkMatrix(n, n, t, ldt)
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var wantq bool
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switch compq {
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default:
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panic("lapack: bad value of compq")
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case lapack.None:
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// Nothing to do because wantq is already false.
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case lapack.UpdateSchur:
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wantq = true
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checkMatrix(n, n, q, ldq)
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}
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if (ifst < 0 || n <= ifst) && n > 0 {
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panic("lapack: ifst out of range")
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}
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if (ilst < 0 || n <= ilst) && n > 0 {
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panic("lapack: ilst out of range")
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}
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if len(work) < n {
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panic(badWork)
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}
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ok = true
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// Quick return if possible.
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if n <= 1 {
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return ifst, ilst, true
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}
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// Determine the first row of specified block
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// and find out it is 1×1 or 2×2.
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if ifst > 0 && t[ifst*ldt+ifst-1] != 0 {
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ifst--
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}
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nbf := 1 // Size of the first block.
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if ifst+1 < n && t[(ifst+1)*ldt+ifst] != 0 {
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nbf = 2
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}
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// Determine the first row of the final block
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// and find out it is 1×1 or 2×2.
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if ilst > 0 && t[ilst*ldt+ilst-1] != 0 {
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ilst--
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}
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nbl := 1 // Size of the last block.
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if ilst+1 < n && t[(ilst+1)*ldt+ilst] != 0 {
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nbl = 2
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}
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switch {
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case ifst == ilst:
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return ifst, ilst, true
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case ifst < ilst:
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// Update ilst.
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switch {
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case nbf == 2 && nbl == 1:
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ilst--
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case nbf == 1 && nbl == 2:
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ilst++
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}
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here := ifst
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for here < ilst {
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// Swap block with next one below.
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if nbf == 1 || nbf == 2 {
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// Current block either 1×1 or 2×2.
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nbnext := 1 // Size of the next block.
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if here+nbf+1 < n && t[(here+nbf+1)*ldt+here+nbf] != 0 {
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nbnext = 2
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}
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, nbf, nbnext, work)
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if !ok {
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return ifst, here, false
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}
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here += nbnext
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// Test if 2×2 block breaks into two 1×1 blocks.
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if nbf == 2 && t[(here+1)*ldt+here] == 0 {
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nbf = 3
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}
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continue
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}
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// Current block consists of two 1×1 blocks each of
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// which must be swapped individually.
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nbnext := 1 // Size of the next block.
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if here+3 < n && t[(here+3)*ldt+here+2] != 0 {
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nbnext = 2
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}
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here+1, 1, nbnext, work)
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if !ok {
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return ifst, here, false
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}
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if nbnext == 1 {
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// Swap two 1×1 blocks, no problems possible.
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, nbnext, work)
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here++
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continue
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}
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// Recompute nbnext in case 2×2 split.
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if t[(here+2)*ldt+here+1] == 0 {
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nbnext = 1
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}
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if nbnext == 2 {
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// 2×2 block did not split.
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, nbnext, work)
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if !ok {
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return ifst, here, false
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}
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} else {
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// 2×2 block did split.
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, 1, work)
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here+1, 1, 1, work)
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}
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here += 2
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}
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return ifst, here, true
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default: // ifst > ilst
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here := ifst
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for here > ilst {
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// Swap block with next one above.
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if nbf == 1 || nbf == 2 {
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// Current block either 1×1 or 2×2.
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nbnext := 1
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if here-2 >= 0 && t[(here-1)*ldt+here-2] != 0 {
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nbnext = 2
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}
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-nbnext, nbnext, nbf, work)
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if !ok {
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return ifst, here, false
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}
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here -= nbnext
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// Test if 2×2 block breaks into two 1×1 blocks.
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if nbf == 2 && t[(here+1)*ldt+here] == 0 {
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nbf = 3
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}
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continue
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}
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// Current block consists of two 1×1 blocks each of
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// which must be swapped individually.
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nbnext := 1
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if here-2 >= 0 && t[(here-1)*ldt+here-2] != 0 {
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nbnext = 2
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}
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-nbnext, nbnext, 1, work)
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if !ok {
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return ifst, here, false
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}
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if nbnext == 1 {
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// Swap two 1×1 blocks, no problems possible.
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, nbnext, 1, work)
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here--
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continue
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}
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// Recompute nbnext in case 2×2 split.
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if t[here*ldt+here-1] == 0 {
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nbnext = 1
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}
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if nbnext == 2 {
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// 2×2 block did not split.
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ok = impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-1, 2, 1, work)
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if !ok {
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return ifst, here, false
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}
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} else {
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// 2×2 block did split.
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here, 1, 1, work)
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impl.Dlaexc(wantq, n, t, ldt, q, ldq, here-1, 1, 1, work)
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}
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here -= 2
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}
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return ifst, here, true
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}
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}
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