lapack: add SchurComp and SchurUpdateComp types and consts, rename EVComp consts

lapack/gonum/dgeev.go

@@ -116,7 +116,7 @@ func (impl Implementation) Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob
 	maxwrk := 2*n + n*impl.Ilaenv(1, "DGEHRD", " ", n, 1, n, 0)
 	if wantvl || wantvr {
 		maxwrk = max(maxwrk, 2*n+(n-1)*impl.Ilaenv(1, "DORGHR", " ", n, 1, n, -1))
-		impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, 0, n-1,
+		impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.SchurOrig, n, 0, n-1,
 			nil, 1, nil, nil, nil, 1, work, -1)
 		maxwrk = max(maxwrk, max(n+1, n+int(work[0])))
 		side := lapack.EVLeft
@@ -176,7 +176,7 @@ func (impl Implementation) Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob
 		impl.Dorghr(n, ilo, ihi, vl, ldvl, tau, work[iwrk:], lwork-iwrk)
 		// Perform QR iteration, accumulating Schur vectors in VL.
 		iwrk = n
-		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, ilo, ihi,
+		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.SchurOrig, n, ilo, ihi,
 			a, lda, wr, wi, vl, ldvl, work[iwrk:], lwork-iwrk)
 		if wantvr {
 			// Want left and right eigenvectors.
@@ -192,7 +192,7 @@ func (impl Implementation) Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob
 		impl.Dorghr(n, ilo, ihi, vr, ldvr, tau, work[iwrk:], lwork-iwrk)
 		// Perform QR iteration, accumulating Schur vectors in VR.
 		iwrk = n
-		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.OriginalEV, n, ilo, ihi,
+		first = impl.Dhseqr(lapack.EigenvaluesAndSchur, lapack.SchurOrig, n, ilo, ihi,
 			a, lda, wr, wi, vr, ldvr, work[iwrk:], lwork-iwrk)
 	} else {
 		// Compute eigenvalues only.

lapack/gonum/dhseqr.go

@@ -27,11 +27,11 @@ import (
 // be computed.
 // For other values of job Dhseqr will panic.
 //
-// If compz == lapack.None, no Schur vectors will be computed and Z will not be
+// If compz == lapack.SchurNone, no Schur vectors will be computed and Z will not be
 // referenced.
-// If compz == lapack.HessEV, on return Z will contain the matrix of Schur
+// If compz == lapack.SchurHess, on return Z will contain the matrix of Schur
 // vectors of H.
-// If compz == lapack.OriginalEV, on entry z is assumed to contain the orthogonal
+// If compz == lapack.SchurOrig, on entry z is assumed to contain the orthogonal
 // matrix Q that is the identity except for the submatrix
 // Q[ilo:ihi+1,ilo:ihi+1]. On return z will be updated to the product Q*Z.
 //
@@ -96,11 +96,11 @@ import (
 // where U is an orthogonal matrix. The final H is upper Hessenberg and
 // H[unconverged:ihi+1,unconverged:ihi+1] is upper quasi-triangular.
 //
-// If unconverged > 0 and compz == lapack.OriginalEV, then on return
+// If unconverged > 0 and compz == lapack.SchurOrig, then on return
 //  (final Z) = (initial Z) U,
 // where U is the orthogonal matrix in (*) regardless of the value of job.
 //
-// If unconverged > 0 and compz == lapack.HessEV, then on return
+// If unconverged > 0 and compz == lapack.SchurHess, then on return
 //  (final Z) = U,
 // where U is the orthogonal matrix in (*) regardless of the value of job.
 //
@@ -118,7 +118,7 @@ import (
 //      URL: http://dx.doi.org/10.1137/S0895479801384585
 //
 // Dhseqr is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dhseqr(job lapack.SchurJob, compz lapack.EVComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, z []float64, ldz int, work []float64, lwork int) (unconverged int) {
+func (impl Implementation) Dhseqr(job lapack.SchurJob, compz lapack.SchurComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, z []float64, ldz int, work []float64, lwork int) (unconverged int) {
 	var wantt bool
 	switch job {
 	default:
@@ -130,9 +130,9 @@ func (impl Implementation) Dhseqr(job lapack.SchurJob, compz lapack.EVComp, n, i
 	var wantz bool
 	switch compz {
 	default:
-		panic(badEVComp)
+		panic(badSchurComp)
-	case lapack.None:
+	case lapack.SchurNone:
-	case lapack.HessEV, lapack.OriginalEV:
+	case lapack.SchurHess, lapack.SchurOrig:
 		wantz = true
 	}
 	switch {
@@ -197,7 +197,7 @@ func (impl Implementation) Dhseqr(job lapack.SchurJob, compz lapack.EVComp, n, i
 	}
 
 	// Initialize Z to identity matrix if requested.
-	if compz == lapack.HessEV {
+	if compz == lapack.SchurHess {
 		impl.Dlaset(blas.All, n, n, 0, 1, z, ldz)
 	}
 

lapack/gonum/dsteqr.go

@@ -26,11 +26,11 @@ import (
 // Dsteqr will panic otherwise.
 //
 // z, on entry, contains the n×n orthogonal matrix used in the reduction to
-// tridiagonal form if compz == lapack.OriginalEV. On exit, if
+// tridiagonal form if compz == lapack.EVOriginal. On exit, if
-// compz == lapack.OriginalEV, z contains the orthonormal eigenvectors of the
+// compz == lapack.EVOriginal, z contains the orthonormal eigenvectors of the
-// original symmetric matrix, and if compz == lapack.TridiagEV, z contains the
+// original symmetric matrix, and if compz == lapack.EVTridiag, z contains the
 // orthonormal eigenvectors of the symmetric tridiagonal matrix. z is not used
-// if compz == lapack.None.
+// if compz == lapack.EVCompNone.
 //
 // work must have length at least max(1, 2*n-2) if the eigenvectors are computed,
 // and Dsteqr will panic otherwise.
@@ -46,10 +46,10 @@ func (impl Implementation) Dsteqr(compz lapack.EVComp, n int, d, e, z []float64,
 	if len(e) < n-1 {
 		panic(badE)
 	}
-	if compz != lapack.None && compz != lapack.TridiagEV && compz != lapack.OriginalEV {
+	if compz != lapack.EVCompNone && compz != lapack.EVTridiag && compz != lapack.EVOrig {
 		panic(badEVComp)
 	}
-	if compz != lapack.None {
+	if compz != lapack.EVCompNone {
 		if len(work) < max(1, 2*n-2) {
 			panic(badWork)
 		}
@@ -57,9 +57,9 @@ func (impl Implementation) Dsteqr(compz lapack.EVComp, n int, d, e, z []float64,
 	}
 
 	var icompz int
-	if compz == lapack.OriginalEV {
+	if compz == lapack.EVOrig {
 		icompz = 1
-	} else if compz == lapack.TridiagEV {
+	} else if compz == lapack.EVTridiag {
 		icompz = 2
 	}
 

lapack/gonum/dtrexc.go

@@ -18,8 +18,8 @@ import "gonum.org/v1/gonum/lapack"
 // as Z^T*T*Z, and will be again in Schur canonical form.
 //
 // If compq is lapack.UpdateSchur, on return the matrix Q of Schur vectors will be
-// updated by postmultiplying it with Z.
+// updated by post-multiplying it with Z.
-// If compq is lapack.None, the matrix Q is not referenced and will not be
+// If compq is lapack.UpdateSchurNone, the matrix Q is not referenced and will not be
 // updated.
 // For other values of compq Dtrexc will panic.
 //
@@ -45,13 +45,13 @@ import "gonum.org/v1/gonum/lapack"
 // work must have length at least n, otherwise Dtrexc will panic.
 //
 // Dtrexc is an internal routine. It is exported for testing purposes.
-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) {
+func (impl Implementation) Dtrexc(compq lapack.UpdateSchurComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool) {
 	checkMatrix(n, n, t, ldt)
 	var wantq bool
 	switch compq {
 	default:
 		panic("lapack: bad value of compq")
-	case lapack.None:
+	case lapack.UpdateSchurNone:
 		// Nothing to do because wantq is already false.
 	case lapack.UpdateSchur:
 		wantq = true

lapack/gonum/general.go

@@ -45,6 +45,7 @@ const (
 	badNorm       = "lapack: bad norm"
 	badPivot      = "lapack: bad pivot"
 	badS          = "lapack: s has insufficient length"
+	badSchurComp  = "lapack: bad SchurComp"
 	badSchurJob   = "lapack: bad SchurJob"
 	badShifts     = "lapack: bad shifts"
 	badSide       = "lapack: bad side"

lapack/lapack.go

@@ -127,23 +127,13 @@ const (
 	GSVDNone GSVDJob = 'N' // Do not compute orthogonal matrix
 )
 
-// EVComp specifies how eigenvectors are computed.
+// EVComp specifies how eigenvectors are computed in Dsteqr.
 type EVComp byte
 
 const (
-	// OriginalEV specifies to compute the eigenvectors of the original
+	EVOrig     EVComp = 'V' // Compute eigenvectors of the original symmetric matrix.
-	// matrix.
+	EVTridiag  EVComp = 'I' // Compute eigenvectors of the tridiagonal matrix.
-	OriginalEV EVComp = 'V'
+	EVCompNone EVComp = 'N' // Do not compute eigenvectors.
-	// TridiagEV specifies to compute both the eigenvectors of the input
-	// tridiagonal matrix.
-	TridiagEV EVComp = 'I'
-	// HessEV specifies to compute both the eigenvectors of the input upper
-	// Hessenberg matrix.
-	HessEV EVComp = 'I'
-
-	// UpdateSchur specifies that the matrix of Schur vectors will be
-	// updated by Dtrexc.
-	UpdateSchur EVComp = 'V'
 )
 
 // EVJob specifies whether eigenvectors are computed in Dsyev.
@@ -188,6 +178,23 @@ const (
 	EigenvaluesAndSchur SchurJob = 'S'
 )
 
+// SchurComp specifies whether and how the Schur vectors are computed in Dhseqr.
+type SchurComp byte
+
+const (
+	SchurNone SchurComp = 'N' // Schur vectors are not computed.
+	SchurHess SchurComp = 'I' // Schur vectors of the upper Hessenberg marix are computed.
+	SchurOrig SchurComp = 'V' // Schur vectors of the original matrix are computed.
+)
+
+// UpdateSchurComp specifies whether the matrix of Schur vectors is updated in Dtrexc.
+type UpdateSchurComp byte
+
+const (
+	UpdateSchur     UpdateSchurComp = 'V' // The matrix of Schur vectors is updated.
+	UpdateSchurNone UpdateSchurComp = 'N' // The matrix of Schur vectors is not updated.
+)
+
 // EVSide specifies what eigenvectors are computed in Dtrevc3.
 type EVSide byte
 

lapack/testlapack/dhseqr.go

@@ -16,7 +16,7 @@ import (
 )
 
 type Dhseqrer interface {
-	Dhseqr(job lapack.SchurJob, compz lapack.EVComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
+	Dhseqr(job lapack.SchurJob, compz lapack.SchurComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
 		z []float64, ldz int, work []float64, lwork int) int
 }
 
@@ -57,11 +57,11 @@ func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.
 	copyGeneral(h, blas64.General{Rows: n, Cols: n, Stride: max(1, n), Data: test.h})
 	hCopy := cloneGeneral(h)
 
-	var compz lapack.EVComp = lapack.None
+	compz := lapack.SchurNone
 	z := blas64.General{Stride: max(1, n)}
 	if wantz {
 		// First, let Dhseqr initialize Z to the identity matrix.
-		compz = lapack.HessEV
+		compz = lapack.SchurHess
 		z = nanGeneral(n, n, n+extra)
 	}
 
@@ -70,7 +70,7 @@ func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.
 
 	work := nanSlice(max(1, n))
 	if optwork {
-		impl.Dhseqr(job, lapack.HessEV, n, ilo, ihi, nil, h.Stride, nil, nil, nil, z.Stride, work, -1)
+		impl.Dhseqr(job, lapack.SchurHess, n, ilo, ihi, nil, h.Stride, nil, nil, nil, z.Stride, work, -1)
 		work = nanSlice(int(work[0]))
 	}
 
@@ -196,7 +196,7 @@ func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.
 	copyGeneral(h, hCopy)
 	// Call Dhseqr again with the identity matrix given explicitly in Q.
 	q := eye(n, n+extra)
-	impl.Dhseqr(job, lapack.OriginalEV, n, ilo, ihi, h.Data, h.Stride, wr, wi, q.Data, q.Stride, work, len(work))
+	impl.Dhseqr(job, lapack.SchurOrig, n, ilo, ihi, h.Data, h.Stride, wr, wi, q.Data, q.Stride, work, len(work))
 	if !equalApproxGeneral(z, q, 0) {
 		t.Errorf("%v: Z and Q are not equal", prefix)
 	}

lapack/testlapack/dsteqr.go

@@ -22,7 +22,7 @@ type Dsteqrer interface {
 
 func DsteqrTest(t *testing.T, impl Dsteqrer) {
 	rnd := rand.New(rand.NewSource(1))
-	for _, compz := range []lapack.EVComp{lapack.OriginalEV, lapack.TridiagEV} {
+	for _, compz := range []lapack.EVComp{lapack.EVOrig, lapack.EVTridiag} {
 		for _, test := range []struct {
 			n, lda int
 		}{
@@ -59,7 +59,7 @@ func DsteqrTest(t *testing.T, impl Dsteqrer) {
 				copy(eCopy, e)
 				aCopy := make([]float64, len(a))
 				copy(aCopy, a)
-				if compz == lapack.OriginalEV {
+				if compz == lapack.EVOrig {
 					uplo := blas.Upper
 					tau := make([]float64, n)
 					work := make([]float64, 1)
@@ -92,7 +92,7 @@ func DsteqrTest(t *testing.T, impl Dsteqrer) {
 				copy(dAns, d)
 
 				var truth blas64.General
-				if compz == lapack.OriginalEV {
+				if compz == lapack.EVOrig {
 					truth = blas64.General{
 						Rows:   n,
 						Cols:   n,
@@ -130,7 +130,7 @@ func DsteqrTest(t *testing.T, impl Dsteqrer) {
 				}
 				if !eigenDecompCorrect(d, truth, V) {
 					t.Errorf("Eigen reconstruction mismatch. fromFull = %v, n = %v",
-						compz == lapack.OriginalEV, n)
+						compz == lapack.EVOrig, n)
 				}
 
 				// Compare eigenvalues when not computing eigenvectors.

lapack/testlapack/dtrexc.go

@@ -17,13 +17,13 @@ import (
 )
 
 type Dtrexcer interface {
-	Dtrexc(compq lapack.EVComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
+	Dtrexc(compq lapack.UpdateSchurComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
 }
 
 func DtrexcTest(t *testing.T, impl Dtrexcer) {
 	rnd := rand.New(rand.NewSource(1))
 
-	for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+	for _, compq := range []lapack.UpdateSchurComp{lapack.UpdateSchurNone, lapack.UpdateSchur} {
 		for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
 			for _, extra := range []int{0, 1, 11} {
 				for cas := 0; cas < 100; cas++ {
@@ -36,7 +36,7 @@ func DtrexcTest(t *testing.T, impl Dtrexcer) {
 		}
 	}
 
-	for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+	for _, compq := range []lapack.UpdateSchurComp{lapack.UpdateSchurNone, lapack.UpdateSchur} {
 		for _, extra := range []int{0, 1, 11} {
 			tmat := randomSchurCanonical(0, extra, rnd)
 			testDtrexc(t, impl, compq, tmat, 0, 0, extra, rnd)
@@ -44,7 +44,7 @@ func DtrexcTest(t *testing.T, impl Dtrexcer) {
 	}
 }
 
-func testDtrexc(t *testing.T, impl Dtrexcer, compq lapack.EVComp, tmat blas64.General, ifst, ilst, extra int, rnd *rand.Rand) {
+func testDtrexc(t *testing.T, impl Dtrexcer, compq lapack.UpdateSchurComp, tmat blas64.General, ifst, ilst, extra int, rnd *rand.Rand) {
 	const tol = 1e-13
 
 	n := tmat.Rows