Golang gomas.NewError函數代碼示例

/*
 * Compute QR factorization of a M-by-N matrix A using compact WY transformation: A = Q * R,
 * where Q = I - Y*T*Y.T, T is block reflector and Y holds elementary reflectors as lower
 * trapezoidal matrix saved below diagonal elements of the matrix A.
 *
 * Arguments:
 *  A    On entry, the M-by-N matrix A. On exit, the elements on and above
 *       the diagonal contain the min(M,N)-by-N upper trapezoidal matrix R.
 *       The elements below the diagonal with the matrix 'T', represent
 *       the ortogonal matrix Q as product of elementary reflectors.
 *
 * T     On exit, the K block reflectors which, together with trilu(A) represent
 *       the ortogonal matrix Q as Q = I - Y*T*Y.T where Y = trilu(A).
 *       K is ceiling(N/LB) where LB is blocking size from used blocking configuration.
 *       The matrix T is LB*N augmented matrix of K block reflectors,
 *       T = [T(0) T(1) .. T(K-1)].  Block reflector T(n) is LB*LB matrix, expect
 *       reflector T(K-1) that is IB*IB matrix  where IB = min(LB, K % LB)
 *
 * W     Workspace, required size returned by QRTFactorWork().
 *
 * conf  Optional blocking configuration. If not provided then default configuration
 *       is used.
 *
 * Returns:
 *      Error indicator.
 *
 * QRTFactor is compatible with lapack.DGEQRT
 */
func QRTFactor(A, T, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)
	ok := false
	rsize := 0

	if m(A) < n(A) {
		return gomas.NewError(gomas.ESIZE, "QRTFactor")
	}
	wsz := QRTFactorWork(A, conf)
	if W == nil || W.Len() < wsz {
		return gomas.NewError(gomas.EWORK, "QRTFactor", wsz)
	}

	tr, tc := T.Size()
	if conf.LB == 0 || conf.LB > n(A) {
		ok = tr == tc && tr == n(A)
		rsize = n(A) * n(A)
	} else {
		ok = tr == conf.LB && tc == n(A)
		rsize = conf.LB * n(A)
	}
	if !ok {
		return gomas.NewError(gomas.ESMALL, "QRTFactor", rsize)
	}

	if conf.LB == 0 || n(A) <= conf.LB {
		err = unblockedQRT(A, T, W)
	} else {
		Wrk := cmat.MakeMatrix(n(A), conf.LB, W.Data())
		err = blockedQRT(A, T, Wrk, conf)
	}
	return err
}

/*
 * Solve a system of linear equations A*X = B or A.T*X = B with general N-by-N
 * matrix A using the LU factorization computed by LUFactor().
 *
 * Arguments:
 *  B      On entry, the right hand side matrix B. On exit, the solution matrix X.
 *
 *  A      The factor L and U from the factorization A = P*L*U as computed by
 *         LUFactor()
 *
 *  pivots The pivot indices from LUFactor().
 *
 *  flags  The indicator of the form of the system of equations.
 *         If flags&TRANSA then system is transposed. All other values
 *         indicate non transposed system.
 *
 * Compatible with lapack.DGETRS.
 */
func LUSolve(B, A *cmat.FloatMatrix, pivots Pivots, flags int, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.DefaultConf()
	if len(confs) > 0 {
		conf = confs[0]
	}
	ar, ac := A.Size()
	br, _ := B.Size()
	if ar != ac {
		return gomas.NewError(gomas.ENOTSQUARE, "SolveLU")
	}
	if br != ac {
		return gomas.NewError(gomas.ESIZE, "SolveLU")
	}
	if pivots != nil {
		applyPivots(B, pivots)
	}
	if flags&gomas.TRANSA != 0 {
		// transposed X = A.-1*B == (L.T*U.T).-1*B == U.-T*(L.-T*B)
		blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
		blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.TRANSA, conf)
	} else {
		// non-transposed X = A.-1*B == (L*U).-1*B == U.-1*(L.-1*B)
		blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT, conf)
		blasd.SolveTrm(B, A, 1.0, gomas.UPPER, conf)
	}

	return err
}

func MVMult(Y, A, X *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
	ok := true
	yr, yc := Y.Size()
	ar, ac := A.Size()
	xr, xc := X.Size()

	if ar*ac == 0 {
		return nil
	}
	if yr != 1 && yc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "MVMult")
	}
	if xr != 1 && xc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "MVMult")
	}
	nx := X.Len()
	ny := Y.Len()

	if bits&gomas.TRANSA != 0 {
		bits |= gomas.TRANS
	}
	if bits&gomas.TRANS != 0 {
		ok = ny == ac && nx == ar
	} else {
		ok = ny == ar && nx == ac
	}
	if !ok {
		return gomas.NewError(gomas.ESIZE, "MVMult")
	}
	if beta != 1.0 {
		vscal(Y, beta, ny)
	}
	gemv(Y, A, X, alpha, beta, bits, 0, nx, 0, ny)
	return nil
}

/*
 * Generate the M by N matrix Q with orthogonal rows which
 * are defined as the first M rows of the product of K first elementary
 * reflectors.
 *
 * Arguments
 *   A     On entry, the elementary reflectors as returned by LQFactor().
 *         stored right of diagonal of the M by N matrix A.
 *         On exit, the orthogonal matrix Q
 *
 *   tau   Scalar coefficents of elementary reflectors
 *
 *   W     Workspace
 *
 *   K     The number of elementary reflector whose product define the matrix Q
 *
 *   conf  Optional blocking configuration.
 *
 * Compatible with lapackd.ORGLQ.
 */
func LQBuild(A, tau, W *cmat.FloatMatrix, K int, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)
	if K <= 0 || K > n(A) {
		return gomas.NewError(gomas.EVALUE, "LQBuild", K)
	}
	wsz := wsBuildLQ(A, 0)
	if W == nil || W.Len() < wsz {
		return gomas.NewError(gomas.EWORK, "LQBuild", wsz)
	}

	// adjust blocking factor for workspace size
	lb := estimateLB(A, W.Len(), wsBuildLQ)
	//lb = imin(lb, conf.LB)
	lb = conf.LB
	if lb == 0 || m(A) <= lb {
		unblkBuildLQ(A, tau, W, m(A)-K, n(A)-K, true)
	} else {
		var Twork, Wrk cmat.FloatMatrix
		Twork.SetBuf(lb, lb, lb, W.Data())
		Wrk.SetBuf(m(A)-lb, lb, m(A)-lb, W.Data()[Twork.Len():])
		blkBuildLQ(A, tau, &Twork, &Wrk, K, lb, conf)
	}
	return err
}

/*
 * Symmetric matrix-vector multiplication. Y = beta*Y + alpha*A*X
 */
func MVMultSym(Y, A, X *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
	ok := true
	yr, yc := Y.Size()
	ar, ac := A.Size()
	xr, xc := X.Size()

	if ar*ac == 0 {
		return nil
	}
	if yr != 1 && yc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "MVMultSym")
	}
	if xr != 1 && xc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "MVMultSym")
	}
	nx := X.Len()
	ny := Y.Len()

	ok = ny == ar && nx == ac && ac == ar
	if !ok {
		return gomas.NewError(gomas.ESIZE, "MVMultSym")
	}
	if beta != 1.0 {
		vscal(Y, beta, ny)
	}
	symv(Y, A, X, alpha, bits, nx)
	return nil
}

/*
 * Compute RQ factorization of a M-by-N matrix A: A = R*Q
 *
 * Arguments:
 *  A    On entry, the M-by-N matrix A, M <= N. On exit, upper triangular matrix R
 *       and the orthogonal matrix Q as product of elementary reflectors.
 *
 * tau  On exit, the scalar factors of the elementary reflectors.
 *
 * W    Workspace, M-by-nb matrix used for work space in blocked invocations.
 *
 * conf The blocking configuration. If nil then default blocking configuration
 *      is used. Member conf.LB defines blocking size of blocked algorithms.
 *      If it is zero then unblocked algorithm is used.
 *
 * Returns:
 *      Error indicator.
 *
 * Additional information
 *
 *  Ortogonal matrix Q is product of elementary reflectors H(k)
 *
 *    Q = H(0)H(1),...,H(K-1), where K = min(M,N)
 *
 *  Elementary reflector H(k) is stored on row k of A right of the diagonal with
 *  implicit unit value on diagonal entry. The vector TAU holds scalar factors of
 *  the elementary reflectors.
 *
 *  Contents of matrix A after factorization is as follow:
 *
 *    ( v0 v0 r  r  r  r )  M=4, N=6
 *    ( v1 v1 v1 r  r  r )
 *    ( v2 v2 v2 v2 r  r )
 *    ( v3 v3 v3 v3 v3 r )
 *
 *  where l is element of L, vk is element of H(k).
 *
 *  RQFactor is compatible with lapack.DGERQF
 */
func RQFactor(A, tau, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)

	// must have: M <= N
	if m(A) > n(A) {
		return gomas.NewError(gomas.ESIZE, "RQFactor")
	}

	wsmin := wsLQ(A, 0)
	if W == nil || W.Len() < wsmin {
		return gomas.NewError(gomas.EWORK, "RQFactor", wsmin)
	}
	lb := estimateLB(A, W.Len(), wsRQ)
	lb = imin(lb, conf.LB)
	if lb == 0 || m(A) <= lb {
		unblockedRQ(A, tau, W)
	} else {
		var Twork, Wrk cmat.FloatMatrix
		// block reflector T in first LB*LB elements in workspace
		// the rest, m(A)-LB*LB, is workspace for intermediate matrix operands
		Twork.SetBuf(lb, lb, lb, W.Data())
		Wrk.SetBuf(m(A)-lb, lb, m(A)-lb, W.Data()[Twork.Len():])
		blockedRQ(A, tau, &Twork, &Wrk, lb, conf)
	}
	return err
}

/*
 * Multiply and replace C with Q*C or Q.T*C where Q is a real orthogonal matrix
 * defined as the product of k elementary reflectors and block reflector T
 *
 *    Q = H(1) H(2) . . . H(k)
 *
 * as returned by DecomposeQRT().
 *
 * Arguments:
 *  C     On entry, the M-by-N matrix C. On exit C is overwritten by Q*C or Q.T*C.
 *
 *  A     QR factorization as returned by QRTFactor() where the lower trapezoidal
 *        part holds the elementary reflectors.
 *
 *  T     The block reflector computed from elementary reflectors as returned by
 *        DecomposeQRT() or computed from elementary reflectors and scalar coefficients
 *        by BuildT()
 *
 *  W     Workspace, size as returned by QRTMultWork()
 *
 *  conf  Blocking configuration
 *
 *  flags Indicators. Valid indicators LEFT, RIGHT, TRANS, NOTRANS
 *
 * Preconditions:
 *   a.   cols(A) == cols(T),
 *          columns A define number of elementary reflector, must match order of block reflector.
 *   b.   if conf.LB == 0, cols(T) == rows(T)
 *          unblocked invocation, block reflector T is upper triangular
 *   c.   if conf.LB != 0, rows(T) == conf.LB
 *          blocked invocation, T is sequence of triangular block reflectors of order LB
 *   d.   if LEFT, rows(C) >= cols(A) && cols(C) >= rows(A)
 *
 *   e.   if RIGHT, cols(C) >= cols(A) && rows(C) >= rows(A)
 *
 * Compatible with lapack.DGEMQRT
 */
func QRTMult(C, A, T, W *cmat.FloatMatrix, flags int, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)

	wsz := QRTMultWork(C, T, flags, conf)
	if W == nil || W.Len() < wsz {
		return gomas.NewError(gomas.EWORK, "QRTMult", wsz)
	}
	ok := false
	switch flags & gomas.RIGHT {
	case gomas.RIGHT:
		ok = n(C) >= m(A)
	default:
		ok = m(C) >= n(A)
	}
	if !ok {
		return gomas.NewError(gomas.ESIZE, "QRTMult")
	}

	var Wrk cmat.FloatMatrix
	if flags&gomas.RIGHT != 0 {
		Wrk.SetBuf(m(C), conf.LB, m(C), W.Data())
		blockedMultQTRight(C, A, T, &Wrk, flags, conf)

	} else {
		Wrk.SetBuf(n(C), conf.LB, n(C), W.Data())
		blockedMultQTLeft(C, A, T, &Wrk, flags, conf)
	}
	return err
}

/*
 * Compute
 *   B = B*diag(D).-1      flags & RIGHT == true
 *   B = diag(D).-1*B      flags & LEFT  == true
 *
 * If flags is LEFT (RIGHT) then element-wise divides columns (rows) of B with vector D.
 *
 * Arguments:
 *   B     M-by-N matrix if flags&RIGHT == true or N-by-M matrix if flags&LEFT == true
 *
 *   D     N element column or row vector or N-by-N matrix
 *
 *   flags Indicator bits, LEFT or RIGHT
 */
func SolveDiag(B, D *cmat.FloatMatrix, flags int, confs ...*gomas.Config) *gomas.Error {
	var c, d0 cmat.FloatMatrix
	var d *cmat.FloatMatrix

	conf := gomas.CurrentConf(confs...)
	d = D
	if !D.IsVector() {
		d0.Diag(D)
		d = &d0
	}
	dn := d0.Len()
	br, bc := B.Size()
	switch flags & (gomas.LEFT | gomas.RIGHT) {
	case gomas.LEFT:
		if br != dn {
			return gomas.NewError(gomas.ESIZE, "SolveDiag")
		}
		// scale rows;
		for k := 0; k < dn; k++ {
			c.Row(B, k)
			blasd.InvScale(&c, d.GetAt(k), conf)
		}
	case gomas.RIGHT:
		if bc != dn {
			return gomas.NewError(gomas.ESIZE, "SolveDiag")
		}
		// scale columns
		for k := 0; k < dn; k++ {
			c.Column(B, k)
			blasd.InvScale(&c, d.GetAt(k), conf)
		}
	}
	return nil
}

// Solve secular function arising in symmetric eigenproblems. On exit 'Y' contains new
// eigenvalues and 'V' the rank-one update vector corresponding new eigenvalues.
// The matrix Qd holds for each eigenvalue then computed deltas as row vectors.
// On entry 'D' holds original eigenvalues and 'Z' is the rank-one update vector.
func TRDSecularSolveAll(y, v, Qd, d, z *cmat.FloatMatrix, rho float64, confs ...*gomas.Config) (err *gomas.Error) {
	var delta cmat.FloatMatrix
	var lmbda float64
	var e, ei int

	ei = 0
	err = nil
	if y.Len() != d.Len() || z.Len() != d.Len() || m(Qd) != n(Qd) || m(Qd) != d.Len() {
		err = gomas.NewError(gomas.ESIZE, "TRDSecularSolveAll")
		return
	}
	for i := 0; i < d.Len(); i++ {
		delta.Row(Qd, i)
		lmbda, e = trdsecRoot(d, z, &delta, i, rho)
		if e < 0 && ei == 0 {
			ei = -(i + 1)
		}
		y.SetAt(i, lmbda)
	}
	if ei == 0 {
		trdsecUpdateVecDelta(v, Qd, d, rho)
	} else {
		err = gomas.NewError(gomas.ECONVERGE, "TRDSecularSolveAll", ei)
	}
	return
}

/*
 * Compute QL factorization of a M-by-N matrix A: A = Q * L.
 *
 * Arguments:
 *  A    On entry, the M-by-N matrix A, M >= N. On exit, lower triangular matrix L
 *       and the orthogonal matrix Q as product of elementary reflectors.
 *
 * tau  On exit, the scalar factors of the elemenentary reflectors.
 *
 * W    Workspace, N-by-nb matrix used for work space in blocked invocations.
 *
 * conf The blocking configuration. If nil then default blocking configuration
 *      is used. Member conf.LB defines blocking size of blocked algorithms.
 *      If it is zero then unblocked algorithm is used.
 *
 * Returns:
 *      Error indicator.
 *
 * Additional information
 *
 *  Ortogonal matrix Q is product of elementary reflectors H(k)
 *
 *    Q = H(K-1)...H(1)H(0), where K = min(M,N)
 *
 *  Elementary reflector H(k) is stored on column k of A above the diagonal with
 *  implicit unit value on diagonal entry. The vector TAU holds scalar factors
 *  of the elementary reflectors.
 *
 *  Contents of matrix A after factorization is as follow:
 *
 *    ( v0 v1 v2 v3 )   for M=6, N=4
 *    ( v0 v1 v2 v3 )
 *    ( l  v1 v2 v3 )
 *    ( l  l  v2 v3 )
 *    ( l  l  l  v3 )
 *    ( l  l  l  l  )
 *
 *  where l is element of L, vk is element of H(k).
 *
 * DecomposeQL is compatible with lapack.DGEQLF
 */
func QLFactor(A, tau, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	var tauh cmat.FloatMatrix
	conf := gomas.CurrentConf(confs...)

	if m(A) < n(A) {
		return gomas.NewError(gomas.ESIZE, "QLFactor")
	}
	wsmin := wsQL(A, 0)
	if W == nil || W.Len() < wsmin {
		return gomas.NewError(gomas.EWORK, "QLFactor", wsmin)
	}
	if tau.Len() < n(A) {
		return gomas.NewError(gomas.ESIZE, "QLFactor")
	}
	tauh.SubMatrix(tau, 0, 0, n(A), 1)
	lb := estimateLB(A, W.Len(), wsQL)
	lb = imin(lb, conf.LB)

	if lb == 0 || n(A) <= lb {
		unblockedQL(A, &tauh, W)
	} else {
		var Twork, Wrk cmat.FloatMatrix
		// block reflector T in first LB*LB elements in workspace
		// the rest, n(A)-LB*LB, is workspace for intermediate matrix operands
		Twork.SetBuf(conf.LB, conf.LB, -1, W.Data())
		Wrk.SetBuf(n(A)-conf.LB, conf.LB, -1, W.Data()[Twork.Len():])
		blockedQL(A, &tauh, &Twork, &Wrk, lb, conf)
	}
	return err
}

func EigenSym(D, A, W *cmat.FloatMatrix, bits int, confs ...*gomas.Config) (err *gomas.Error) {

	var sD, sE, E, tau, Wred cmat.FloatMatrix
	var vv *cmat.FloatMatrix

	err = nil
	vv = nil
	conf := gomas.CurrentConf(confs...)

	if m(A) != n(A) || D.Len() != m(A) {
		err = gomas.NewError(gomas.ESIZE, "EigenSym")
		return
	}
	if bits&gomas.WANTV != 0 && W.Len() < 3*n(A) {
		err = gomas.NewError(gomas.EWORK, "EigenSym")
		return
	}

	if bits&(gomas.LOWER|gomas.UPPER) == 0 {
		bits = bits | gomas.LOWER
	}
	ioff := 1
	if bits&gomas.LOWER != 0 {
		ioff = -1
	}
	E.SetBuf(n(A)-1, 1, n(A)-1, W.Data())
	tau.SetBuf(n(A), 1, n(A), W.Data()[n(A)-1:])
	wrl := W.Len() - 2*n(A) - 1
	Wred.SetBuf(wrl, 1, wrl, W.Data()[2*n(A)-1:])

	// reduce to tridiagonal
	if err = TRDReduce(A, &tau, &Wred, bits, conf); err != nil {
		err.Update("EigenSym")
		return
	}
	sD.Diag(A)
	sE.Diag(A, ioff)
	blasd.Copy(D, &sD)
	blasd.Copy(&E, &sE)

	if bits&gomas.WANTV != 0 {
		if err = TRDBuild(A, &tau, &Wred, n(A), bits, conf); err != nil {
			err.Update("EigenSym")
			return
		}
		vv = A
	}

	// resize workspace
	wrl = W.Len() - n(A) - 1
	Wred.SetBuf(wrl, 1, wrl, W.Data()[n(A)-1:])

	if err = TRDEigen(D, &E, vv, &Wred, bits, conf); err != nil {
		err.Update("EigenSym")
		return
	}
	return
}

// Computes eigenvectors corresponding the updated eigenvalues and rank-one update vector.
// The matrix Qd holds precomputed deltas as returned by TRDSecularSolveAll(). If Qd is nil or
// Qd same as the matrix Q then computation is in-place and Q is assumed to hold precomputed
// deltas. On exit, Q holds the column eigenvectors.
func TRDSecularEigen(Q, v, Qd *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	if m(Q) != n(Q) || (Qd != nil && (m(Qd) != n(Qd) || m(Qd) != m(Q))) {
		return gomas.NewError(gomas.ESIZE, "TRDSecularEigen")
	}
	if m(Q) != v.Len() {
		return gomas.NewError(gomas.ESIZE, "TRDSecularEigen")
	}
	if Qd == nil || Qd == Q {
		trdsecEigenBuildInplace(Q, v)
	} else {
		trdsecEigenBuild(Q, v, Qd)
	}
	return nil
}

func Swap(X, Y *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	xr, xc := X.Size()
	yr, yc := Y.Size()
	if xr != 1 && xc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "Swap")
	}
	if yr != 1 && yc != 1 {
		return gomas.NewError(gomas.ENEED_VECTOR, "Swap")
	}
	if X.Len() != Y.Len() {
		return gomas.NewError(gomas.ESIZE, "Swap")
	}
	vswap(X, Y, X.Len())
	return nil
}

/*
 * Reduce general matrix A to upper Hessenberg form H by similiarity
 * transformation H = Q.T*A*Q.
 *
 * Arguments:
 *  A    On entry, the general matrix A. On exit, the elements on and
 *       above the first subdiagonal contain the reduced matrix H.
 *       The elements below the first subdiagonal with the vector tau
 *       represent the ortogonal matrix A as product of elementary reflectors.
 *
 *  tau  On exit, the scalar factors of the elementary reflectors.
 *
 *  W    Workspace, as defined by HessReduceWork()
 *
 *  conf The blocking configration.
 *
 * HessReduce is compatible with lapack.DGEHRD.
 */
func HessReduce(A, tau, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)

	wmin := m(A)
	wopt := HessReduceWork(A, conf)
	wsz := W.Len()
	if wsz < wmin {
		return gomas.NewError(gomas.EWORK, "ReduceHess", wmin)
	}
	// use blocked version if workspace big enough for blocksize 4
	lb := conf.LB
	if wsz < wopt {
		lb = estimateLB(A, wsz, wsHess)
	}
	if lb == 0 || n(A) <= lb {
		unblkHessGQvdG(A, tau, W, 0)
	} else {
		// blocked version
		var W0 cmat.FloatMatrix
		// shape workspace for blocked algorithm
		W0.SetBuf(m(A)+lb, lb, m(A)+lb, W.Data())
		blkHessGQvdG(A, tau, &W0, lb, conf)
	}
	return err
}

/*
 * Reduce a general M-by-N matrix A to upper or lower bidiagonal form B
 * by an ortogonal transformation A = Q*B*P.T,  B = Q.T*A*P
 *
 *
 * Arguments
 *   A     On entry, the real M-by-N matrix. On exit the upper/lower
 *         bidiagonal matrix and ortogonal matrices Q and P.
 *
 *   tauq  Scalar factors for elementary reflector forming the
 *         ortogonal matrix Q.
 *
 *   taup  Scalar factors for elementary reflector forming the
 *         ortogonal matrix P.
 *
 *   W     Workspace needed for reduction.
 *
 *   conf  Current blocking configuration. Optional.
 *
 *
 * Details
 *
 * Matrices Q and P are products of elementary reflectors H(k) and G(k)
 *
 * If M > N:
 *     Q = H(1)*H(2)*...*H(N)   and P = G(1)*G(2)*...*G(N-1)
 *
 * where H(k) = 1 - tauq*u*u.T and G(k) = 1 - taup*v*v.T
 *
 * Elementary reflector H(k) are stored on columns of A below the diagonal with
 * implicit unit value on diagonal entry. Vector TAUQ holds corresponding scalar
 * factors. Reflector G(k) are stored on rows of A right of first superdiagonal
 * with implicit unit value on superdiagonal. Corresponding scalar factors are
 * stored on vector TAUP.
 *
 * If M < N:
 *   Q = H(1)*H(2)*...*H(N-1)   and P = G(1)*G(2)*...*G(N)
 *
 * where H(k) = 1 - tauq*u*u.T and G(k) = 1 - taup*v*v.T
 *
 * Elementary reflector H(k) are stored on columns of A below the first sub diagonal
 * with implicit unit value on sub diagonal entry. Vector TAUQ holds corresponding
 * scalar factors. Reflector G(k) are sotre on rows of A right of diagonal with
 * implicit unit value on superdiagonal. Corresponding scalar factors are stored
 * on vector TAUP.
 *
 * Contents of matrix A after reductions are as follows.
 *
 *    M = 6 and N = 5:                  M = 5 and N = 6:
 *
 *    (  d   e   v1  v1  v1 )           (  d   v1  v1  v1  v1  v1 )
 *    (  u1  d   e   v2  v2 )           (  e   d   v2  v2  v2  v2 )
 *    (  u1  u2  d   e   v3 )           (  u1  e   d   v3  v3  v3 )
 *    (  u1  u2  u3  d   e  )           (  u1  u2  e   d   v4  v4 )
 *    (  u1  u2  u3  u4  d  )           (  u1  u2  u3  e   d   v5 )
 *    (  u1  u2  u3  u4  u5 )
 */
func BDReduce(A, tauq, taup, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
	var err *gomas.Error = nil
	conf := gomas.CurrentConf(confs...)
	_ = conf

	wmin := wsBired(A, 0)
	wsz := W.Len()
	if wsz < wmin {
		return gomas.NewError(gomas.EWORK, "ReduceBidiag", wmin)
	}
	lb := conf.LB
	wneed := wsBired(A, lb)
	if wneed > wsz {
		lb = estimateLB(A, wsz, wsBired)
	}
	if m(A) >= n(A) {
		if lb > 0 && n(A) > lb {
			blkBidiagLeft(A, tauq, taup, W, lb, conf)
		} else {
			unblkReduceBidiagLeft(A, tauq, taup, W)
		}
	} else {
		if lb > 0 && m(A) > lb {
			blkBidiagRight(A, tauq, taup, W, lb, conf)
		} else {
			unblkReduceBidiagRight(A, tauq, taup, W)
		}
	}
	return err
}