shesha.ao.basis Namespace Reference

Functions for modal basis (DM basis, KL, Btt, etc...) More...

Functions
def	compute_KL2V (conf.Param_controller p_controller, Dms dms, list p_dms, conf.Param_geom p_geom, conf.Param_atmos p_atmos, conf.Param_tel p_tel)
	Compute the Karhunen-Loeve to Volt matrix (transfer matrix between the KL space and volt space for a pzt dm) More...
def	compute_dm_basis (g_dm, conf.Param_dm p_dm, conf.Param_geom p_geom)
	Compute a the DM basis as a sparse matrix : More...
def	compute_IFsparse (Dms g_dm, list p_dms, conf.Param_geom p_geom)
	Compute the influence functions of all DMs as a sparse matrix : More...
def	command_on_Btt (Rtc rtc, Dms dms, list p_dms, conf.Param_geom p_geom, int nfilt)
	Compute a command matrix in Btt modal basis (see error breakdown) and set it on the sutra_rtc. More...
def	compute_cmat_with_Btt (Rtc rtc, np.ndarray Btt, int nfilt)
	Compute a command matrix on the Btt basis and load it in the GPU. More...
def	command_on_KL (Rtc rtc, Dms dms, conf.Param_controller p_controller, List[conf.Param_dm] p_dms, conf.Param_geom p_geom, conf.Param_atmos p_atmos, conf.Param_tel p_tel, int nfilt)
	Compute a command matrix in KL modal basis and set it on the sutra_rtc. More...
def	compute_cmat_with_KL (Rtc rtc, np.ndarray KL2V, int nfilt)
	Compute a command matrix on the KL basis and load it in the GPU. More...
def	compute_fourier (int nActu, float pitch, np.ndarray actu_x_pos, np.ndarray actu_y_pos, periodic='n')
def	compute_btt (IFpzt, IFtt, influ_petal=None, return_delta=False)
	Returns Btt to Volts and Volts to Btt matrices. More...

Detailed Description

Functions for modal basis (DM basis, KL, Btt, etc...)

Author

COMPASS Team https://github.com/ANR-COMPASS

Version

5.0.0

Date

2020/05/18

Copyright

GNU Lesser General Public License

This file is part of COMPASS https://anr-compass.github.io/compass/

Copyright (C) 2011-2019 COMPASS Team https://github.com/ANR-COMPASS All rights reserved. Distributed under GNU - LGPL

COMPASS is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.

COMPASS: End-to-end AO simulation tool using GPU acceleration The COMPASS platform was designed to meet the need of high-performance for the simulation of AO systems.

The final product includes a software package for simulating all the critical subcomponents of AO, particularly in the context of the ELT and a real-time core based on several control approaches, with performances consistent with its integration into an instrument. Taking advantage of the specific hardware architecture of the GPU, the COMPASS tool allows to achieve adequate execution speeds to conduct large simulation campaigns called to the ELT.

The COMPASS platform can be used to carry a wide variety of simulations to both testspecific components of AO of the E-ELT (such as wavefront analysis device with a pyramid or elongated Laser star), and various systems configurations such as multi-conjugate AO.

COMPASS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with COMPASS. If not, see https://www.gnu.org/licenses/lgpl-3.0.txt.

Function Documentation

command_on_Btt()

def shesha.ao.basis.command_on_Btt	(	Rtc	rtc,
		Dms	dms,
		list	p_dms,
		conf.Param_geom	p_geom,
		int	nfilt
	)

Compute a command matrix in Btt modal basis (see error breakdown) and set it on the sutra_rtc.

It computes by itself the volts to Btt matrix.

:parameters:

rtc (Rtc) : rtc object

dms (Dms): dms object

p_dms (list of Param_dm): dms settings

p_geom (Param_geom): geometry settings

nfilt (int): number of modes to filter

Definition at line 205 of file basis.py.

    """
 
    IFs = compute_IFsparse(dms, p_dms, p_geom).T
    n = IFs.shape[1]
    IFtt = IFs[:, -2:].copy().toarray()
    IFpzt = IFs[:, :n - 2]
 
    Btt, P = compute_btt(IFpzt, IFtt)
    compute_cmat_with_Btt(rtc, Btt, nfilt)
 
 

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command_on_KL()

def shesha.ao.basis.command_on_KL	(	Rtc	rtc,
		Dms	dms,
		conf.Param_controller	p_controller,
		List[conf.Param_dm]	p_dms,
		conf.Param_geom	p_geom,
		conf.Param_atmos	p_atmos,
		conf.Param_tel	p_tel,
		int	nfilt
	)

Compute a command matrix in KL modal basis and set it on the sutra_rtc.

It computes by itself the volts to KL matrix.

:parameters:

rtc (Rtc) : rtc object

dms (Dms): dms object

p_dms (list of Param_dm): dms settings

p_geom (Param_geom): geometry settings

p_atmos (Param_atmos) : atmos parameters

p_tel (Param_tel) : telescope parameters

nfilt (int): number of modes to filter

Definition at line 264 of file basis.py.

 
        nfilt: (int): number of modes to filter
    """
    KL2V = compute_KL2V(p_controller, dms, p_dms, p_geom, p_atmos, p_tel)
    return compute_cmat_with_KL(rtc, KL2V, nfilt)
 
 

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compute_btt()

def shesha.ao.basis.compute_btt	(		IFpzt,
			IFtt,
			influ_petal = None,
			return_delta = False
	)

Returns Btt to Volts and Volts to Btt matrices.

:parameters:

IFpzt (csr_matrix) : influence function matrix of pzt DM, sparse and arrange as (Npts in pup x nactus)

IFtt (np.ndarray(ndim=2,dtype=np.float32)) : Influence function matrix of the TT mirror arrange as (Npts in pup x 2)

influ_petal (np.ndarray) : Influence function matrix of M4 petals. Default is None, if set, the Btt produced is also orthogonal to petal modes, then only driven by petal DM

return_delta (bool, optional) : If True, returns delta instead of P. Default is False

:returns:

Btt (np.ndarray(ndim=2,dtype=np.float32)) : Btt to Volts matrix

P (np.ndarray(ndim=2,dtype=np.float32)) : Volts to Btt matrix

Definition at line 368 of file basis.py.

    """
    N = IFpzt.shape[0]
    n = IFpzt.shape[1]
    if (n > N):
        raise ValueError("Influence functions must be arrange as (Npts_pup x nactus)")
 
    delta = IFpzt.T.dot(IFpzt).toarray() / N
 
    # Tip-tilt + piston
    Tp = np.ones((IFtt.shape[0], IFtt.shape[1] + 1))
    Tp[:, :2] = IFtt.copy(
    )  # THIS IS NOT A SPARSE OBJECT !!!!! STOP PUTTING .toarray() HERE PLEASE !!!
    deltaT = IFpzt.T.dot(Tp) / N
    # Tip tilt projection on the pzt dm
    tau = np.linalg.inv(delta).dot(deltaT)
    nfilt = 3  # Piston + tip + tilt
 
    if influ_petal is not None:
        # Petal basis generation (orthogonal to global piston)
        nseg = influ_petal.toarray().shape[0]
        petal_modes = -1 / (nseg - 1) * np.ones((nseg, (nseg - 1)))
        petal_modes += nseg / (nseg - 1) * np.eye(nseg)[:, 0:(
                nseg - 1)]  # petal modes within the petal dm space
        tau_petal = IFpzt.T.dot(influ_petal).toarray().dot(petal_modes.T)
        tau = np.concatenate((tau_petal, np.linalg.inv(delta).dot(deltaT)), axis=1)
        nfilt = 8
    # Famille generatrice sans tip tilt
    G = np.identity(n)
    tdt = tau.T.dot(delta).dot(tau)
    subTT = tau.dot(np.linalg.inv(tdt)).dot(tau.T).dot(delta)
    G -= subTT
 
    # Base orthonormee sans TT
    gdg = G.T.dot(delta).dot(G)
    U, s, V = np.linalg.svd(gdg)
    U = U[:, :U.shape[1] - nfilt]
    s = s[:s.size - nfilt]
    L = np.identity(s.size) / np.sqrt(s)
    B = G.dot(U).dot(L)
 
    # Rajout du TT
    TT = IFtt.T.dot(IFtt) / N
    Btt = np.zeros((n + 2, n - 1))
    Btt[:B.shape[0], :B.shape[1]] = B
    mini = 1. / np.sqrt(np.abs(TT))
    mini[0, 1] = 0
    mini[1, 0] = 0
    Btt[n:, -2:] = mini
    if influ_petal is not None:
        Btt[:n, -7:-2] = tau_petal
 
    # Calcul du projecteur actus-->modes
    Delta = np.zeros((n + IFtt.shape[1], n + IFtt.shape[1]))
    #IFpzt = rtc.get_IFpztsparse(1).T
    Delta[:-2, :-2] = delta
    Delta[-2:, -2:] = TT
    if return_delta:
        P = Delta
    else:
        P = Btt.T.dot(Delta)
 
    return Btt.astype(np.float32), P.astype(np.float32)

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compute_cmat_with_Btt()

def shesha.ao.basis.compute_cmat_with_Btt	(	Rtc	rtc,
		np.ndarray	Btt,
		int	nfilt
	)

Compute a command matrix on the Btt basis and load it in the GPU.

:parameters:

rtc (Rtc): rtc object

Btt (np.ndarray[ndim=2, dtype=np.float32]) : volts to Btt matrix

nfilt (int): number of modes to filter

Definition at line 226 of file basis.py.

    """
    D = np.array(rtc.d_control[0].d_imat)
    #D = ao.imat_geom(wfs,config.p_wfss,config.p_controllers[0],dms,config.p_dms,meth=0)
    # Filtering on Btt modes
    Btt_filt = np.zeros((Btt.shape[0], Btt.shape[1] - nfilt))
    Btt_filt[:, :Btt_filt.shape[1] - 2] = Btt[:, :Btt.shape[1] - (nfilt + 2)]
    Btt_filt[:, Btt_filt.shape[1] - 2:] = Btt[:, Btt.shape[1] - 2:]
 
    # Modal interaction basis
    Dm = D.dot(Btt_filt)
    # Direct inversion
    Dmp = np.linalg.inv(Dm.T.dot(Dm)).dot(Dm.T)
    # Command matrix
    cmat = Btt_filt.dot(Dmp)
    rtc.d_control[0].set_cmat(cmat.astype(np.float32))
 
    return cmat.astype(np.float32)
 
 

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compute_cmat_with_KL()

def shesha.ao.basis.compute_cmat_with_KL	(	Rtc	rtc,
		np.ndarray	KL2V,
		int	nfilt
	)

Compute a command matrix on the KL basis and load it in the GPU.

:parameters:

rtc (Rtc): rtc object

KL2V (np.ndarray[ndim=2, dtype=np.float32]) : volts to KL matrix

nfilt (int): number of modes to filter

Definition at line 281 of file basis.py.

    """
    D = np.array(rtc.d_control[0].d_imat)
    KL2V_filt = np.zeros((KL2V.shape[0], KL2V.shape[1] - nfilt))
    KL2V_filt[:, :KL2V_filt.shape[1] - 2] = KL2V[:, :KL2V.shape[1] - (nfilt + 2)]
    KL2V_filt[:, KL2V_filt.shape[1] - 2:] = KL2V[:, KL2V.shape[1] - 2:]
 
    # Modal interaction basis
    Dm = D.dot(KL2V_filt)
    # Direct inversion
    Dmp = np.linalg.inv(Dm.T.dot(Dm)).dot(Dm.T)
    # Command matrix
    cmat = KL2V_filt.dot(Dmp)
    rtc.d_control[0].set_cmat(cmat.astype(np.float32))
 
    return cmat.astype(np.float32)
 
 
def compute_fourier(nActu: int, pitch: float, actu_x_pos: np.ndarray,
                    actu_y_pos: np.ndarray, periodic='n'):
    '''
        Values you are looking for are:
            config.p_dm0.nact
            config.p_dm0._pitch
            config.p_dm0._i1

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compute_dm_basis()

def shesha.ao.basis.compute_dm_basis	(		g_dm,
		conf.Param_dm	p_dm,
		conf.Param_geom	p_geom
	)

Compute a the DM basis as a sparse matrix :

• push on each actuator
• get the corresponding dm shape
• apply pupil mask and store in a column

:parameters: g_dm (Dm) : Dm object

p_dm (Param_dm) : dm settings

p_geom (Param_geom) : geom settings

:return:

IFbasis = (csr_matrix) : DM IF basis

Definition at line 131 of file basis.py.

    """
    tmp = (p_geom._ipupil.shape[0] - (p_dm._n2 - p_dm._n1 + 1)) // 2
    tmp_e0 = p_geom._ipupil.shape[0] - tmp
    tmp_e1 = p_geom._ipupil.shape[1] - tmp
    pup = p_geom._ipupil[tmp:tmp_e0, tmp:tmp_e1]
    indx_valid = np.where(pup.flatten("F") > 0)[0].astype(np.int32)
 
    #IFbasis = np.ndarray((indx_valid.size, p_dm._ntotact), dtype=np.float32)
    for i in trange(p_dm._ntotact):
        g_dm.reset_shape()
        g_dm.comp_oneactu(i, 1.0)
        shape = np.array(g_dm.d_shape)
        IFvec = csr_matrix(shape.flatten("F")[indx_valid])
        if (i == 0):
            val = IFvec.data
            col = IFvec.indices
            row = np.append(0, IFvec.getnnz())
        else:
            val = np.append(val, IFvec.data)
            col = np.append(col, IFvec.indices)
            row = np.append(row, row[-1] + IFvec.getnnz())
    g_dm.reset_shape()
    IFbasis = csr_matrix((val, col, row))
    return IFbasis
 
 

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compute_fourier()

def shesha.ao.basis.compute_fourier	(	int	nActu,
		float	pitch,
		np.ndarray	actu_x_pos,
		np.ndarray	actu_y_pos,
			periodic = 'n'
	)

Definition at line 305 of file basis.py.

            config.p_dm0._j1
    '''
    # Offset xpos and ypos to get integer indices.
    # Compute nact x nact x nact x nact Fourier basis # Periodic condition n / n-1 as option
    # Extract values for actuators - flatten
 
    # Periodic may be 'n' or 'n-1'
    # Will work only for squared pitch mirrors so far
    if periodic == 'n':
        n = nActu
    elif periodic == 'n-1':
        n = nActu - 1
    else:
        raise ValueError('periodic can only be "n" or "n-1" to set boundary condition.')
    xnorm = (np.round((actu_x_pos - np.min(actu_x_pos)) / pitch).astype(np.int32)) % n
    ynorm = (np.round((actu_y_pos - np.min(actu_y_pos)) / pitch).astype(np.int32)) % n
    totActu = len(xnorm)
 
    data = np.zeros((n, n, n, n), dtype=np.float32)
    for i in range(n):
        for j in range(n):
            data[i, j, i, j] = 1.
 
    data = np.fft.fftn(data, axes=(2, 3))
 
    takeSine = np.zeros((n, n), dtype=bool)  # Where to take sine instead of cosine
    takeSine[0, n // 2 + 1:] = 1  # Half of first line
    if n % 2 == 0:
        takeSine[n // 2, n // 2 + 1:] = 1  # Half of waffle line
 
    takeSine[n // 2 + 1:, :] = 1  # Bottom half
 
    data[takeSine] *= 1j
    data = data.real
 
    # Extract actuators
    actuPush = data[:, :, xnorm, ynorm]
 
    # Add a renorm ?
 
    return actuPush
 
 

compute_IFsparse()

def shesha.ao.basis.compute_IFsparse	(	Dms	g_dm,
		list	p_dms,
		conf.Param_geom	p_geom
	)

Compute the influence functions of all DMs as a sparse matrix :

• push on each actuator
• get the corresponding dm shape
• apply pupil mask and store in a column

:parameters:

g_dm (Dms) : Dms object

p_dms (Param_dms) : dms settings

p_geom (Param_geom) : geom settings

:return:

IFbasis = (csr_matrix) : DM IF basis

Definition at line 174 of file basis.py.

    """
    ndm = len(p_dms)
    for i in range(ndm):
        IFi = compute_dm_basis(g_dm.d_dms[i], p_dms[i], p_geom)
        if (i == 0):
            val = IFi.data
            col = IFi.indices
            row = IFi.indptr
        else:
            val = np.append(val, IFi.data)
            col = np.append(col, IFi.indices)
            row = np.append(row, row[-1] + IFi.indptr[1:])
    IFsparse = csr_matrix((val, col, row))
    return IFsparse
 
 

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compute_KL2V()

def shesha.ao.basis.compute_KL2V	(	conf.Param_controller	p_controller,
		Dms	dms,
		list	p_dms,
		conf.Param_geom	p_geom,
		conf.Param_atmos	p_atmos,
		conf.Param_tel	p_tel
	)

Compute the Karhunen-Loeve to Volt matrix (transfer matrix between the KL space and volt space for a pzt dm)

:parameters:

p_controller (Param_controller) : p_controller settings

dms (shesha_dms) : Dms object

p_dms (list of Param_dm) : dms settings

p_geom (Param_geom) : geometry parameters

p_atmos (Param_atmos) : atmos parameters

p_tel (Param_tel) : telescope parameters

:return:

KL2V (np.array(np.float32,dim=2)) : KL to Volt matrix

Definition at line 72 of file basis.py.

 
        KL2V : (np.array(np.float32,dim=2)) : KL to Volt matrix
    """
    ntotact = np.array([p_dms[i]._ntotact for i in range(len(p_dms))], dtype=np.int64)
    KL2V = np.zeros((np.sum(ntotact), np.sum(ntotact)), dtype=np.float32)
 
    indx_act = 0
    nTT = 0
 
    for i in range(p_controller.ndm.size):
        ndm = p_controller.ndm[i]
        if (p_dms[ndm].type == scons.DmType.PZT):
            tmp = (p_geom._ipupil.shape[0] - (p_dms[ndm]._n2 - p_dms[ndm]._n1 + 1)) // 2
            tmp_e0 = p_geom._ipupil.shape[0] - tmp
            tmp_e1 = p_geom._ipupil.shape[1] - tmp
            pup = p_geom._ipupil[tmp:tmp_e0, tmp:tmp_e1]
            indx_valid = np.where(pup.flatten("F") > 0)[0].astype(np.int32)
            p2m = p_tel.diam / p_geom.pupdiam
            norm = -(p2m * p_tel.diam / (2 * p_atmos.r0))**(5. / 3)
 
            dms.d_dms[ndm].compute_KLbasis(p_dms[ndm]._xpos, p_dms[ndm]._ypos,
                                           indx_valid, indx_valid.size, norm, 1.0)
 
            KL2V[indx_act:indx_act + ntotact[ndm], indx_act:indx_act + ntotact[ndm]] = \
                np.fliplr(dms.d_dms[ndm].d_KLbasis)
            indx_act += ntotact[ndm]
        elif (p_dms[ndm].type == scons.DmType.TT):
            nTT += 1
    if (p_controller.nmodes is not None and
                p_controller.nmodes < KL2V.shape[1] - 2 * nTT):
        KL2V = KL2V[:, :p_controller.nmodes]
    else:
        KL2V = KL2V[:, :KL2V.shape[1] - 2 * nTT]
    if (nTT > 1):
        raise ValueError("More than 1 TipTilt found! Stupid")
    if (nTT != 0):
        KL2V[:, :KL2V.shape[1] - 2] = KL2V[:, 2:]
        KL2V[:, KL2V.shape[1] - 2:] = np.zeros((np.sum(ntotact), 2), dtype=np.float32)
        KL2V[np.sum(ntotact) - 2:, KL2V.shape[1] - 2:] = np.identity(2, dtype=np.float32)
 
    return KL2V
 
 

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