PCG

Preconditioned Conjugate Gradient. More...

Functions
__global__ void	tinker::pcgUdirV1 (int n, const real *polarity, real(*udir)[3], const real(*field)[3])
	Calculates the direct induced dipoles 2b. More...
__global__ void	tinker::pcgUdirV2 (int n, const real *polarity, real(*udir)[3], real(*udirp)[3], const real(*field)[3], const real(*fieldp)[3])
	Calculates the direct induced dipoles 2b. More...
__global__ void	tinker::pcgRsd0V1 (int n, const real *polarity_inv, real(*rsd)[3], const real(*udir)[3], const real(*uind)[3], const real(*field)[3])
	Calculates the initial residuals for the predictor 3a. More...
__global__ void	tinker::pcgRsd0V2 (int n, const real *polarity_inv, real(*rsd)[3], real(*rsp)[3], const real(*udir)[3], const real(*udip)[3], const real(*uind)[3], const real(*uinp)[3], const real(*field)[3], const real(*fielp)[3])
	Calculates the initial residuals for the predictor 3a. More...
__global__ void	tinker::pcgRsd0V3 (int n, const real *polarity_inv, real(*rsd)[3], const real(*udir)[3], const real(*uind)[3], const real(*field)[3], const real(*polscale)[3][3])
	Calculates the initial residuals for the predictor 3a using the Exchange-Polarization Model. More...
__global__ void	tinker::pcgRsd0 (int n, const real *polarity, real(*rsd)[3], real(*rsdp)[3])
	Sets the residual to zero for atoms with zero polarizability. More...
__global__ void	tinker::pcgRsd1 (int n, const real *polarity, real(*rsd)[3])
	Sets the residual to zero for atoms with zero polarizability. More...
__global__ void	tinker::pcgP1 (int n, const real *polarity_inv, real(*vec)[3], real(*vecp)[3], const real(*conj)[3], const real(*conjp)[3], const real(*field)[3], const real(*fieldp)[3])
	Calculates the vector Ap – step 5a. More...
__global__ void	tinker::pcgP2 (int n, const real *polarity, const real *ka, const real *kap, const real *ksum, const real *ksump, real(*uind)[3], real(*uinp)[3], const real(*conj)[3], const real(*conjp)[3], real(*rsd)[3], real(*rsdp)[3], const real(*vec)[3], const real(*vecp)[3])
	Updates the induced dipoles and residuals – step 5bc. More...
__global__ void	tinker::pcgP3 (int n, const real *ksum, const real *ksump, const real *ksum1, const real *ksump1, real(*conj)[3], real(*conjp)[3], const real(*zrsd)[3], const real(*zrsdp)[3])
	Calculates the scalar b from s0 and s, then updates the vector p – 5ef. More...
__global__ void	tinker::pcgP4 (int n, const real *polarity_inv, real(*vec)[3], const real(*conj)[3], const real(*field)[3])
	Calculates the vector Ap – step 5a. More...
__global__ void	tinker::pcgP5 (int n, const real *polarity, const real *ka, const real *ksum, real(*uind)[3], const real(*conj)[3], real(*rsd)[3], const real(*vec)[3])
	Updates the induced dipoles and residuals – step 5bc. More...
__global__ void	tinker::pcgP6 (int n, const real *ksum, const real *ksum1, real(*conj)[3], const real(*zrsd)[3])
	Calculates the scalar b from s0 and s, then updates the vector p – 5ef. More...
__global__ void	tinker::pcgPeek (int n, float pcgpeek, const real *polarity, real(*uind)[3], real(*uinp)[3], const real(*rsd)[3], const real(*rsdp)[3])
	Applies the peek step. More...
__global__ void	tinker::pcgPeek1 (int n, float pcgpeek, const real *polarity, real(*uind)[3], const real(*rsd)[3])
	Applies the peek step. More...

Detailed Description

Preconditioned Conjugate Gradient.

The PCG method in Tinker9 is implemented as follows

1. Goal: To solve Au = E, where A = 1/a + T.
   • (a) E: external field;
   • (b) a: polarizability;
   • (c) -Tu: mutual induced field; i.e., ufield(u).
2. Guess initial induced dipole: u.
   • (a) Predict: u = fromPrediction
   • (b) Direct guess: u = aE
   • (c) Zero: u = 0
3. Compute initial residual: r = E - Au
   • (a) Predict: r = (aE-u)/a + ufield(u)
   • (b) Direct guess: r = ufield(aE)
   • (c) Zero: r = E
4. p = Mr; s0 = rMr
   • M is the preconditioner which approximates A.
5. While not converged (r is still big):
   • (a) g = s0 / pAp, where Ap = p/a - ufield(p)
   • (b) u = u + gp
   • (c) r = r - gAp
   • (d) s = rMr
   • (e) b = s / s0
   • (f) p = Mr + bp; s0 = s
6. Peek: u = u + peek*a*r – optional, empirical.

Function Documentation

pcgP1()

__global__ void tinker::pcgP1	(	int	n,
		const real *	polarity_inv,
		real(*)	vec[3],
		real(*)	vecp[3],
		const real(*)	conj[3],
		const real(*)	conjp[3],
		const real(*)	field[3],
		const real(*)	fieldp[3]
	)

Calculates the vector Ap – step 5a.

Parameters

	n	Number of atoms.
	polarity_inv	Multiplicative inverse of polarizabilities.
[out]	vec	d-vector Ap.
[out]	vecp	p-vector Ap.
	conj	d-vector p.
	conjp	p-vector p.
	field	d-ufield(p).
	fieldp	p-ufield(p).

pcgP2()

__global__ void tinker::pcgP2	(	int	n,
		const real *	polarity,
		const real *	ka,
		const real *	kap,
		const real *	ksum,
		const real *	ksump,
		real(*)	uind[3],
		real(*)	uinp[3],
		const real(*)	conj[3],
		const real(*)	conjp[3],
		real(*)	rsd[3],
		real(*)	rsdp[3],
		const real(*)	vec[3],
		const real(*)	vecp[3]
	)

Updates the induced dipoles and residuals – step 5bc.

Parameters

	n	Number of atoms.
	polarity	Polarizabilities.
	ka	Device pointer to the dot product d-pAp.
	kap	Device pointer to the dot product p-pAp.
	ksum	Device pointer to the dot product d-s0.
	ksump	Device pointer to the dot product p-s0.
[in,out]	uind	d-dipoles.
[in,out]	uinp	p-dipoles.
	conj	d-vector p.
	conjp	p-vector p.
[in,out]	rsd	d-residuals.
[in,out]	rsdp	p-residuals.
	vec	d-vector Ap.
	vecp	p-vector Ap.

pcgP3()

__global__ void tinker::pcgP3	(	int	n,
		const real *	ksum,
		const real *	ksump,
		const real *	ksum1,
		const real *	ksump1,
		real(*)	conj[3],
		real(*)	conjp[3],
		const real(*)	zrsd[3],
		const real(*)	zrsdp[3]
	)

Calculates the scalar b from s0 and s, then updates the vector p – 5ef.

Parameters

	n	Number of atoms.
	ksum	Device pointer to the d-scalar s0.
	ksump	Device pointer to the p-scalar s0.
	ksum1	Device pointer to the d-scalar s.
	ksump1	Device pointer to the p-scalar s.
[in,out]	conj	d-vector p.
[in,out]	conjp	p-vector p.
	zrsd	d-vector Mr.
	zrsdp	p-vector Mr.

pcgP4()

__global__ void tinker::pcgP4	(	int	n,
		const real *	polarity_inv,
		real(*)	vec[3],
		const real(*)	conj[3],
		const real(*)	field[3]
	)

Calculates the vector Ap – step 5a.

Parameters

	n	Number of atoms.
	polarity_inv	Multiplicative inverse of polarizabilities.
[out]	vec	Vector Ap.
	conj	Vector p.
	field	ufield(p).

pcgP5()

__global__ void tinker::pcgP5	(	int	n,
		const real *	polarity,
		const real *	ka,
		const real *	ksum,
		real(*)	uind[3],
		const real(*)	conj[3],
		real(*)	rsd[3],
		const real(*)	vec[3]
	)

Updates the induced dipoles and residuals – step 5bc.

Vector Ap.

Parameters

	n	Number of atoms.
	polarity	Polarizabilities.
	ka	Device pointer to the dot product pAp.
	ksum	Device pointer to the dot product s0.
[in,out]	uind	Induced dipoles.
	conj	Vector p.
[in,out]	rsd	Residuals.

pcgP6()

__global__ void tinker::pcgP6	(	int	n,
		const real *	ksum,
		const real *	ksum1,
		real(*)	conj[3],
		const real(*)	zrsd[3]
	)

Calculates the scalar b from s0 and s, then updates the vector p – 5ef.

Parameters

	n	Number of atoms.
	ksum	Deivce pointer to the scalar s0.
	ksum1	Device pointer to the scalar s.
[in,out]	conj	Vector p.
	zrsd	Vector Mr.

pcgPeek()

__global__ void tinker::pcgPeek	(	int	n,
		float	pcgpeek,
		const real *	polarity,
		real(*)	uind[3],
		real(*)	uinp[3],
		const real(*)	rsd[3],
		const real(*)	rsdp[3]
	)

Applies the peek step.

Parameters

	n	Number of atoms.
	pcgpeek	The "peek" parameter.
	polarity	Polarizabilities.
[in,out]	uind	d-dipoles.
[in,out]	uinp	p-dipoles.
	rsd	Final d-residual.
	rsdp	Final p-residual.

pcgPeek1()

__global__ void tinker::pcgPeek1	(	int	n,
		float	pcgpeek,
		const real *	polarity,
		real(*)	uind[3],
		const real(*)	rsd[3]
	)

Applies the peek step.

Parameters

	n	Number of atoms.
	pcgpeek	The "peek" parameter.
	polarity	Polarizabilities.
[in,out]	uind	Dipoles.
	rsd	Final residual.

pcgRsd0()

__global__ void tinker::pcgRsd0	(	int	n,
		const real *	polarity,
		real(*)	rsd[3],
		real(*)	rsdp[3]
	)

Sets the residual to zero for atoms with zero polarizability.

Parameters

	n	Number of atoms.
	polarity	polarizabilities.
[out]	rsd	Zero d-residuals.
[out]	rsdp	Zero p-residuals.

pcgRsd0V1()

__global__ void tinker::pcgRsd0V1	(	int	n,
		const real *	polarity_inv,
		real(*)	rsd[3],
		const real(*)	udir[3],
		const real(*)	uind[3],
		const real(*)	field[3]
	)

Calculates the initial residuals for the predictor 3a.

Parameters

	n	Number of atoms.
	polarity_inv	Multiplicative inverse of polarizabilities.
[out]	rsd	Initial residuals.
	udir	Direct induced dipoles 2b.
	uind	Initial induced dipoles 2a.
	field	Mutual field.

pcgRsd0V2()

__global__ void tinker::pcgRsd0V2	(	int	n,
		const real *	polarity_inv,
		real(*)	rsd[3],
		real(*)	rsp[3],
		const real(*)	udir[3],
		const real(*)	udip[3],
		const real(*)	uind[3],
		const real(*)	uinp[3],
		const real(*)	field[3],
		const real(*)	fielp[3]
	)

Calculates the initial residuals for the predictor 3a.

Parameters

	n	Number of atoms.
	polarity_inv	Multiplicative inverse of polarizabilities.
[out]	rsd	Initial d-residuals.
[out]	rsp	Initial p-residuals.
	udir	Direct induced d-dipoles 2b.
	udip	Direct induced p-dipoles 2b.
	uind	Initial induced d-dipoles 2a.
	uinp	Initial induced p-dipoles 2a.
	field	Mutual d-field.
	fielp	Mutual p-field.

pcgRsd0V3()

__global__ void tinker::pcgRsd0V3	(	int	n,
		const real *	polarity_inv,
		real(*)	rsd[3],
		const real(*)	udir[3],
		const real(*)	uind[3],
		const real(*)	field[3],
		const real(*)	polscale[3][3]
	)

Calculates the initial residuals for the predictor 3a using the Exchange-Polarization Model.

Parameters

	n	Number of atoms.
	polarity_inv	Multiplicative inverse of polarizabilities.
[out]	rsd	Initial residuals.
	udir	Direct induced dipoles 2b.
	uind	Initial induced dipoles 2a.
	field	Mutual field.
	polscale	The \( I+kS^2 \) matrices for every atom (Eq. (7d)).

pcgRsd1()

__global__ void tinker::pcgRsd1	(	int	n,
		const real *	polarity,
		real(*)	rsd[3]
	)

Sets the residual to zero for atoms with zero polarizability.

Parameters

	n	Number of atoms.
	polarity	polarizabilities.
[out]	rsd	Zero residuals.

pcgUdirV1()

__global__ void tinker::pcgUdirV1	(	int	n,
		const real *	polarity,
		real(*)	udir[3],
		const real(*)	field[3]
	)

Calculates the direct induced dipoles 2b.

Parameters

	n	Number of atoms.
	polarity	Polarizabilities.
[out]	udir	Direct induced dipoles 2b.
	field	External field.

pcgUdirV2()

__global__ void tinker::pcgUdirV2	(	int	n,
		const real *	polarity,
		real(*)	udir[3],
		real(*)	udirp[3],
		const real(*)	field[3],
		const real(*)	fieldp[3]
	)

Calculates the direct induced dipoles 2b.

Parameters

	n	Number of atoms.
	polarity	Polarizabilities.
[out]	udir	Direct induced d-dipoles 2b.
[out]	udirp	Direct induced p-dipoles 2b.
	field	External d-field.
	fieldp	External p-field.