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//******************************************************************************
//
// File: SpinSignal.java
// Package: edu.rit.mri
// Unit: Class edu.rit.mri.SpinSignal
//
// This Java source file is copyright (C) 2008 by Alan Kaminsky. All rights
// reserved. For further information, contact the author, Alan Kaminsky, at
// ark@cs.rit.edu.
//
// This Java source file is part of the Parallel Java Library ("PJ"). PJ is free
// software; you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// PJ 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 General Public License for more details.
//
// Linking this library statically or dynamically with other modules is making a
// combined work based on this library. Thus, the terms and conditions of the
// GNU General Public License cover the whole combination.
//
// As a special exception, the copyright holders of this library give you
// permission to link this library with independent modules to produce an
// executable, regardless of the license terms of these independent modules, and
// to copy and distribute the resulting executable under terms of your choice,
// provided that you also meet, for each linked independent module, the terms
// and conditions of the license of that module. An independent module is a
// module which is not derived from or based on this library. If you modify this
// library, you may extend this exception to your version of the library, but
// you are not obligated to do so. If you do not wish to do so, delete this
// exception statement from your version.
//
// A copy of the GNU General Public License is provided in the file gpl.txt. You
// may also obtain a copy of the GNU General Public License on the World Wide
// Web at http://www.gnu.org/licenses/gpl.html.
//
//******************************************************************************
package edu.rit.mri;
/**
* Class SpinSignal provides static methods for computing the spin signal model
* function.
*
* @author Alan Kaminsky
* @version 11-Jun-2008
*/
public class SpinSignal
{
// Prevent construction.
private SpinSignal()
{
}
// Exported operations.
/**
* Compute the spin signal for the given spin relaxation rate and time. A
* spin density of <I>ρ</I> = 1 is used. The formula is
* <CENTER>
* <I>S</I>(<I>t</I>) = <I>ρ</I> [1 − 2 exp(−<I>R</I> <I>t</I>)]
* </CENTER>
*
* @param R Spin relaxation rate, <I>R</I>.
* @param t Time, <I>t</I>.
*
* @return Spin signal, <I>S</I>(<I>t</I>).
*/
public static double S
(double R,
double t)
{
return 1.0 - 2.0*Math.exp(-R*t);
}
/**
* Compute the spin signal for the given spin density, spin relaxation rate,
* and time. The formula is
* <CENTER>
* <I>S</I>(<I>t</I>) = <I>ρ</I> [1 − 2 exp(−<I>R</I> <I>t</I>)]
* </CENTER>
*
* @param rho Spin density, <I>ρ</I>.
* @param R Spin relaxation rate, <I>R</I>.
* @param t Time, <I>t</I>.
*
* @return Spin signal, <I>S</I>(<I>t</I>).
*/
public static double S
(double rho,
double R,
double t)
{
return rho*(1.0 - 2.0*Math.exp(-R*t));
}
/**
* Compute the partial derivative of the spin signal with respect to spin
* density for the given spin relaxation rate and time. The formula is
* <CENTER>
* ∂<I>S</I>(<I>t</I>) ⁄ ∂<I>ρ</I> = 1 − 2 exp(−<I>R</I> <I>t</I>)
* </CENTER>
*
* @param R Spin relaxation rate, <I>R</I>.
* @param t Time, <I>t</I>.
*
* @return Partial derivative, ∂<I>S</I>(<I>t</I>) ⁄ ∂<I>ρ</I>.
*/
public static double dSdrho
(double R,
double t)
{
return 1.0 - 2.0*Math.exp(-R*t);
}
/**
* Compute the partial derivative of the spin signal with respect to spin
* relaxation rate for the given spin density, spin relaxation rate, and
* time. The formula is
* <CENTER>
* ∂<I>S</I>(<I>t</I>) ⁄ ∂<I>R</I> = 2 <I>ρ</I> <I>t</I> exp(−<I>R</I> <I>t</I>)
* </CENTER>
*
* @param rho Spin density, <I>ρ</I>.
* @param R Spin relaxation rate, <I>R</I>.
* @param t Time, <I>t</I>.
*
* @return Partial derivative, ∂<I>S</I>(<I>t</I>) ⁄ ∂<I>R</I>.
*/
public static double dSdR
(double rho,
double R,
double t)
{
return 2.0*rho*t*Math.exp(-R*t);
}
}
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