#pragma once

#include <petsc/private/tsimpl.h>

typedef enum {
  TSGLLEERROR_FORWARD,
  TSGLLEERROR_BACKWARD
} TSGLLEErrorDirection;

typedef struct _TSGLLEScheme *TSGLLEScheme;
struct _TSGLLEScheme {
  PetscInt     p;             /* order of the method */
  PetscInt     q;             /* stage-order of the method */
  PetscInt     r;             /* number of items carried between stages */
  PetscInt     s;             /* number of stages */
  PetscScalar *c;             /* location of the stages */
  PetscScalar *a, *b, *u, *v; /* tableau for the method */

  /* For use in rescale & modify */
  PetscScalar *alpha; /* X_n(t_n) - X_{n-1}(t_n) = - alpha^T h^{p+1} x^{(p+1)}(t_n)        */
  PetscScalar *beta;  /*                 - beta^T h^{p+2} x^{(p+2)}(t_n)                   */
  PetscScalar *gamma; /*                 - gamma^T h^{p+2} f' x^{(p+1)}(t_n)  + O(h^{p+3}) */

  /* Error estimates */
  /* h^{p+1}x^{(p+1)}(t_n)     ~= phi[0]*h*Ydot + psi[0]*X[1:] */
  /* h^{p+2}x^{(p+2)}(t_n)     ~= phi[1]*h*Ydot + psi[1]*X[1:] */
  /* h^{p+2}f' x^{(p+1)}(t_n)  ~= phi[2]*h*Ydot + psi[2]*X[1:] */
  PetscScalar *phi; /* dim=[3][s] for estimating higher moments, see B,J,W 2007 */
  PetscScalar *psi; /* dim=[3][r-1], [0 psi^T] of B,J,W 2007 */
  PetscScalar *stage_error;

  /* Desirable properties which enable extra optimizations */
  PetscBool stiffly_accurate; /* Last row of [A U] is equal t first row of [B V]? */
  PetscBool fsal;             /* First Same As Last: X[1] = h*Ydot[s-1] (and stiffly accurate) */
};

typedef struct TS_GLLE {
  TSGLLEAcceptFunction Accept; /* Decides whether to accept a given time step, given estimates of local truncation error */
  TSGLLEAdapt          adapt;

  /* These names are only stored so that they can be printed in TSView_GLLE() without making these schemes full-blown
   objects (the implementations I'm thinking of do not have state and I'm lazy). */
  char accept_name[256];

  /* specific to the family of GL method */
  PetscErrorCode (*EstimateHigherMoments)(TSGLLEScheme, PetscReal, Vec *, Vec *, Vec *); /* Provide local error estimates */
  PetscErrorCode (*CompleteStep)(TSGLLEScheme, PetscReal, TSGLLEScheme, PetscReal, Vec *, Vec *, Vec *);
  PetscErrorCode (*Destroy)(struct TS_GLLE *);
  PetscErrorCode (*View)(struct TS_GLLE *, PetscViewer);
  char          type_name[256];
  PetscInt      nschemes;
  TSGLLEScheme *schemes;

  Vec      *X;     /* Items to carry between steps */
  Vec      *Xold;  /* Values of these items at the last step */
  Vec       W;     /* = 1/(atol+rtol*|X0|), used for WRMS norm */
  Vec      *himom; /* len=3, Estimates of h^{p+1}x^{(p+1)}, h^{p+2}x^{(p+2)}, h^{p+2}(df/dx) x^{(p+1)} */
  PetscReal wrms_atol, wrms_rtol;

  /* Stages (Y,Ydot) are computed sequentially */
  Vec      *Ydot;       /* Derivatives of stage vectors, must be stored */
  Vec       Y;          /* Stage vector, only used while solving the stage so we don't need to store it */
  Vec       Z;          /* Affine vector */
  PetscReal scoeff;     /* Ydot = Z + shift*Y; shift = scoeff/ts->time_step */
  PetscReal stage_time; /* time at current stage */
  PetscInt  stage;      /* index of the stage we are currently solving for */

  /* Runtime options */
  PetscInt             current_scheme;
  PetscInt             max_order, min_order, start_order;
  PetscBool            extrapolate;     /* use extrapolation to produce initial Newton iterate? */
  TSGLLEErrorDirection error_direction; /* TSGLLEERROR_FORWARD or TSGLLEERROR_BACKWARD */

  PetscInt max_step_rejections;

  PetscBool setupcalled;
  void     *data;
} TS_GLLE;
