/*
     Provides the interface functions for vector operations that have PetscScalar/PetscReal in the signature
   These are the vector functions the user calls.
*/
#include <petsc/private/vecimpl.h> /*I  "petscvec.h"   I*/

PetscInt VecGetSubVectorSavedStateId = -1;

#if PetscDefined(USE_DEBUG)
// this is a no-op '0' macro in optimized builds
PetscErrorCode VecValidValues_Internal(Vec vec, PetscInt argnum, PetscBool begin)
{
  PetscFunctionBegin;
  if (vec->petscnative || vec->ops->getarray) {
    PetscInt           n;
    const PetscScalar *x;
    PetscOffloadMask   mask;

    PetscCall(VecGetOffloadMask(vec, &mask));
    if (!PetscOffloadHost(mask)) PetscFunctionReturn(PETSC_SUCCESS);
    PetscCall(VecGetLocalSize(vec, &n));
    PetscCall(VecGetArrayRead(vec, &x));
    for (PetscInt i = 0; i < n; i++) {
      if (begin) {
        PetscCheck(!PetscIsInfOrNanScalar(x[i]), PETSC_COMM_SELF, PETSC_ERR_FP, "Vec entry at local location %" PetscInt_FMT " is not-a-number or infinite at beginning of function: Parameter number %" PetscInt_FMT, i, argnum);
      } else {
        PetscCheck(!PetscIsInfOrNanScalar(x[i]), PETSC_COMM_SELF, PETSC_ERR_FP, "Vec entry at local location %" PetscInt_FMT " is not-a-number or infinite at end of function: Parameter number %" PetscInt_FMT, i, argnum);
      }
    }
    PetscCall(VecRestoreArrayRead(vec, &x));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

/*@
  VecMaxPointwiseDivide - Computes the maximum of the componentwise division `max = max_i abs(x[i]/y[i])`.

  Logically Collective

  Input Parameters:
+ x - the numerators
- y - the denominators

  Output Parameter:
. max - the result

  Level: advanced

  Notes:
  `x` and `y` may be the same vector

  if a particular `y[i]` is zero, it is treated as 1 in the above formula

.seealso: [](ch_vectors), `Vec`, `VecPointwiseDivide()`, `VecPointwiseMult()`, `VecPointwiseMax()`, `VecPointwiseMin()`, `VecPointwiseMaxAbs()`
@*/
PetscErrorCode VecMaxPointwiseDivide(Vec x, Vec y, PetscReal *max)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 2);
  PetscAssertPointer(max, 3);
  PetscValidType(x, 1);
  PetscValidType(y, 2);
  PetscCheckSameTypeAndComm(x, 1, y, 2);
  VecCheckSameSize(x, 1, y, 2);
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  PetscCall(VecLockReadPush(x));
  PetscCall(VecLockReadPush(y));
  PetscUseTypeMethod(x, maxpointwisedivide, y, max);
  PetscCall(VecLockReadPop(x));
  PetscCall(VecLockReadPop(y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecDot - Computes the vector dot product.

  Collective

  Input Parameters:
+ x - first vector
- y - second vector

  Output Parameter:
. val - the dot product

  Level: intermediate

  Note:
  For complex vectors, `VecDot()` computes
.vb
  val = (x,y) = y^H x,
.ve
  where $y^H$ denotes the conjugate transpose of `y`. Note that this corresponds to the usual "mathematicians" complex
  inner product where the SECOND argument gets the complex conjugate. Since the `BLASdot()` complex conjugates the first
  first argument we call the `BLASdot()` with the arguments reversed.

  Use `VecTDot()` for the indefinite form
.vb
  val = (x,y) = y^T x,
.ve
  where $y^T$ denotes the transpose of `y`.

.seealso: [](ch_vectors), `Vec`, `VecMDot()`, `VecTDot()`, `VecNorm()`, `VecDotBegin()`, `VecDotEnd()`, `VecDotRealPart()`
@*/
PetscErrorCode VecDot(Vec x, Vec y, PetscScalar *val)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 2);
  PetscAssertPointer(val, 3);
  PetscValidType(x, 1);
  PetscValidType(y, 2);
  PetscCheckSameTypeAndComm(x, 1, y, 2);
  VecCheckSameSize(x, 1, y, 2);
  VecCheckAssembled(x);
  VecCheckAssembled(y);

  PetscCall(VecLockReadPush(x));
  PetscCall(VecLockReadPush(y));
  PetscCall(PetscLogEventBegin(VEC_Dot, x, y, 0, 0));
  PetscUseTypeMethod(x, dot, y, val);
  PetscCall(PetscLogEventEnd(VEC_Dot, x, y, 0, 0));
  PetscCall(VecLockReadPop(x));
  PetscCall(VecLockReadPop(y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecDotRealPart - Computes the real part of the vector dot product.

  Collective

  Input Parameters:
+ x - first vector
- y - second vector

  Output Parameter:
. val - the real part of the dot product;

  Level: intermediate

  Notes for Users of Complex Numbers:
  See `VecDot()` for more details on the definition of the dot product for complex numbers

  For real numbers this returns the same value as `VecDot()`

  For complex numbers in C^n (that is a vector of n components with a complex number for each component) this is equal to the usual real dot product on the
  the space R^{2n} (that is a vector of 2n components with the real or imaginary part of the complex numbers for components)

  Developer Notes:
  This is not currently optimized to compute only the real part of the dot product.

.seealso: [](ch_vectors), `Vec`, `VecMDot()`, `VecTDot()`, `VecNorm()`, `VecDotBegin()`, `VecDotEnd()`, `VecDot()`, `VecDotNorm2()`
@*/
PetscErrorCode VecDotRealPart(Vec x, Vec y, PetscReal *val)
{
  PetscScalar fdot;

  PetscFunctionBegin;
  PetscCall(VecDot(x, y, &fdot));
  *val = PetscRealPart(fdot);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecNorm  - Computes the vector norm.

  Collective

  Input Parameters:
+ x    - the vector
- type - the type of the norm requested

  Output Parameter:
. val - the norm

  Level: intermediate

  Notes:
  See `NormType` for descriptions of each norm.

  For complex numbers `NORM_1` will return the traditional 1 norm of the 2 norm of the complex
  numbers; that is the 1 norm of the absolute values of the complex entries. In PETSc 3.6 and
  earlier releases it returned the 1 norm of the 1 norm of the complex entries (what is
  returned by the BLAS routine `asum()`). Both are valid norms but most people expect the former.

  This routine stashes the computed norm value, repeated calls before the vector entries are
  changed are then rapid since the precomputed value is immediately available. Certain vector
  operations such as `VecSet()` store the norms so the value is immediately available and does
  not need to be explicitly computed. `VecScale()` updates any stashed norm values, thus calls
  after `VecScale()` do not need to explicitly recompute the norm.

.seealso: [](ch_vectors), `Vec`, `NormType`, `VecDot()`, `VecTDot()`, `VecDotBegin()`, `VecDotEnd()`, `VecNormAvailable()`,
          `VecNormBegin()`, `VecNormEnd()`, `NormType()`
@*/
PetscErrorCode VecNorm(Vec x, NormType type, PetscReal *val)
{
  PetscBool flg = PETSC_TRUE;

  PetscFunctionBegin;
  PetscCall(VecLockReadPush(x));
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  PetscValidLogicalCollectiveEnum(x, type, 2);
  PetscAssertPointer(val, 3);

  PetscCall(VecNormAvailable(x, type, &flg, val));
  // check that all MPI processes call this routine together and have same availability
  if (PetscDefined(USE_DEBUG)) {
    PetscMPIInt b0 = (PetscMPIInt)flg, b1[2], b2[2];
    b1[0]          = -b0;
    b1[1]          = b0;
    PetscCallMPI(MPIU_Allreduce(b1, b2, 2, MPI_INT, MPI_MAX, PetscObjectComm((PetscObject)x)));
    PetscCheck(-b2[0] == b2[1], PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "Some MPI processes have cached %s norm, others do not. This may happen when some MPI processes call VecGetArray() and some others do not.", NormTypes[type]);
    if (flg) {
      PetscReal b1[2], b2[2];
      b1[0] = -(*val);
      b1[1] = *val;
      PetscCallMPI(MPIU_Allreduce(b1, b2, 2, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)x)));
      PetscCheck((PetscIsNanReal(b2[0]) && PetscIsNanReal(b2[1])) || (-b2[0] == b2[1]), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Difference in cached %s norms: local %g", NormTypes[type], (double)*val);
    }
  }
  if (!flg) {
    PetscCall(PetscLogEventBegin(VEC_Norm, x, 0, 0, 0));
    PetscUseTypeMethod(x, norm, type, val);
    PetscCall(PetscLogEventEnd(VEC_Norm, x, 0, 0, 0));

    if (type != NORM_1_AND_2) PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[type], *val));
  }
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecNormAvailable  - Returns the vector norm if it is already known. That is, it has been previously computed and cached in the vector

  Not Collective

  Input Parameters:
+ x    - the vector
- type - one of `NORM_1` (sum_i |x[i]|), `NORM_2` sqrt(sum_i (x[i])^2), `NORM_INFINITY` max_i |x[i]|.  Also available
          `NORM_1_AND_2`, which computes both norms and stores them
          in a two element array.

  Output Parameters:
+ available - `PETSC_TRUE` if the val returned is valid
- val       - the norm

  Level: intermediate

.seealso: [](ch_vectors), `Vec`, `VecDot()`, `VecTDot()`, `VecNorm()`, `VecDotBegin()`, `VecDotEnd()`,
          `VecNormBegin()`, `VecNormEnd()`
@*/
PetscErrorCode VecNormAvailable(Vec x, NormType type, PetscBool *available, PetscReal *val)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscAssertPointer(available, 3);
  PetscAssertPointer(val, 4);

  if (type == NORM_1_AND_2) {
    *available = PETSC_FALSE;
  } else {
    PetscCall(PetscObjectComposedDataGetReal((PetscObject)x, NormIds[type], *val, *available));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecNormalize - Normalizes a vector by its 2-norm.

  Collective

  Input Parameter:
. x - the vector

  Output Parameter:
. val - the vector norm before normalization. May be `NULL` if the value is not needed.

  Level: intermediate

.seealso: [](ch_vectors), `Vec`, `VecNorm()`, `NORM_2`, `NormType`
@*/
PetscErrorCode VecNormalize(Vec x, PetscReal *val)
{
  PetscReal norm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecSetErrorIfLocked(x, 1));
  if (val) PetscAssertPointer(val, 2);
  PetscCall(PetscLogEventBegin(VEC_Normalize, x, 0, 0, 0));
  PetscCall(VecNorm(x, NORM_2, &norm));
  if (norm == 0.0) PetscCall(PetscInfo(x, "Vector of zero norm can not be normalized; Returning only the zero norm\n"));
  else if (PetscIsInfOrNanReal(norm)) PetscCall(PetscInfo(x, "Vector with infinity or NaN norm can not be normalized; Returning only the norm\n"));
  else {
    PetscScalar s = 1.0 / norm;
    PetscCall(VecScale(x, s));
  }
  PetscCall(PetscLogEventEnd(VEC_Normalize, x, 0, 0, 0));
  if (val) *val = norm;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMax - Determines the vector component with maximum real part and its location.

  Collective

  Input Parameter:
. x - the vector

  Output Parameters:
+ p   - the index of `val` (pass `NULL` if you don't want this) in the vector
- val - the maximum component

  Level: intermediate

  Notes:
  Returns the value `PETSC_MIN_REAL` and negative `p` if the vector is of length 0.

  Returns the smallest index with the maximum value

  Developer Note:
  The Nag Fortran compiler does not like the symbol name VecMax

.seealso: [](ch_vectors), `Vec`, `VecNorm()`, `VecMin()`
@*/
PetscErrorCode VecMax(Vec x, PetscInt *p, PetscReal *val)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  if (p) PetscAssertPointer(p, 2);
  PetscAssertPointer(val, 3);
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(VEC_Max, x, 0, 0, 0));
  PetscUseTypeMethod(x, max, p, val);
  PetscCall(PetscLogEventEnd(VEC_Max, x, 0, 0, 0));
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMin - Determines the vector component with minimum real part and its location.

  Collective

  Input Parameter:
. x - the vector

  Output Parameters:
+ p   - the index of `val` (pass `NULL` if you don't want this location) in the vector
- val - the minimum component

  Level: intermediate

  Notes:
  Returns the value `PETSC_MAX_REAL` and negative `p` if the vector is of length 0.

  This returns the smallest index with the minimum value

  Developer Note:
  The Nag Fortran compiler does not like the symbol name VecMin

.seealso: [](ch_vectors), `Vec`, `VecMax()`
@*/
PetscErrorCode VecMin(Vec x, PetscInt *p, PetscReal *val)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  if (p) PetscAssertPointer(p, 2);
  PetscAssertPointer(val, 3);
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(VEC_Min, x, 0, 0, 0));
  PetscUseTypeMethod(x, min, p, val);
  PetscCall(PetscLogEventEnd(VEC_Min, x, 0, 0, 0));
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecTDot - Computes an indefinite vector dot product. That is, this
  routine does NOT use the complex conjugate.

  Collective

  Input Parameters:
+ x - first vector
- y - second vector

  Output Parameter:
. val - the dot product

  Level: intermediate

  Notes for Users of Complex Numbers:
  For complex vectors, `VecTDot()` computes the indefinite form
.vb
  val = (x,y) = y^T x,
.ve
  where y^T denotes the transpose of y.

  Use `VecDot()` for the inner product
.vb
  val = (x,y) = y^H x,
.ve
  where y^H denotes the conjugate transpose of y.

.seealso: [](ch_vectors), `Vec`, `VecDot()`, `VecMTDot()`
@*/
PetscErrorCode VecTDot(Vec x, Vec y, PetscScalar *val)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 2);
  PetscAssertPointer(val, 3);
  PetscValidType(x, 1);
  PetscValidType(y, 2);
  PetscCheckSameTypeAndComm(x, 1, y, 2);
  VecCheckSameSize(x, 1, y, 2);
  VecCheckAssembled(x);
  VecCheckAssembled(y);

  PetscCall(VecLockReadPush(x));
  PetscCall(VecLockReadPush(y));
  PetscCall(PetscLogEventBegin(VEC_TDot, x, y, 0, 0));
  PetscUseTypeMethod(x, tdot, y, val);
  PetscCall(PetscLogEventEnd(VEC_TDot, x, y, 0, 0));
  PetscCall(VecLockReadPop(x));
  PetscCall(VecLockReadPop(y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecScaleAsync_Private(Vec x, PetscScalar alpha, PetscDeviceContext dctx)
{
  PetscReal   norms[4];
  PetscBool   flgs[4];
  PetscScalar one = 1.0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  PetscCall(VecSetErrorIfLocked(x, 1));
  PetscValidLogicalCollectiveScalar(x, alpha, 2);
  if (alpha == one) PetscFunctionReturn(PETSC_SUCCESS);

  /* get current stashed norms */
  for (PetscInt i = 0; i < 4; i++) PetscCall(PetscObjectComposedDataGetReal((PetscObject)x, NormIds[i], norms[i], flgs[i]));

  PetscCall(PetscLogEventBegin(VEC_Scale, x, 0, 0, 0));
  VecMethodDispatch(x, dctx, VecAsyncFnName(Scale), scale, (Vec, PetscScalar, PetscDeviceContext), alpha);
  PetscCall(PetscLogEventEnd(VEC_Scale, x, 0, 0, 0));

  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  /* put the scaled stashed norms back into the Vec */
  for (PetscInt i = 0; i < 4; i++) {
    PetscReal ar = PetscAbsScalar(alpha);
    if (flgs[i]) PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[i], ar * norms[i]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecScale - Scales a vector.

  Logically Collective

  Input Parameters:
+ x     - the vector
- alpha - the scalar

  Level: intermediate

  Note:
  For a vector with n components, `VecScale()` computes  x[i] = alpha * x[i], for i=1,...,n.

.seealso: [](ch_vectors), `Vec`, `VecSet()`
@*/
PetscErrorCode VecScale(Vec x, PetscScalar alpha)
{
  PetscFunctionBegin;
  PetscCall(VecScaleAsync_Private(x, alpha, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecSetAsync_Private(Vec x, PetscScalar alpha, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  PetscValidLogicalCollectiveScalar(x, alpha, 2);
  PetscCall(VecSetErrorIfLocked(x, 1));

  if (alpha == 0) {
    PetscReal norm;
    PetscBool set;

    PetscCall(VecNormAvailable(x, NORM_2, &set, &norm));
    if (set == PETSC_TRUE && norm == 0) PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscLogEventBegin(VEC_Set, x, 0, 0, 0));
  VecMethodDispatch(x, dctx, VecAsyncFnName(Set), set, (Vec, PetscScalar, PetscDeviceContext), alpha);
  PetscCall(PetscLogEventEnd(VEC_Set, x, 0, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)x));

  /*  norms can be simply set (if |alpha|*N not too large) */
  {
    PetscReal      val = PetscAbsScalar(alpha);
    const PetscInt N   = x->map->N;

    if (N == 0) {
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_1], 0.0));
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_INFINITY], 0.0));
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_2], 0.0));
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_FROBENIUS], 0.0));
    } else if (val > PETSC_MAX_REAL / N) {
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_INFINITY], val));
    } else {
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_1], N * val));
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_INFINITY], val));
      val *= PetscSqrtReal((PetscReal)N);
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_2], val));
      PetscCall(PetscObjectComposedDataSetReal((PetscObject)x, NormIds[NORM_FROBENIUS], val));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecSet - Sets all components of a vector to a single scalar value.

  Logically Collective

  Input Parameters:
+ x     - the vector
- alpha - the scalar

  Level: beginner

  Notes:
  For a vector of dimension n, `VecSet()` sets x[i] = alpha, for i=1,...,n,
  so that all vector entries then equal the identical
  scalar value, `alpha`.  Use the more general routine
  `VecSetValues()` to set different vector entries.

  You CANNOT call this after you have called `VecSetValues()` but before you call
  `VecAssemblyBegin()`

  If `alpha` is zero and the norm of the vector is known to be zero then this skips the unneeded zeroing process

.seealso: [](ch_vectors), `Vec`, `VecSetValues()`, `VecSetValuesBlocked()`, `VecSetRandom()`
@*/
PetscErrorCode VecSet(Vec x, PetscScalar alpha)
{
  PetscFunctionBegin;
  PetscCall(VecSetAsync_Private(x, alpha, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecAXPYAsync_Private(Vec y, PetscScalar alpha, Vec x, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 1);
  PetscValidType(x, 3);
  PetscValidType(y, 1);
  PetscCheckSameTypeAndComm(x, 3, y, 1);
  VecCheckSameSize(x, 3, y, 1);
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveScalar(y, alpha, 2);
  if (alpha == (PetscScalar)0.0) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(VecSetErrorIfLocked(y, 1));
  if (x == y) {
    PetscCall(VecScale(y, alpha + 1.0));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(VEC_AXPY, x, y, 0, 0));
  VecMethodDispatch(y, dctx, VecAsyncFnName(AXPY), axpy, (Vec, PetscScalar, Vec, PetscDeviceContext), alpha, x);
  PetscCall(PetscLogEventEnd(VEC_AXPY, x, y, 0, 0));
  PetscCall(VecLockReadPop(x));
  PetscCall(PetscObjectStateIncrease((PetscObject)y));
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*@
  VecAXPY - Computes `y = alpha x + y`.

  Logically Collective

  Input Parameters:
+ alpha - the scalar
. x     - vector scale by `alpha`
- y     - vector accumulated into

  Output Parameter:
. y - output vector

  Level: intermediate

  Notes:
  This routine is optimized for alpha of 0.0, otherwise it calls the BLAS routine
.vb
    VecAXPY(y,alpha,x)                   y = alpha x           +      y
    VecAYPX(y,beta,x)                    y =       x           + beta y
    VecAXPBY(y,alpha,beta,x)             y = alpha x           + beta y
    VecWAXPY(w,alpha,x,y)                w = alpha x           +      y
    VecAXPBYPCZ(z,alpha,beta,gamma,x,y)  z = alpha x           + beta y + gamma z
    VecMAXPY(y,nv,alpha[],x[])           y = sum alpha[i] x[i] +      y
.ve

.seealso: [](ch_vectors), `Vec`, `VecAYPX()`, `VecMAXPY()`, `VecWAXPY()`, `VecAXPBYPCZ()`, `VecAXPBY()`
@*/
PetscErrorCode VecAXPY(Vec y, PetscScalar alpha, Vec x)
{
  PetscFunctionBegin;
  PetscCall(VecAXPYAsync_Private(y, alpha, x, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecAYPXAsync_Private(Vec y, PetscScalar beta, Vec x, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 1);
  PetscValidType(x, 3);
  PetscValidType(y, 1);
  PetscCheckSameTypeAndComm(x, 3, y, 1);
  VecCheckSameSize(x, 1, y, 3);
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveScalar(y, beta, 2);
  PetscCall(VecSetErrorIfLocked(y, 1));
  if (x == y) {
    PetscCall(VecScale(y, beta + 1.0));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(VecLockReadPush(x));
  if (beta == (PetscScalar)0.0) {
    PetscCall(VecCopy(x, y));
  } else {
    PetscCall(PetscLogEventBegin(VEC_AYPX, x, y, 0, 0));
    VecMethodDispatch(y, dctx, VecAsyncFnName(AYPX), aypx, (Vec, PetscScalar, Vec, PetscDeviceContext), beta, x);
    PetscCall(PetscLogEventEnd(VEC_AYPX, x, y, 0, 0));
    PetscCall(PetscObjectStateIncrease((PetscObject)y));
  }
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecAYPX - Computes `y = x + beta y`.

  Logically Collective

  Input Parameters:
+ beta - the scalar
. x    - the unscaled vector
- y    - the vector to be scaled

  Output Parameter:
. y - output vector

  Level: intermediate

  Developer Notes:
  The implementation is optimized for `beta` of -1.0, 0.0, and 1.0

.seealso: [](ch_vectors), `Vec`, `VecMAXPY()`, `VecWAXPY()`, `VecAXPY()`, `VecAXPBYPCZ()`, `VecAXPBY()`
@*/
PetscErrorCode VecAYPX(Vec y, PetscScalar beta, Vec x)
{
  PetscFunctionBegin;
  PetscCall(VecAYPXAsync_Private(y, beta, x, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecAXPBYAsync_Private(Vec y, PetscScalar alpha, PetscScalar beta, Vec x, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 4);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 1);
  PetscValidType(x, 4);
  PetscValidType(y, 1);
  PetscCheckSameTypeAndComm(x, 4, y, 1);
  VecCheckSameSize(y, 1, x, 4);
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveScalar(y, alpha, 2);
  PetscValidLogicalCollectiveScalar(y, beta, 3);
  if (alpha == (PetscScalar)0.0 && beta == (PetscScalar)1.0) PetscFunctionReturn(PETSC_SUCCESS);
  if (x == y) {
    PetscCall(VecScale(y, alpha + beta));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(VecSetErrorIfLocked(y, 1));
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(VEC_AXPY, y, x, 0, 0));
  VecMethodDispatch(y, dctx, VecAsyncFnName(AXPBY), axpby, (Vec, PetscScalar, PetscScalar, Vec, PetscDeviceContext), alpha, beta, x);
  PetscCall(PetscLogEventEnd(VEC_AXPY, y, x, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)y));
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecAXPBY - Computes `y = alpha x + beta y`.

  Logically Collective

  Input Parameters:
+ alpha - first scalar
. beta  - second scalar
. x     - the first scaled vector
- y     - the second scaled vector

  Output Parameter:
. y - output vector

  Level: intermediate

  Developer Notes:
  The implementation is optimized for `alpha` and/or `beta` values of 0.0 and 1.0

.seealso: [](ch_vectors), `Vec`, `VecAYPX()`, `VecMAXPY()`, `VecWAXPY()`, `VecAXPY()`, `VecAXPBYPCZ()`
@*/
PetscErrorCode VecAXPBY(Vec y, PetscScalar alpha, PetscScalar beta, Vec x)
{
  PetscFunctionBegin;
  PetscCall(VecAXPBYAsync_Private(y, alpha, beta, x, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecAXPBYPCZAsync_Private(Vec z, PetscScalar alpha, PetscScalar beta, PetscScalar gamma, Vec x, Vec y, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(z, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 5);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 6);
  PetscValidType(z, 1);
  PetscValidType(x, 5);
  PetscValidType(y, 6);
  PetscCheckSameTypeAndComm(x, 5, y, 6);
  PetscCheckSameTypeAndComm(x, 5, z, 1);
  VecCheckSameSize(x, 5, y, 6);
  VecCheckSameSize(x, 5, z, 1);
  PetscCheck(x != y && x != z, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_IDN, "x, y, and z must be different vectors");
  PetscCheck(y != z, PetscObjectComm((PetscObject)y), PETSC_ERR_ARG_IDN, "x, y, and z must be different vectors");
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  VecCheckAssembled(z);
  PetscValidLogicalCollectiveScalar(z, alpha, 2);
  PetscValidLogicalCollectiveScalar(z, beta, 3);
  PetscValidLogicalCollectiveScalar(z, gamma, 4);
  if (alpha == (PetscScalar)0.0 && beta == (PetscScalar)0.0 && gamma == (PetscScalar)1.0) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(VecSetErrorIfLocked(z, 1));
  PetscCall(VecLockReadPush(x));
  PetscCall(VecLockReadPush(y));
  PetscCall(PetscLogEventBegin(VEC_AXPBYPCZ, x, y, z, 0));
  VecMethodDispatch(z, dctx, VecAsyncFnName(AXPBYPCZ), axpbypcz, (Vec, PetscScalar, PetscScalar, PetscScalar, Vec, Vec, PetscDeviceContext), alpha, beta, gamma, x, y);
  PetscCall(PetscLogEventEnd(VEC_AXPBYPCZ, x, y, z, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)z));
  PetscCall(VecLockReadPop(x));
  PetscCall(VecLockReadPop(y));
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*@
  VecAXPBYPCZ - Computes `z = alpha x + beta y + gamma z`

  Logically Collective

  Input Parameters:
+ alpha - first scalar
. beta  - second scalar
. gamma - third scalar
. x     - first vector
. y     - second vector
- z     - third vector

  Output Parameter:
. z - output vector

  Level: intermediate

  Note:
  `x`, `y` and `z` must be different vectors

  Developer Notes:
  The implementation is optimized for `alpha` of 1.0 and `gamma` of 1.0 or 0.0

.seealso: [](ch_vectors), `Vec`, `VecAYPX()`, `VecMAXPY()`, `VecWAXPY()`, `VecAXPY()`, `VecAXPBY()`
@*/
PetscErrorCode VecAXPBYPCZ(Vec z, PetscScalar alpha, PetscScalar beta, PetscScalar gamma, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(VecAXPBYPCZAsync_Private(z, alpha, beta, gamma, x, y, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecWAXPYAsync_Private(Vec w, PetscScalar alpha, Vec x, Vec y, PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(w, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 4);
  PetscValidType(w, 1);
  PetscValidType(x, 3);
  PetscValidType(y, 4);
  PetscCheckSameTypeAndComm(x, 3, y, 4);
  PetscCheckSameTypeAndComm(y, 4, w, 1);
  VecCheckSameSize(x, 3, y, 4);
  VecCheckSameSize(x, 3, w, 1);
  PetscCheck(w != y, PETSC_COMM_SELF, PETSC_ERR_SUP, "Result vector w cannot be same as input vector y, suggest VecAXPY()");
  PetscCheck(w != x, PETSC_COMM_SELF, PETSC_ERR_SUP, "Result vector w cannot be same as input vector x, suggest VecAYPX()");
  VecCheckAssembled(x);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveScalar(y, alpha, 2);
  PetscCall(VecSetErrorIfLocked(w, 1));

  PetscCall(VecLockReadPush(x));
  PetscCall(VecLockReadPush(y));
  if (alpha == (PetscScalar)0.0) {
    PetscCall(VecCopyAsync_Private(y, w, dctx));
  } else {
    PetscCall(PetscLogEventBegin(VEC_WAXPY, x, y, w, 0));
    VecMethodDispatch(w, dctx, VecAsyncFnName(WAXPY), waxpy, (Vec, PetscScalar, Vec, Vec, PetscDeviceContext), alpha, x, y);
    PetscCall(PetscLogEventEnd(VEC_WAXPY, x, y, w, 0));
    PetscCall(PetscObjectStateIncrease((PetscObject)w));
  }
  PetscCall(VecLockReadPop(x));
  PetscCall(VecLockReadPop(y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecWAXPY - Computes `w = alpha x + y`.

  Logically Collective

  Input Parameters:
+ alpha - the scalar
. x     - first vector, multiplied by `alpha`
- y     - second vector

  Output Parameter:
. w - the result

  Level: intermediate

  Note:
  `w` cannot be either `x` or `y`, but `x` and `y` can be the same

  Developer Notes:
  The implementation is optimized for alpha of -1.0, 0.0, and 1.0

.seealso: [](ch_vectors), `Vec`, `VecAXPY()`, `VecAYPX()`, `VecAXPBY()`, `VecMAXPY()`, `VecAXPBYPCZ()`
@*/
PetscErrorCode VecWAXPY(Vec w, PetscScalar alpha, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(VecWAXPYAsync_Private(w, alpha, x, y, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecSetValues - Inserts or adds values into certain locations of a vector.

  Not Collective

  Input Parameters:
+ x    - vector to insert in
. ni   - number of elements to add
. ix   - indices where to add
. y    - array of values. Pass `NULL` to set all zeroes.
- iora - either `INSERT_VALUES` to replace the current values or `ADD_VALUES` to add values to any existing entries

  Level: beginner

  Notes:
.vb
   `VecSetValues()` sets x[ix[i]] = y[i], for i=0,...,ni-1.
.ve

  Calls to `VecSetValues()` with the `INSERT_VALUES` and `ADD_VALUES`
  options cannot be mixed without intervening calls to the assembly
  routines.

  These values may be cached, so `VecAssemblyBegin()` and `VecAssemblyEnd()`
  MUST be called after all calls to `VecSetValues()` have been completed.

  VecSetValues() uses 0-based indices in Fortran as well as in C.

  If you call `VecSetOption`(x, `VEC_IGNORE_NEGATIVE_INDICES`,`PETSC_TRUE`),
  negative indices may be passed in ix. These rows are
  simply ignored. This allows easily inserting element load matrices
  with homogeneous Dirichlet boundary conditions that you don't want represented
  in the vector.

  Fortran Note:
  If any of `ix` and `y` are scalars pass them using, for example,
.vb
  call VecSetValues(mat, one, [ix], [y], INSERT_VALUES, ierr)
.ve

.seealso: [](ch_vectors), `Vec`, `VecAssemblyBegin()`, `VecAssemblyEnd()`, `VecSetValuesLocal()`,
          `VecSetValue()`, `VecSetValuesBlocked()`, `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`, `VecGetValues()`
@*/
PetscErrorCode VecSetValues(Vec x, PetscInt ni, const PetscInt ix[], const PetscScalar y[], InsertMode iora)
{
  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (!ni) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(ix, 3);
  if (y) PetscAssertPointer(y, 4);
  PetscValidType(x, 1);

  PetscCall(PetscLogEventBegin(VEC_SetValues, x, 0, 0, 0));
  PetscUseTypeMethod(x, setvalues, ni, ix, y, iora);
  PetscCall(PetscLogEventEnd(VEC_SetValues, x, 0, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecGetValues - Gets values from certain locations of a vector. Currently
  can only get values on the same processor on which they are owned

  Not Collective

  Input Parameters:
+ x  - vector to get values from
. ni - number of elements to get
- ix - indices where to get them from (in global 1d numbering)

  Output Parameter:
. y - array of values, must be passed in with a length of `ni`

  Level: beginner

  Notes:
  The user provides the allocated array y; it is NOT allocated in this routine

  `VecGetValues()` gets y[i] = x[ix[i]], for i=0,...,ni-1.

  `VecAssemblyBegin()` and `VecAssemblyEnd()`  MUST be called before calling this if `VecSetValues()` or related routine has been called

  VecGetValues() uses 0-based indices in Fortran as well as in C.

  If you call `VecSetOption`(x, `VEC_IGNORE_NEGATIVE_INDICES`,`PETSC_TRUE`),
  negative indices may be passed in ix. These rows are
  simply ignored.

.seealso: [](ch_vectors), `Vec`, `VecAssemblyBegin()`, `VecAssemblyEnd()`, `VecSetValues()`
@*/
PetscErrorCode VecGetValues(Vec x, PetscInt ni, const PetscInt ix[], PetscScalar y[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (!ni) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(ix, 3);
  PetscAssertPointer(y, 4);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  PetscUseTypeMethod(x, getvalues, ni, ix, y);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecSetValuesBlocked - Inserts or adds blocks of values into certain locations of a vector.

  Not Collective

  Input Parameters:
+ x    - vector to insert in
. ni   - number of blocks to add
. ix   - indices where to add in block count, rather than element count
. y    - array of values. Pass `NULL` to set all zeroes.
- iora - either `INSERT_VALUES` replaces existing entries with new values, `ADD_VALUES`, adds values to any existing entries

  Level: intermediate

  Notes:
  `VecSetValuesBlocked()` sets x[bs*ix[i]+j] = y[bs*i+j],
  for j=0,...,bs-1, for i=0,...,ni-1. where bs was set with VecSetBlockSize().

  Calls to `VecSetValuesBlocked()` with the `INSERT_VALUES` and `ADD_VALUES`
  options cannot be mixed without intervening calls to the assembly
  routines.

  These values may be cached, so `VecAssemblyBegin()` and `VecAssemblyEnd()`
  MUST be called after all calls to `VecSetValuesBlocked()` have been completed.

  `VecSetValuesBlocked()` uses 0-based indices in Fortran as well as in C.

  Negative indices may be passed in ix, these rows are
  simply ignored. This allows easily inserting element load matrices
  with homogeneous Dirichlet boundary conditions that you don't want represented
  in the vector.

  Fortran Note:
  If any of `ix` and `y` are scalars pass them using, for example,
.vb
  call VecSetValuesBlocked(mat, one, [ix], [y], INSERT_VALUES, ierr)
.ve

.seealso: [](ch_vectors), `Vec`, `VecAssemblyBegin()`, `VecAssemblyEnd()`, `VecSetValuesBlockedLocal()`,
          `VecSetValues()`
@*/
PetscErrorCode VecSetValuesBlocked(Vec x, PetscInt ni, const PetscInt ix[], const PetscScalar y[], InsertMode iora)
{
  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (!ni) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(ix, 3);
  if (y) PetscAssertPointer(y, 4);
  PetscValidType(x, 1);

  PetscCall(PetscLogEventBegin(VEC_SetValues, x, 0, 0, 0));
  PetscUseTypeMethod(x, setvaluesblocked, ni, ix, y, iora);
  PetscCall(PetscLogEventEnd(VEC_SetValues, x, 0, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecSetValuesLocal - Inserts or adds values into certain locations of a vector,
  using a local ordering of the nodes.

  Not Collective

  Input Parameters:
+ x    - vector to insert in
. ni   - number of elements to add
. ix   - indices where to add
. y    - array of values. Pass `NULL` to set all zeroes.
- iora - either `INSERT_VALUES` replaces existing entries with new values, `ADD_VALUES` adds values to any existing entries

  Level: intermediate

  Notes:
  `VecSetValuesLocal()` sets x[ix[i]] = y[i], for i=0,...,ni-1.

  Calls to `VecSetValuesLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
  options cannot be mixed without intervening calls to the assembly
  routines.

  These values may be cached, so `VecAssemblyBegin()` and `VecAssemblyEnd()`
  MUST be called after all calls to `VecSetValuesLocal()` have been completed.

  `VecSetValuesLocal()` uses 0-based indices in Fortran as well as in C.

  Fortran Note:
  If any of `ix` and `y` are scalars pass them using, for example,
.vb
  call VecSetValuesLocal(mat, one, [ix], [y], INSERT_VALUES, ierr)
.ve

.seealso: [](ch_vectors), `Vec`, `VecAssemblyBegin()`, `VecAssemblyEnd()`, `VecSetValues()`, `VecSetLocalToGlobalMapping()`,
          `VecSetValuesBlockedLocal()`
@*/
PetscErrorCode VecSetValuesLocal(Vec x, PetscInt ni, const PetscInt ix[], const PetscScalar y[], InsertMode iora)
{
  PetscInt lixp[128], *lix = lixp;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (!ni) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(ix, 3);
  if (y) PetscAssertPointer(y, 4);
  PetscValidType(x, 1);

  PetscCall(PetscLogEventBegin(VEC_SetValues, x, 0, 0, 0));
  if (PetscUnlikely(!x->map->mapping && x->ops->getlocaltoglobalmapping)) PetscUseTypeMethod(x, getlocaltoglobalmapping, &x->map->mapping);
  if (x->map->mapping) {
    if (ni > 128) PetscCall(PetscMalloc1(ni, &lix));
    PetscCall(ISLocalToGlobalMappingApply(x->map->mapping, ni, (PetscInt *)ix, lix));
    PetscUseTypeMethod(x, setvalues, ni, lix, y, iora);
    if (ni > 128) PetscCall(PetscFree(lix));
  } else PetscUseTypeMethod(x, setvalues, ni, ix, y, iora);
  PetscCall(PetscLogEventEnd(VEC_SetValues, x, 0, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecSetValuesBlockedLocal - Inserts or adds values into certain locations of a vector,
  using a local ordering of the nodes.

  Not Collective

  Input Parameters:
+ x    - vector to insert in
. ni   - number of blocks to add
. ix   - indices where to add in block count, not element count
. y    - array of values. Pass `NULL` to set all zeroes.
- iora - either `INSERT_VALUES` replaces existing entries with new values, `ADD_VALUES` adds values to any existing entries

  Level: intermediate

  Notes:
  `VecSetValuesBlockedLocal()` sets x[bs*ix[i]+j] = y[bs*i+j],
  for j=0,..bs-1, for i=0,...,ni-1, where bs has been set with `VecSetBlockSize()`.

  Calls to `VecSetValuesBlockedLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
  options cannot be mixed without intervening calls to the assembly
  routines.

  These values may be cached, so `VecAssemblyBegin()` and `VecAssemblyEnd()`
  MUST be called after all calls to `VecSetValuesBlockedLocal()` have been completed.

  `VecSetValuesBlockedLocal()` uses 0-based indices in Fortran as well as in C.

  Fortran Note:
  If any of `ix` and `y` are scalars pass them using, for example,
.vb
  call VecSetValuesBlockedLocal(mat, one, [ix], [y], INSERT_VALUES, ierr)
.ve

.seealso: [](ch_vectors), `Vec`, `VecAssemblyBegin()`, `VecAssemblyEnd()`, `VecSetValues()`, `VecSetValuesBlocked()`,
          `VecSetLocalToGlobalMapping()`
@*/
PetscErrorCode VecSetValuesBlockedLocal(Vec x, PetscInt ni, const PetscInt ix[], const PetscScalar y[], InsertMode iora)
{
  PetscInt lixp[128], *lix = lixp;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (!ni) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(ix, 3);
  if (y) PetscAssertPointer(y, 4);
  PetscValidType(x, 1);
  PetscCall(PetscLogEventBegin(VEC_SetValues, x, 0, 0, 0));
  if (PetscUnlikely(!x->map->mapping && x->ops->getlocaltoglobalmapping)) PetscUseTypeMethod(x, getlocaltoglobalmapping, &x->map->mapping);
  if (x->map->mapping) {
    if (ni > (PetscInt)PETSC_STATIC_ARRAY_LENGTH(lixp)) PetscCall(PetscMalloc1(ni, &lix));
    PetscCall(ISLocalToGlobalMappingApplyBlock(x->map->mapping, ni, (PetscInt *)ix, lix));
    PetscUseTypeMethod(x, setvaluesblocked, ni, lix, y, iora);
    if (ni > (PetscInt)PETSC_STATIC_ARRAY_LENGTH(lixp)) PetscCall(PetscFree(lix));
  } else {
    PetscUseTypeMethod(x, setvaluesblocked, ni, ix, y, iora);
  }
  PetscCall(PetscLogEventEnd(VEC_SetValues, x, 0, 0, 0));
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecMXDot_Private(Vec x, PetscInt nv, const Vec y[], PetscScalar result[], PetscErrorCode (*mxdot)(Vec, PetscInt, const Vec[], PetscScalar[]), PetscLogEvent event)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  VecCheckAssembled(x);
  PetscValidLogicalCollectiveInt(x, nv, 2);
  if (!nv) PetscFunctionReturn(PETSC_SUCCESS);
  PetscAssertPointer(y, 3);
  for (PetscInt i = 0; i < nv; ++i) {
    PetscValidHeaderSpecific(y[i], VEC_CLASSID, 3);
    PetscValidType(y[i], 3);
    PetscCheckSameTypeAndComm(x, 1, y[i], 3);
    VecCheckSameSize(x, 1, y[i], 3);
    VecCheckAssembled(y[i]);
    PetscCall(VecLockReadPush(y[i]));
  }
  PetscAssertPointer(result, 4);
  PetscValidFunction(mxdot, 5);

  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(event, x, *y, 0, 0));
  PetscCall((*mxdot)(x, nv, y, result));
  PetscCall(PetscLogEventEnd(event, x, *y, 0, 0));
  PetscCall(VecLockReadPop(x));
  for (PetscInt i = 0; i < nv; ++i) PetscCall(VecLockReadPop(y[i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMTDot - Computes indefinite vector multiple dot products.
  That is, it does NOT use the complex conjugate.

  Collective

  Input Parameters:
+ x  - one vector
. nv - number of vectors
- y  - array of vectors.  Note that vectors are pointers

  Output Parameter:
. val - array of the dot products

  Level: intermediate

  Notes for Users of Complex Numbers:
  For complex vectors, `VecMTDot()` computes the indefinite form
.vb
  val = (x,y) = y^T x,
.ve
  where y^T denotes the transpose of y.

  Use `VecMDot()` for the inner product
.vb
  val = (x,y) = y^H x,
.ve
  where y^H denotes the conjugate transpose of y.

.seealso: [](ch_vectors), `Vec`, `VecMDot()`, `VecTDot()`
@*/
PetscErrorCode VecMTDot(Vec x, PetscInt nv, const Vec y[], PetscScalar val[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscCall(VecMXDot_Private(x, nv, y, val, x->ops->mtdot, VEC_MTDot));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMDot - Computes multiple vector dot products.

  Collective

  Input Parameters:
+ x  - one vector
. nv - number of vectors
- y  - array of vectors.

  Output Parameter:
. val - array of the dot products (does not allocate the array)

  Level: intermediate

  Notes for Users of Complex Numbers:
  For complex vectors, `VecMDot()` computes
.vb
  val = (x,y) = y^H x,
.ve
  where y^H denotes the conjugate transpose of y.

  Use `VecMTDot()` for the indefinite form
.vb
  val = (x,y) = y^T x,
.ve
  where y^T denotes the transpose of y.

  Note:
  The implementation may use BLAS 2 operations when the vectors `y` have been obtained with `VecDuplicateVecs()`

.seealso: [](ch_vectors), `Vec`, `VecMTDot()`, `VecDot()`, `VecDuplicateVecs()`
@*/
PetscErrorCode VecMDot(Vec x, PetscInt nv, const Vec y[], PetscScalar val[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscCall(VecMXDot_Private(x, nv, y, val, x->ops->mdot, VEC_MDot));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecMAXPYAsync_Private(Vec y, PetscInt nv, const PetscScalar alpha[], Vec x[], PetscDeviceContext dctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(y, VEC_CLASSID, 1);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveInt(y, nv, 2);
  PetscCall(VecSetErrorIfLocked(y, 1));
  PetscCheck(nv >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of vectors (given %" PetscInt_FMT ") cannot be negative", nv);
  if (nv) {
    PetscInt zeros = 0;

    PetscAssertPointer(alpha, 3);
    PetscAssertPointer(x, 4);
    for (PetscInt i = 0; i < nv; ++i) {
      PetscValidLogicalCollectiveScalar(y, alpha[i], 3);
      PetscValidHeaderSpecific(x[i], VEC_CLASSID, 4);
      PetscValidType(x[i], 4);
      PetscCheckSameTypeAndComm(y, 1, x[i], 4);
      VecCheckSameSize(y, 1, x[i], 4);
      PetscCheck(y != x[i], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Array of vectors 'x' cannot contain y, found x[%" PetscInt_FMT "] == y", i);
      VecCheckAssembled(x[i]);
      PetscCall(VecLockReadPush(x[i]));
      zeros += alpha[i] == (PetscScalar)0.0;
    }

    if (zeros < nv) {
      PetscCall(PetscLogEventBegin(VEC_MAXPY, y, *x, 0, 0));
      VecMethodDispatch(y, dctx, VecAsyncFnName(MAXPY), maxpy, (Vec, PetscInt, const PetscScalar[], Vec[], PetscDeviceContext), nv, alpha, x);
      PetscCall(PetscLogEventEnd(VEC_MAXPY, y, *x, 0, 0));
      PetscCall(PetscObjectStateIncrease((PetscObject)y));
    }

    for (PetscInt i = 0; i < nv; ++i) PetscCall(VecLockReadPop(x[i]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMAXPY - Computes `y = y + sum alpha[i] x[i]`

  Logically Collective

  Input Parameters:
+ nv    - number of scalars and `x` vectors
. alpha - array of scalars
. y     - one vector
- x     - array of vectors

  Level: intermediate

  Notes:
  `y` cannot be any of the `x` vectors

  The implementation may use BLAS 2 operations when the vectors `y` have been obtained with `VecDuplicateVecs()`

.seealso: [](ch_vectors), `Vec`, `VecMAXPBY()`, `VecAYPX()`, `VecWAXPY()`, `VecAXPY()`, `VecAXPBYPCZ()`, `VecAXPBY()`, `VecDuplicateVecs()`
@*/
PetscErrorCode VecMAXPY(Vec y, PetscInt nv, const PetscScalar alpha[], Vec x[])
{
  PetscFunctionBegin;
  PetscCall(VecMAXPYAsync_Private(y, nv, alpha, x, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMAXPBY - Computes `y = beta y + sum alpha[i] x[i]`

  Logically Collective

  Input Parameters:
+ nv    - number of scalars and `x` vectors
. alpha - array of scalars
. beta  - scalar
. y     - one vector
- x     - array of vectors

  Level: intermediate

  Note:
  `y` cannot be any of the `x` vectors.

  Developer Notes:
  This is a convenience routine, but implementations might be able to optimize it, for example, when `beta` is zero.

.seealso: [](ch_vectors), `Vec`, `VecMAXPY()`, `VecAYPX()`, `VecWAXPY()`, `VecAXPY()`, `VecAXPBYPCZ()`, `VecAXPBY()`
@*/
PetscErrorCode VecMAXPBY(Vec y, PetscInt nv, const PetscScalar alpha[], PetscScalar beta, Vec x[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(y, VEC_CLASSID, 1);
  VecCheckAssembled(y);
  PetscValidLogicalCollectiveInt(y, nv, 2);
  PetscCall(VecSetErrorIfLocked(y, 1));
  PetscCheck(nv >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of vectors (given %" PetscInt_FMT ") cannot be negative", nv);

  PetscValidLogicalCollectiveScalar(y, beta, 4);
  if (y->ops->maxpby) {
    PetscInt zeros = 0;

    if (nv) {
      PetscAssertPointer(alpha, 3);
      PetscAssertPointer(x, 5);
    }

    for (PetscInt i = 0; i < nv; ++i) { // scan all alpha[]
      PetscValidLogicalCollectiveScalar(y, alpha[i], 3);
      PetscValidHeaderSpecific(x[i], VEC_CLASSID, 5);
      PetscValidType(x[i], 5);
      PetscCheckSameTypeAndComm(y, 1, x[i], 5);
      VecCheckSameSize(y, 1, x[i], 5);
      PetscCheck(y != x[i], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Array of vectors 'x' cannot contain y, found x[%" PetscInt_FMT "] == y", i);
      VecCheckAssembled(x[i]);
      PetscCall(VecLockReadPush(x[i]));
      zeros += alpha[i] == (PetscScalar)0.0;
    }

    if (zeros < nv) { // has nonzero alpha
      PetscCall(PetscLogEventBegin(VEC_MAXPY, y, *x, 0, 0));
      PetscUseTypeMethod(y, maxpby, nv, alpha, beta, x);
      PetscCall(PetscLogEventEnd(VEC_MAXPY, y, *x, 0, 0));
      PetscCall(PetscObjectStateIncrease((PetscObject)y));
    } else {
      PetscCall(VecScale(y, beta));
    }

    for (PetscInt i = 0; i < nv; ++i) PetscCall(VecLockReadPop(x[i]));
  } else { // no maxpby
    if (beta == 0.0) PetscCall(VecSet(y, 0.0));
    else PetscCall(VecScale(y, beta));
    PetscCall(VecMAXPY(y, nv, alpha, x));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecConcatenate - Creates a new vector that is a vertical concatenation of all the given array of vectors
  in the order they appear in the array. The concatenated vector resides on the same
  communicator and is the same type as the source vectors.

  Collective

  Input Parameters:
+ nx - number of vectors to be concatenated
- X  - array containing the vectors to be concatenated in the order of concatenation

  Output Parameters:
+ Y    - concatenated vector
- x_is - array of index sets corresponding to the concatenated components of `Y` (pass `NULL` if not needed)

  Level: advanced

  Notes:
  Concatenation is similar to the functionality of a `VECNEST` object; they both represent combination of
  different vector spaces. However, concatenated vectors do not store any information about their
  sub-vectors and own their own data. Consequently, this function provides index sets to enable the
  manipulation of data in the concatenated vector that corresponds to the original components at creation.

  This is a useful tool for outer loop algorithms, particularly constrained optimizers, where the solver
  has to operate on combined vector spaces and cannot utilize `VECNEST` objects due to incompatibility with
  bound projections.

.seealso: [](ch_vectors), `Vec`, `VECNEST`, `VECSCATTER`, `VecScatterCreate()`
@*/
PetscErrorCode VecConcatenate(PetscInt nx, const Vec X[], Vec *Y, IS *x_is[])
{
  MPI_Comm comm;
  VecType  vec_type;
  Vec      Ytmp, Xtmp;
  IS      *is_tmp;
  PetscInt i, shift = 0, Xnl, Xng, Xbegin;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveInt(*X, nx, 1);
  PetscValidHeaderSpecific(*X, VEC_CLASSID, 2);
  PetscValidType(*X, 2);
  PetscAssertPointer(Y, 3);

  if ((*X)->ops->concatenate) {
    /* use the dedicated concatenation function if available */
    PetscCall((*(*X)->ops->concatenate)(nx, X, Y, x_is));
  } else {
    /* loop over vectors and start creating IS */
    comm = PetscObjectComm((PetscObject)*X);
    PetscCall(VecGetType(*X, &vec_type));
    PetscCall(PetscMalloc1(nx, &is_tmp));
    for (i = 0; i < nx; i++) {
      PetscCall(VecGetSize(X[i], &Xng));
      PetscCall(VecGetLocalSize(X[i], &Xnl));
      PetscCall(VecGetOwnershipRange(X[i], &Xbegin, NULL));
      PetscCall(ISCreateStride(comm, Xnl, shift + Xbegin, 1, &is_tmp[i]));
      shift += Xng;
    }
    /* create the concatenated vector */
    PetscCall(VecCreate(comm, &Ytmp));
    PetscCall(VecSetType(Ytmp, vec_type));
    PetscCall(VecSetSizes(Ytmp, PETSC_DECIDE, shift));
    PetscCall(VecSetUp(Ytmp));
    /* copy data from X array to Y and return */
    for (i = 0; i < nx; i++) {
      PetscCall(VecGetSubVector(Ytmp, is_tmp[i], &Xtmp));
      PetscCall(VecCopy(X[i], Xtmp));
      PetscCall(VecRestoreSubVector(Ytmp, is_tmp[i], &Xtmp));
    }
    *Y = Ytmp;
    if (x_is) {
      *x_is = is_tmp;
    } else {
      for (i = 0; i < nx; i++) PetscCall(ISDestroy(&is_tmp[i]));
      PetscCall(PetscFree(is_tmp));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* A helper function for VecGetSubVector to check if we can implement it with no-copy (i.e. the subvector shares
   memory with the original vector), and the block size of the subvector.

    Input Parameters:
+   X - the original vector
-   is - the index set of the subvector

    Output Parameters:
+   contig - PETSC_TRUE if the index set refers to contiguous entries on this process, else PETSC_FALSE
.   start  - start of contiguous block, as an offset from the start of the ownership range of the original vector
-   blocksize - the block size of the subvector

*/
PetscErrorCode VecGetSubVectorContiguityAndBS_Private(Vec X, IS is, PetscBool *contig, PetscInt *start, PetscInt *blocksize)
{
  PetscInt  gstart, gend, lstart;
  PetscBool red[2] = {PETSC_TRUE /*contiguous*/, PETSC_TRUE /*validVBS*/};
  PetscInt  n, N, ibs, vbs, bs = 1;

  PetscFunctionBegin;
  PetscCall(ISGetLocalSize(is, &n));
  PetscCall(ISGetSize(is, &N));
  PetscCall(ISGetBlockSize(is, &ibs));
  PetscCall(VecGetBlockSize(X, &vbs));
  PetscCall(VecGetOwnershipRange(X, &gstart, &gend));
  PetscCall(ISContiguousLocal(is, gstart, gend, &lstart, &red[0]));
  /* block size is given by IS if ibs > 1; otherwise, check the vector */
  if (ibs > 1) {
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, red, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)is)));
    bs = ibs;
  } else {
    if (n % vbs || vbs == 1) red[1] = PETSC_FALSE; /* this process invalidate the collectiveness of block size */
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, red, 2, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)is)));
    if (red[0] && red[1]) bs = vbs; /* all processes have a valid block size and the access will be contiguous */
  }

  *contig    = red[0];
  *start     = lstart;
  *blocksize = bs;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* A helper function for VecGetSubVector, to be used when we have to build a standalone subvector through VecScatter

    Input Parameters:
+   X - the original vector
.   is - the index set of the subvector
-   bs - the block size of the subvector, gotten from VecGetSubVectorContiguityAndBS_Private()

    Output Parameter:
.   Z  - the subvector, which will compose the VecScatter context on output
*/
PetscErrorCode VecGetSubVectorThroughVecScatter_Private(Vec X, IS is, PetscInt bs, Vec *Z)
{
  PetscInt   n, N;
  VecScatter vscat;
  Vec        Y;

  PetscFunctionBegin;
  PetscCall(ISGetLocalSize(is, &n));
  PetscCall(ISGetSize(is, &N));
  PetscCall(VecCreate(PetscObjectComm((PetscObject)is), &Y));
  PetscCall(VecSetSizes(Y, n, N));
  PetscCall(VecSetBlockSize(Y, bs));
  PetscCall(VecSetType(Y, ((PetscObject)X)->type_name));
  PetscCall(VecScatterCreate(X, is, Y, NULL, &vscat));
  PetscCall(VecScatterBegin(vscat, X, Y, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(vscat, X, Y, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(PetscObjectCompose((PetscObject)Y, "VecGetSubVector_Scatter", (PetscObject)vscat));
  PetscCall(VecScatterDestroy(&vscat));
  *Z = Y;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecGetSubVector - Gets a vector representing part of another vector

  Collective

  Input Parameters:
+ X  - vector from which to extract a subvector
- is - index set representing portion of `X` to extract

  Output Parameter:
. Y - subvector corresponding to `is`

  Level: advanced

  Notes:
  The subvector `Y` should be returned with `VecRestoreSubVector()`.
  `X` and `is` must be defined on the same communicator

  Changes to the subvector will be reflected in the `X` vector on the call to `VecRestoreSubVector()`.

  This function may return a subvector without making a copy, therefore it is not safe to use the original vector while
  modifying the subvector.  Other non-overlapping subvectors can still be obtained from `X` using this function.

  The resulting subvector inherits the block size from `is` if greater than one. Otherwise, the block size is guessed from the block size of the original `X`.

.seealso: [](ch_vectors), `Vec`, `IS`, `VECNEST`, `MatCreateSubMatrix()`
@*/
PetscErrorCode VecGetSubVector(Vec X, IS is, Vec *Y)
{
  Vec Z;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(X, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(is, IS_CLASSID, 2);
  PetscCheckSameComm(X, 1, is, 2);
  PetscAssertPointer(Y, 3);
  if (X->ops->getsubvector) {
    PetscUseTypeMethod(X, getsubvector, is, &Z);
  } else { /* Default implementation currently does no caching */
    PetscBool contig;
    PetscInt  n, N, start, bs;

    PetscCall(ISGetLocalSize(is, &n));
    PetscCall(ISGetSize(is, &N));
    PetscCall(VecGetSubVectorContiguityAndBS_Private(X, is, &contig, &start, &bs));
    if (contig) { /* We can do a no-copy implementation */
      const PetscScalar *x;
      PetscInt           state = 0;
      PetscBool          isstd, iscuda, iship;

      PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &isstd, VECSEQ, VECMPI, VECSTANDARD, ""));
      PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &iscuda, VECSEQCUDA, VECMPICUDA, ""));
      PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &iship, VECSEQHIP, VECMPIHIP, ""));
      if (iscuda) {
#if defined(PETSC_HAVE_CUDA)
        const PetscScalar *x_d;
        PetscMPIInt        size;
        PetscOffloadMask   flg;

        PetscCall(VecCUDAGetArrays_Private(X, &x, &x_d, &flg));
        PetscCheck(flg != PETSC_OFFLOAD_UNALLOCATED, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for PETSC_OFFLOAD_UNALLOCATED");
        PetscCheck(!n || x || x_d, PETSC_COMM_SELF, PETSC_ERR_SUP, "Missing vector data");
        if (x) x += start;
        if (x_d) x_d += start;
        PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)X), &size));
        if (size == 1) {
          PetscCall(VecCreateSeqCUDAWithArrays(PetscObjectComm((PetscObject)X), bs, n, x, x_d, &Z));
        } else {
          PetscCall(VecCreateMPICUDAWithArrays(PetscObjectComm((PetscObject)X), bs, n, N, x, x_d, &Z));
        }
        Z->offloadmask = flg;
#endif
      } else if (iship) {
#if defined(PETSC_HAVE_HIP)
        const PetscScalar *x_d;
        PetscMPIInt        size;
        PetscOffloadMask   flg;

        PetscCall(VecHIPGetArrays_Private(X, &x, &x_d, &flg));
        PetscCheck(flg != PETSC_OFFLOAD_UNALLOCATED, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for PETSC_OFFLOAD_UNALLOCATED");
        PetscCheck(!n || x || x_d, PETSC_COMM_SELF, PETSC_ERR_SUP, "Missing vector data");
        if (x) x += start;
        if (x_d) x_d += start;
        PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)X), &size));
        if (size == 1) {
          PetscCall(VecCreateSeqHIPWithArrays(PetscObjectComm((PetscObject)X), bs, n, x, x_d, &Z));
        } else {
          PetscCall(VecCreateMPIHIPWithArrays(PetscObjectComm((PetscObject)X), bs, n, N, x, x_d, &Z));
        }
        Z->offloadmask = flg;
#endif
      } else if (isstd) {
        PetscMPIInt size;

        PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)X), &size));
        PetscCall(VecGetArrayRead(X, &x));
        if (x) x += start;
        if (size == 1) {
          PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)X), bs, n, x, &Z));
        } else {
          PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)X), bs, n, N, x, &Z));
        }
        PetscCall(VecRestoreArrayRead(X, &x));
      } else { /* default implementation: use place array */
        PetscCall(VecGetArrayRead(X, &x));
        PetscCall(VecCreate(PetscObjectComm((PetscObject)X), &Z));
        PetscCall(VecSetType(Z, ((PetscObject)X)->type_name));
        PetscCall(VecSetSizes(Z, n, N));
        PetscCall(VecSetBlockSize(Z, bs));
        PetscCall(VecPlaceArray(Z, PetscSafePointerPlusOffset(x, start)));
        PetscCall(VecRestoreArrayRead(X, &x));
      }

      /* this is relevant only in debug mode */
      PetscCall(VecLockGet(X, &state));
      if (state) PetscCall(VecLockReadPush(Z));
      Z->ops->placearray   = NULL;
      Z->ops->replacearray = NULL;
    } else { /* Have to create a scatter and do a copy */
      PetscCall(VecGetSubVectorThroughVecScatter_Private(X, is, bs, &Z));
    }
  }
  /* Record the state when the subvector was gotten so we know whether its values need to be put back */
  if (VecGetSubVectorSavedStateId < 0) PetscCall(PetscObjectComposedDataRegister(&VecGetSubVectorSavedStateId));
  PetscCall(PetscObjectComposedDataSetInt((PetscObject)Z, VecGetSubVectorSavedStateId, 1));
  *Y = Z;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecRestoreSubVector - Restores a subvector extracted using `VecGetSubVector()`

  Collective

  Input Parameters:
+ X  - vector from which subvector was obtained
. is - index set representing the subset of `X`
- Y  - subvector being restored

  Level: advanced

.seealso: [](ch_vectors), `Vec`, `IS`, `VecGetSubVector()`
@*/
PetscErrorCode VecRestoreSubVector(Vec X, IS is, Vec *Y)
{
  PETSC_UNUSED PetscObjectState dummystate = 0;
  PetscBool                     unchanged;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(X, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(is, IS_CLASSID, 2);
  PetscCheckSameComm(X, 1, is, 2);
  PetscAssertPointer(Y, 3);
  PetscValidHeaderSpecific(*Y, VEC_CLASSID, 3);

  if (X->ops->restoresubvector) PetscUseTypeMethod(X, restoresubvector, is, Y);
  else {
    PetscCall(PetscObjectComposedDataGetInt((PetscObject)*Y, VecGetSubVectorSavedStateId, dummystate, unchanged));
    if (!unchanged) { /* If Y's state has not changed since VecGetSubVector(), we only need to destroy Y */
      VecScatter scatter;
      PetscInt   state;

      PetscCall(VecLockGet(X, &state));
      PetscCheck(state == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vec X is locked for read-only or read/write access");

      PetscCall(PetscObjectQuery((PetscObject)*Y, "VecGetSubVector_Scatter", (PetscObject *)&scatter));
      if (scatter) {
        PetscCall(VecScatterBegin(scatter, *Y, X, INSERT_VALUES, SCATTER_REVERSE));
        PetscCall(VecScatterEnd(scatter, *Y, X, INSERT_VALUES, SCATTER_REVERSE));
      } else {
        PetscBool iscuda, iship;
        PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &iscuda, VECSEQCUDA, VECMPICUDA, ""));
        PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &iship, VECSEQHIP, VECMPIHIP, ""));

        if (iscuda) {
#if defined(PETSC_HAVE_CUDA)
          PetscOffloadMask ymask = (*Y)->offloadmask;

          /* The offloadmask of X dictates where to move memory
              If X GPU data is valid, then move Y data on GPU if needed
              Otherwise, move back to the CPU */
          switch (X->offloadmask) {
          case PETSC_OFFLOAD_BOTH:
            if (ymask == PETSC_OFFLOAD_CPU) {
              PetscCall(VecCUDAResetArray(*Y));
            } else if (ymask == PETSC_OFFLOAD_GPU) {
              X->offloadmask = PETSC_OFFLOAD_GPU;
            }
            break;
          case PETSC_OFFLOAD_GPU:
            if (ymask == PETSC_OFFLOAD_CPU) PetscCall(VecCUDAResetArray(*Y));
            break;
          case PETSC_OFFLOAD_CPU:
            if (ymask == PETSC_OFFLOAD_GPU) PetscCall(VecResetArray(*Y));
            break;
          case PETSC_OFFLOAD_UNALLOCATED:
          case PETSC_OFFLOAD_KOKKOS:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
          }
#endif
        } else if (iship) {
#if defined(PETSC_HAVE_HIP)
          PetscOffloadMask ymask = (*Y)->offloadmask;

          /* The offloadmask of X dictates where to move memory
              If X GPU data is valid, then move Y data on GPU if needed
              Otherwise, move back to the CPU */
          switch (X->offloadmask) {
          case PETSC_OFFLOAD_BOTH:
            if (ymask == PETSC_OFFLOAD_CPU) {
              PetscCall(VecHIPResetArray(*Y));
            } else if (ymask == PETSC_OFFLOAD_GPU) {
              X->offloadmask = PETSC_OFFLOAD_GPU;
            }
            break;
          case PETSC_OFFLOAD_GPU:
            if (ymask == PETSC_OFFLOAD_CPU) PetscCall(VecHIPResetArray(*Y));
            break;
          case PETSC_OFFLOAD_CPU:
            if (ymask == PETSC_OFFLOAD_GPU) PetscCall(VecResetArray(*Y));
            break;
          case PETSC_OFFLOAD_UNALLOCATED:
          case PETSC_OFFLOAD_KOKKOS:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
          }
#endif
        } else {
          /* If OpenCL vecs updated the device memory, this triggers a copy on the CPU */
          PetscCall(VecResetArray(*Y));
        }
        PetscCall(PetscObjectStateIncrease((PetscObject)X));
      }
    }
  }
  PetscCall(VecDestroy(Y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateLocalVector - Creates a vector object suitable for use with `VecGetLocalVector()` and friends. You must call `VecDestroy()` when the
  vector is no longer needed.

  Not Collective.

  Input Parameter:
. v - The vector for which the local vector is desired.

  Output Parameter:
. w - Upon exit this contains the local vector.

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetLocalVectorRead()`, `VecRestoreLocalVectorRead()`, `VecGetLocalVector()`, `VecRestoreLocalVector()`
@*/
PetscErrorCode VecCreateLocalVector(Vec v, Vec *w)
{
  VecType  roottype;
  PetscInt n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(v, VEC_CLASSID, 1);
  PetscAssertPointer(w, 2);
  if (v->ops->createlocalvector) {
    PetscUseTypeMethod(v, createlocalvector, w);
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(VecGetRootType_Private(v, &roottype));
  PetscCall(VecCreate(PETSC_COMM_SELF, w));
  PetscCall(VecGetLocalSize(v, &n));
  PetscCall(VecSetSizes(*w, n, n));
  PetscCall(VecGetBlockSize(v, &n));
  PetscCall(VecSetBlockSize(*w, n));
  PetscCall(VecSetType(*w, roottype));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecGetLocalVectorRead - Maps the local portion of a vector into a
  vector.

  Not Collective.

  Input Parameter:
. v - The vector for which the local vector is desired.

  Output Parameter:
. w - Upon exit this contains the local vector.

  Level: beginner

  Notes:
  You must call `VecRestoreLocalVectorRead()` when the local
  vector is no longer needed.

  This function is similar to `VecGetArrayRead()` which maps the local
  portion into a raw pointer.  `VecGetLocalVectorRead()` is usually
  almost as efficient as `VecGetArrayRead()` but in certain circumstances
  `VecGetLocalVectorRead()` can be much more efficient than
  `VecGetArrayRead()`.  This is because the construction of a contiguous
  array representing the vector data required by `VecGetArrayRead()` can
  be an expensive operation for certain vector types.  For example, for
  GPU vectors `VecGetArrayRead()` requires that the data between device
  and host is synchronized.

  Unlike `VecGetLocalVector()`, this routine is not collective and
  preserves cached information.

.seealso: [](ch_vectors), `Vec`, `VecCreateLocalVector()`, `VecRestoreLocalVectorRead()`, `VecGetLocalVector()`, `VecGetArrayRead()`, `VecGetArray()`
@*/
PetscErrorCode VecGetLocalVectorRead(Vec v, Vec w)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(v, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(w, VEC_CLASSID, 2);
  VecCheckSameLocalSize(v, 1, w, 2);
  if (v->ops->getlocalvectorread) {
    PetscUseTypeMethod(v, getlocalvectorread, w);
  } else {
    PetscScalar *a;

    PetscCall(VecGetArrayRead(v, (const PetscScalar **)&a));
    PetscCall(VecPlaceArray(w, a));
  }
  PetscCall(PetscObjectStateIncrease((PetscObject)w));
  PetscCall(VecLockReadPush(v));
  PetscCall(VecLockReadPush(w));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecRestoreLocalVectorRead - Unmaps the local portion of a vector
  previously mapped into a vector using `VecGetLocalVectorRead()`.

  Not Collective.

  Input Parameters:
+ v - The local portion of this vector was previously mapped into `w` using `VecGetLocalVectorRead()`.
- w - The vector into which the local portion of `v` was mapped.

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecCreateLocalVector()`, `VecGetLocalVectorRead()`, `VecGetLocalVector()`, `VecGetArrayRead()`, `VecGetArray()`
@*/
PetscErrorCode VecRestoreLocalVectorRead(Vec v, Vec w)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(v, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(w, VEC_CLASSID, 2);
  if (v->ops->restorelocalvectorread) {
    PetscUseTypeMethod(v, restorelocalvectorread, w);
  } else {
    const PetscScalar *a;

    PetscCall(VecGetArrayRead(w, &a));
    PetscCall(VecRestoreArrayRead(v, &a));
    PetscCall(VecResetArray(w));
  }
  PetscCall(VecLockReadPop(v));
  PetscCall(VecLockReadPop(w));
  PetscCall(PetscObjectStateIncrease((PetscObject)w));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecGetLocalVector - Maps the local portion of a vector into a
  vector.

  Collective

  Input Parameter:
. v - The vector for which the local vector is desired.

  Output Parameter:
. w - Upon exit this contains the local vector.

  Level: beginner

  Notes:
  You must call `VecRestoreLocalVector()` when the local
  vector is no longer needed.

  This function is similar to `VecGetArray()` which maps the local
  portion into a raw pointer.  `VecGetLocalVector()` is usually about as
  efficient as `VecGetArray()` but in certain circumstances
  `VecGetLocalVector()` can be much more efficient than `VecGetArray()`.
  This is because the construction of a contiguous array representing
  the vector data required by `VecGetArray()` can be an expensive
  operation for certain vector types.  For example, for GPU vectors
  `VecGetArray()` requires that the data between device and host is
  synchronized.

.seealso: [](ch_vectors), `Vec`, `VecCreateLocalVector()`, `VecRestoreLocalVector()`, `VecGetLocalVectorRead()`, `VecGetArrayRead()`, `VecGetArray()`
@*/
PetscErrorCode VecGetLocalVector(Vec v, Vec w)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(v, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(w, VEC_CLASSID, 2);
  VecCheckSameLocalSize(v, 1, w, 2);
  if (v->ops->getlocalvector) {
    PetscUseTypeMethod(v, getlocalvector, w);
  } else {
    PetscScalar *a;

    PetscCall(VecGetArray(v, &a));
    PetscCall(VecPlaceArray(w, a));
  }
  PetscCall(PetscObjectStateIncrease((PetscObject)w));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecRestoreLocalVector - Unmaps the local portion of a vector
  previously mapped into a vector using `VecGetLocalVector()`.

  Logically Collective.

  Input Parameters:
+ v - The local portion of this vector was previously mapped into `w` using `VecGetLocalVector()`.
- w - The vector into which the local portion of `v` was mapped.

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecCreateLocalVector()`, `VecGetLocalVector()`, `VecGetLocalVectorRead()`, `VecRestoreLocalVectorRead()`, `LocalVectorRead()`, `VecGetArrayRead()`, `VecGetArray()`
@*/
PetscErrorCode VecRestoreLocalVector(Vec v, Vec w)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(v, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(w, VEC_CLASSID, 2);
  if (v->ops->restorelocalvector) {
    PetscUseTypeMethod(v, restorelocalvector, w);
  } else {
    PetscScalar *a;
    PetscCall(VecGetArray(w, &a));
    PetscCall(VecRestoreArray(v, &a));
    PetscCall(VecResetArray(w));
  }
  PetscCall(PetscObjectStateIncrease((PetscObject)w));
  PetscCall(PetscObjectStateIncrease((PetscObject)v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray - Returns a pointer to a contiguous array that contains this
  MPI processes's portion of the vector data

  Logically Collective

  Input Parameter:
. x - the vector

  Output Parameter:
. a - location to put pointer to the array

  Level: beginner

  Notes:
  For the standard PETSc vectors, `VecGetArray()` returns a pointer to the local data array and
  does not use any copies. If the underlying vector data is not stored in a contiguous array
  this routine will copy the data to a contiguous array and return a pointer to that. You MUST
  call `VecRestoreArray()` when you no longer need access to the array.

  For vectors that may also have the array data in GPU memory, for example, `VECCUDA`, this call ensures the CPU array has the
  most recent array values by copying the data from the GPU memory if needed.

  Fortran Note:
.vb
  PetscScalar, pointer :: a(:)
.ve

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecGetArrays()`, `VecPlaceArray()`, `VecGetArray2d()`,
          `VecGetArrayPair()`, `VecRestoreArrayPair()`, `VecGetArrayWrite()`, `VecRestoreArrayWrite()`, `VecGetArrayAndMemType()`
@*/
PetscErrorCode VecGetArray(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscCall(VecSetErrorIfLocked(x, 1));
  if (x->ops->getarray) { /* The if-else order matters! VECNEST, VECCUDA etc should have ops->getarray while VECCUDA etc are petscnative */
    PetscUseTypeMethod(x, getarray, a);
  } else if (x->petscnative) { /* VECSTANDARD */
    *a = *((PetscScalar **)x->data);
  } else SETERRQ(PetscObjectComm((PetscObject)x), PETSC_ERR_SUP, "Cannot get array for vector type \"%s\"", ((PetscObject)x)->type_name);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray - Restores a vector after `VecGetArray()` has been called and the array is no longer needed

  Logically Collective

  Input Parameters:
+ x - the vector
- a - location of pointer to array obtained from `VecGetArray()`

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArrayRead()`, `VecRestoreArrays()`, `VecPlaceArray()`, `VecRestoreArray2d()`,
          `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecRestoreArray(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (a) PetscAssertPointer(a, 2);
  if (x->ops->restorearray) {
    PetscUseTypeMethod(x, restorearray, a);
  } else PetscCheck(x->petscnative, PetscObjectComm((PetscObject)x), PETSC_ERR_SUP, "Cannot restore array for vector type \"%s\"", ((PetscObject)x)->type_name);
  if (a) *a = NULL;
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*@C
  VecGetArrayRead - Get read-only pointer to contiguous array containing this processor's portion of the vector data.

  Not Collective

  Input Parameter:
. x - the vector

  Output Parameter:
. a - the array

  Level: beginner

  Notes:
  The array must be returned using a matching call to `VecRestoreArrayRead()`.

  Unlike `VecGetArray()`, preserves cached information like vector norms.

  Standard PETSc vectors use contiguous storage so that this routine does not perform a copy.  Other vector
  implementations may require a copy, but such implementations should cache the contiguous representation so that
  only one copy is performed when this routine is called multiple times in sequence.

  For vectors that may also have the array data in GPU memory, for example, `VECCUDA`, this call ensures the CPU array has the
  most recent array values by copying the data from the GPU memory if needed.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`,
          `VecGetArrayAndMemType()`
@*/
PetscErrorCode VecGetArrayRead(Vec x, const PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 2);
  if (x->ops->getarrayread) {
    PetscUseTypeMethod(x, getarrayread, a);
  } else if (x->ops->getarray) {
    PetscObjectState state;

    /* VECNEST, VECCUDA, VECKOKKOS etc */
    // x->ops->getarray may bump the object state, but since we know this is a read-only get
    // we can just undo that
    PetscCall(PetscObjectStateGet((PetscObject)x, &state));
    PetscUseTypeMethod(x, getarray, (PetscScalar **)a);
    PetscCall(PetscObjectStateSet((PetscObject)x, state));
  } else if (x->petscnative) {
    /* VECSTANDARD */
    *a = *((PetscScalar **)x->data);
  } else SETERRQ(PetscObjectComm((PetscObject)x), PETSC_ERR_SUP, "Cannot get array read for vector type \"%s\"", ((PetscObject)x)->type_name);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrayRead - Restore array obtained with `VecGetArrayRead()`

  Not Collective

  Input Parameters:
+ x - the vector
- a - the array

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecRestoreArrayRead(Vec x, const PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (a) PetscAssertPointer(a, 2);
  if (x->petscnative) { /* VECSTANDARD, VECCUDA, VECKOKKOS etc */
    /* nothing */
  } else if (x->ops->restorearrayread) { /* VECNEST */
    PetscUseTypeMethod(x, restorearrayread, a);
  } else { /* No one? */
    PetscObjectState state;

    // x->ops->restorearray may bump the object state, but since we know this is a read-restore
    // we can just undo that
    PetscCall(PetscObjectStateGet((PetscObject)x, &state));
    PetscUseTypeMethod(x, restorearray, (PetscScalar **)a);
    PetscCall(PetscObjectStateSet((PetscObject)x, state));
  }
  if (a) *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArrayWrite - Returns a pointer to a contiguous array that WILL contain this
  MPI processes's portion of the vector data.

  Logically Collective

  Input Parameter:
. x - the vector

  Output Parameter:
. a - location to put pointer to the array

  Level: intermediate

  Note:
  The values in this array are NOT valid, the caller of this routine is responsible for putting
  values into the array; any values it does not set will be invalid.

  The array must be returned using a matching call to `VecRestoreArrayWrite()`.

  For vectors associated with GPUs, the host and device vectors are not synchronized before
  giving access. If you need correct values in the array use `VecGetArray()`

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecGetArrays()`, `VecPlaceArray()`, `VecGetArray2d()`,
          `VecGetArrayPair()`, `VecRestoreArrayPair()`, `VecGetArray()`, `VecRestoreArrayWrite()`, `VecGetArrayAndMemType()`
@*/
PetscErrorCode VecGetArrayWrite(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCall(VecSetErrorIfLocked(x, 1));
  if (x->ops->getarraywrite) {
    PetscUseTypeMethod(x, getarraywrite, a);
  } else {
    PetscCall(VecGetArray(x, a));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrayWrite - Restores a vector after `VecGetArrayWrite()` has been called.

  Logically Collective

  Input Parameters:
+ x - the vector
- a - location of pointer to array obtained from `VecGetArray()`

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArrayRead()`, `VecRestoreArrays()`, `VecPlaceArray()`, `VecRestoreArray2d()`,
          `VecGetArrayPair()`, `VecRestoreArrayPair()`, `VecGetArrayWrite()`
@*/
PetscErrorCode VecRestoreArrayWrite(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (a) PetscAssertPointer(a, 2);
  if (x->ops->restorearraywrite) {
    PetscUseTypeMethod(x, restorearraywrite, a);
  } else if (x->ops->restorearray) {
    PetscUseTypeMethod(x, restorearray, a);
  }
  if (a) *a = NULL;
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArrays - Returns a pointer to the arrays in a set of vectors
  that were created by a call to `VecDuplicateVecs()`.

  Logically Collective; No Fortran Support

  Input Parameters:
+ x - the vectors
- n - the number of vectors

  Output Parameter:
. a - location to put pointer to the array

  Level: intermediate

  Note:
  You MUST call `VecRestoreArrays()` when you no longer need access to the arrays.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArrays()`
@*/
PetscErrorCode VecGetArrays(const Vec x[], PetscInt n, PetscScalar **a[])
{
  PetscInt      i;
  PetscScalar **q;

  PetscFunctionBegin;
  PetscAssertPointer(x, 1);
  PetscValidHeaderSpecific(*x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 3);
  PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must get at least one array n = %" PetscInt_FMT, n);
  PetscCall(PetscMalloc1(n, &q));
  for (i = 0; i < n; ++i) PetscCall(VecGetArray(x[i], &q[i]));
  *a = q;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrays - Restores a group of vectors after `VecGetArrays()`
  has been called.

  Logically Collective; No Fortran Support

  Input Parameters:
+ x - the vector
. n - the number of vectors
- a - location of pointer to arrays obtained from `VecGetArrays()`

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the arrays obtained with `VecGetArrays()`.

  Level: intermediate

.seealso: [](ch_vectors), `Vec`, `VecGetArrays()`, `VecRestoreArray()`
@*/
PetscErrorCode VecRestoreArrays(const Vec x[], PetscInt n, PetscScalar **a[])
{
  PetscInt      i;
  PetscScalar **q = *a;

  PetscFunctionBegin;
  PetscAssertPointer(x, 1);
  PetscValidHeaderSpecific(*x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 3);

  for (i = 0; i < n; ++i) PetscCall(VecRestoreArray(x[i], &q[i]));
  PetscCall(PetscFree(q));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArrayAndMemType - Like `VecGetArray()`, but if this is a standard device vector (e.g.,
  `VECCUDA`), the returned pointer will be a device pointer to the device memory that contains
  this MPI processes's portion of the vector data.

  Logically Collective; No Fortran Support

  Input Parameter:
. x - the vector

  Output Parameters:
+ a     - location to put pointer to the array
- mtype - memory type of the array

  Level: beginner

  Note:
  Device data is guaranteed to have the latest value. Otherwise, when this is a host vector
  (e.g., `VECMPI`), this routine functions the same as `VecGetArray()` and returns a host
  pointer.

  For `VECKOKKOS`, if Kokkos is configured without device (e.g., use serial or openmp), per
  this function, the vector works like `VECSEQ`/`VECMPI`; otherwise, it works like `VECCUDA` or
  `VECHIP` etc.

  Use `VecRestoreArrayAndMemType()` when the array access is no longer needed.

.seealso: [](ch_vectors), `Vec`, `VecRestoreArrayAndMemType()`, `VecGetArrayReadAndMemType()`, `VecGetArrayWriteAndMemType()`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecGetArrays()`,
          `VecPlaceArray()`, `VecGetArray2d()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`, `VecGetArrayWrite()`, `VecRestoreArrayWrite()`
@*/
PetscErrorCode VecGetArrayAndMemType(Vec x, PetscScalar *a[], PetscMemType *mtype)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  if (a) PetscAssertPointer(a, 2);
  if (mtype) PetscAssertPointer(mtype, 3);
  PetscCall(VecSetErrorIfLocked(x, 1));
  if (x->ops->getarrayandmemtype) {
    /* VECCUDA, VECKOKKOS etc */
    PetscUseTypeMethod(x, getarrayandmemtype, a, mtype);
  } else {
    /* VECSTANDARD, VECNEST, VECVIENNACL */
    PetscCall(VecGetArray(x, a));
    if (mtype) *mtype = PETSC_MEMTYPE_HOST;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrayAndMemType - Restores a vector after `VecGetArrayAndMemType()` has been called.

  Logically Collective; No Fortran Support

  Input Parameters:
+ x - the vector
- a - location of pointer to array obtained from `VecGetArrayAndMemType()`

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArrayAndMemType()`, `VecGetArray()`, `VecRestoreArrayRead()`, `VecRestoreArrays()`,
          `VecPlaceArray()`, `VecRestoreArray2d()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecRestoreArrayAndMemType(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  if (a) PetscAssertPointer(a, 2);
  if (x->ops->restorearrayandmemtype) {
    /* VECCUDA, VECKOKKOS etc */
    PetscUseTypeMethod(x, restorearrayandmemtype, a);
  } else {
    /* VECNEST, VECVIENNACL */
    PetscCall(VecRestoreArray(x, a));
  } /* VECSTANDARD does nothing */
  if (a) *a = NULL;
  PetscCall(PetscObjectStateIncrease((PetscObject)x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArrayReadAndMemType - Like `VecGetArrayRead()`, but if the input vector is a device vector, it will return a read-only device pointer.
  The returned pointer is guaranteed to point to up-to-date data. For host vectors, it functions as `VecGetArrayRead()`.

  Not Collective; No Fortran Support

  Input Parameter:
. x - the vector

  Output Parameters:
+ a     - the array
- mtype - memory type of the array

  Level: beginner

  Notes:
  The array must be returned using a matching call to `VecRestoreArrayReadAndMemType()`.

.seealso: [](ch_vectors), `Vec`, `VecRestoreArrayReadAndMemType()`, `VecGetArrayAndMemType()`, `VecGetArrayWriteAndMemType()`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecGetArrayReadAndMemType(Vec x, const PetscScalar *a[], PetscMemType *mtype)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscAssertPointer(a, 2);
  if (mtype) PetscAssertPointer(mtype, 3);
  if (x->ops->getarrayreadandmemtype) {
    /* VECCUDA/VECHIP though they are also petscnative */
    PetscUseTypeMethod(x, getarrayreadandmemtype, a, mtype);
  } else if (x->ops->getarrayandmemtype) {
    /* VECKOKKOS */
    PetscObjectState state;

    // see VecGetArrayRead() for why
    PetscCall(PetscObjectStateGet((PetscObject)x, &state));
    PetscUseTypeMethod(x, getarrayandmemtype, (PetscScalar **)a, mtype);
    PetscCall(PetscObjectStateSet((PetscObject)x, state));
  } else {
    PetscCall(VecGetArrayRead(x, a));
    if (mtype) *mtype = PETSC_MEMTYPE_HOST;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrayReadAndMemType - Restore array obtained with `VecGetArrayReadAndMemType()`

  Not Collective; No Fortran Support

  Input Parameters:
+ x - the vector
- a - the array

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArrayReadAndMemType()`, `VecRestoreArrayAndMemType()`, `VecRestoreArrayWriteAndMemType()`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecRestoreArrayReadAndMemType(Vec x, const PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  if (a) PetscAssertPointer(a, 2);
  if (x->ops->restorearrayreadandmemtype) {
    /* VECCUDA/VECHIP */
    PetscUseTypeMethod(x, restorearrayreadandmemtype, a);
  } else if (!x->petscnative) {
    /* VECNEST */
    PetscCall(VecRestoreArrayRead(x, a));
  }
  if (a) *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArrayWriteAndMemType - Like `VecGetArrayWrite()`, but if this is a device vector it will always return
  a device pointer to the device memory that contains this processor's portion of the vector data.

  Logically Collective; No Fortran Support

  Input Parameter:
. x - the vector

  Output Parameters:
+ a     - the array
- mtype - memory type of the array

  Level: beginner

  Note:
  The array must be returned using a matching call to `VecRestoreArrayWriteAndMemType()`, where it will label the device memory as most recent.

.seealso: [](ch_vectors), `Vec`, `VecRestoreArrayWriteAndMemType()`, `VecGetArrayReadAndMemType()`, `VecGetArrayAndMemType()`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecGetArrayWriteAndMemType(Vec x, PetscScalar *a[], PetscMemType *mtype)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecSetErrorIfLocked(x, 1));
  PetscAssertPointer(a, 2);
  if (mtype) PetscAssertPointer(mtype, 3);
  if (x->ops->getarraywriteandmemtype) {
    /* VECCUDA, VECHIP, VECKOKKOS etc, though they are also petscnative */
    PetscUseTypeMethod(x, getarraywriteandmemtype, a, mtype);
  } else if (x->ops->getarrayandmemtype) {
    PetscCall(VecGetArrayAndMemType(x, a, mtype));
  } else {
    /* VECNEST, VECVIENNACL */
    PetscCall(VecGetArrayWrite(x, a));
    if (mtype) *mtype = PETSC_MEMTYPE_HOST;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArrayWriteAndMemType - Restore array obtained with `VecGetArrayWriteAndMemType()`

  Logically Collective; No Fortran Support

  Input Parameters:
+ x - the vector
- a - the array

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecGetArrayWriteAndMemType()`, `VecRestoreArrayAndMemType()`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrayPair()`, `VecRestoreArrayPair()`
@*/
PetscErrorCode VecRestoreArrayWriteAndMemType(Vec x, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecSetErrorIfLocked(x, 1));
  if (a) PetscAssertPointer(a, 2);
  if (x->ops->restorearraywriteandmemtype) {
    /* VECCUDA/VECHIP */
    PetscMemType PETSC_UNUSED mtype; // since this function doesn't accept a memtype?
    PetscUseTypeMethod(x, restorearraywriteandmemtype, a, &mtype);
  } else if (x->ops->restorearrayandmemtype) {
    PetscCall(VecRestoreArrayAndMemType(x, a));
  } else {
    PetscCall(VecRestoreArray(x, a));
  }
  if (a) *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecPlaceArray - Allows one to replace the array in a vector with an
  array provided by the user. This is useful to avoid copying an array
  into a vector.

  Logically Collective

  Input Parameters:
+ vec   - the vector
- array - the array

  Level: developer

  Notes:
  Adding `const` to `array` was an oversight, as subsequent operations on `vec` would
  likely modify the data in `array`. However, we have kept it to avoid breaking APIs.

  Use `VecReplaceArray()` instead to permanently replace the array

  You can return to the original array with a call to `VecResetArray()`. `vec` does not take
  ownership of `array` in any way.

  The user must free `array` themselves but be careful not to
  do so before the vector has either been destroyed, had its original array restored with
  `VecResetArray()` or permanently replaced with `VecReplaceArray()`.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecReplaceArray()`, `VecResetArray()`
@*/
PetscErrorCode VecPlaceArray(Vec vec, const PetscScalar array[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 1);
  PetscValidType(vec, 1);
  if (array) PetscAssertPointer(array, 2);
  PetscUseTypeMethod(vec, placearray, array);
  PetscCall(PetscObjectStateIncrease((PetscObject)vec));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecReplaceArray - Allows one to replace the array in a vector with an
  array provided by the user. This is useful to avoid copying an array
  into a vector.

  Logically Collective; No Fortran Support

  Input Parameters:
+ vec   - the vector
- array - the array

  Level: developer

  Notes:
  Adding `const` to `array` was an oversight, as subsequent operations on `vec` would
  likely modify the data in `array`. However, we have kept it to avoid breaking APIs.

  This permanently replaces the array and frees the memory associated
  with the old array. Use `VecPlaceArray()` to temporarily replace the array.

  The memory passed in MUST be obtained with `PetscMalloc()` and CANNOT be
  freed by the user. It will be freed when the vector is destroyed.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecPlaceArray()`, `VecResetArray()`
@*/
PetscErrorCode VecReplaceArray(Vec vec, const PetscScalar array[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 1);
  PetscValidType(vec, 1);
  PetscUseTypeMethod(vec, replacearray, array);
  PetscCall(PetscObjectStateIncrease((PetscObject)vec));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray2d - Returns a pointer to a 2d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray2d()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- nstart - first index in the second coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` and `nstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray2d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray2d(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  PetscInt     i, N;
  PetscScalar *aa;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 2d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n);
  PetscCall(VecGetArray(x, &aa));

  PetscCall(PetscMalloc1(m, a));
  for (i = 0; i < m; i++) (*a)[i] = aa + i * n - nstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray2dWrite - Returns a pointer to a 2d contiguous array that will contain this
  processor's portion of the vector data.  You MUST call `VecRestoreArray2dWrite()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- nstart - first index in the second coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` and `nstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray2d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray2dWrite(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  PetscInt     i, N;
  PetscScalar *aa;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 2d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n);
  PetscCall(VecGetArrayWrite(x, &aa));

  PetscCall(PetscMalloc1(m, a));
  for (i = 0; i < m; i++) (*a)[i] = aa + i * n - nstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray2d - Restores a vector after `VecGetArray2d()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of the two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray2d()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray2d(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArray(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray2dWrite - Restores a vector after `VecGetArray2dWrite()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of the two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray2d()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray2dWrite(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayWrite(x, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray1d - Returns a pointer to a 1d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray1d()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
- mstart - first index you will use in first coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` is likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray2d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray1d(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscInt N;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 4);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m == N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local array size %" PetscInt_FMT " does not match 1d array dimensions %" PetscInt_FMT, N, m);
  PetscCall(VecGetArray(x, a));
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray1dWrite - Returns a pointer to a 1d contiguous array that will contain this
  processor's portion of the vector data.  You MUST call `VecRestoreArray1dWrite()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
- mstart - first index you will use in first coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` is likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray2d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray1dWrite(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscInt N;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 4);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m == N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local array size %" PetscInt_FMT " does not match 1d array dimensions %" PetscInt_FMT, N, m);
  PetscCall(VecGetArrayWrite(x, a));
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray1d - Restores a vector after `VecGetArray1d()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray1d()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray1d()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray2d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray1d(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecRestoreArray(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray1dWrite - Restores a vector after `VecGetArray1dWrite()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray1d()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray1d()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray2d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray1dWrite(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecRestoreArrayWrite(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray3d - Returns a pointer to a 3d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray3d()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of three dimensional array
. p      - third dimension of three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- pstart - first index in the third coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray3d(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  PetscInt     i, N, j;
  PetscScalar *aa, **b;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 3d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p);
  PetscCall(VecGetArray(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar **) + m * n * sizeof(PetscScalar *), a));
  b = (PetscScalar **)((*a) + m);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = PetscSafePointerPlusOffset(aa, i * n * p + j * p - pstart);
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray3dWrite - Returns a pointer to a 3d contiguous array that will contain this
  processor's portion of the vector data.  You MUST call `VecRestoreArray3dWrite()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of three dimensional array
. p      - third dimension of three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- pstart - first index in the third coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray3dWrite(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  PetscInt     i, N, j;
  PetscScalar *aa, **b;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 3d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p);
  PetscCall(VecGetArrayWrite(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar **) + m * n * sizeof(PetscScalar *), a));
  b = (PetscScalar **)((*a) + m);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = aa + i * n * p + j * p - pstart;

  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray3d - Restores a vector after `VecGetArray3d()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of the three dimensional array
. p      - third dimension of the three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- a      - location of pointer to array obtained from VecGetArray3d()

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray3d(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArray(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray3dWrite - Restores a vector after `VecGetArray3dWrite()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of the three dimensional array
. p      - third dimension of the three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- a      - location of pointer to array obtained from VecGetArray3d()

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray3dWrite(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayWrite(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray4d - Returns a pointer to a 4d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray4d()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of four dimensional array
. p      - third dimension of four dimensional array
. q      - fourth dimension of four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- qstart - first index in the fourth coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray4d(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  PetscInt     i, N, j, k;
  PetscScalar *aa, ***b, **c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p * q == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 4d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p, q);
  PetscCall(VecGetArray(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar ***) + m * n * sizeof(PetscScalar **) + m * n * p * sizeof(PetscScalar *), a));
  b = (PetscScalar ***)((*a) + m);
  c = (PetscScalar **)(b + m * n);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = c + i * n * p + j * p - pstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++)
      for (k = 0; k < p; k++) c[i * n * p + j * p + k] = aa + i * n * p * q + j * p * q + k * q - qstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray4dWrite - Returns a pointer to a 4d contiguous array that will contain this
  processor's portion of the vector data.  You MUST call `VecRestoreArray4dWrite()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of four dimensional array
. p      - third dimension of four dimensional array
. q      - fourth dimension of four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- qstart - first index in the fourth coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray4dWrite(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  PetscInt     i, N, j, k;
  PetscScalar *aa, ***b, **c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p * q == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 4d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p, q);
  PetscCall(VecGetArrayWrite(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar ***) + m * n * sizeof(PetscScalar **) + m * n * p * sizeof(PetscScalar *), a));
  b = (PetscScalar ***)((*a) + m);
  c = (PetscScalar **)(b + m * n);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = c + i * n * p + j * p - pstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++)
      for (k = 0; k < p; k++) c[i * n * p + j * p + k] = aa + i * n * p * q + j * p * q + k * q - qstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray4d - Restores a vector after `VecGetArray4d()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of the four dimensional array
. p      - third dimension of the four dimensional array
. q      - fourth dimension of the four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
. qstart - first index in the fourth coordinate direction (often 0)
- a      - location of pointer to array obtained from VecGetArray4d()

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`
@*/
PetscErrorCode VecRestoreArray4d(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArray(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray4dWrite - Restores a vector after `VecGetArray4dWrite()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of the four dimensional array
. p      - third dimension of the four dimensional array
. q      - fourth dimension of the four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
. qstart - first index in the fourth coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray4d()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray4dWrite(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayWrite(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray2dRead - Returns a pointer to a 2d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray2dRead()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- nstart - first index in the second coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` and `nstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray2d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray2dRead(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  PetscInt           i, N;
  const PetscScalar *aa;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 2d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n);
  PetscCall(VecGetArrayRead(x, &aa));

  PetscCall(PetscMalloc1(m, a));
  for (i = 0; i < m; i++) (*a)[i] = (PetscScalar *)aa + i * n - nstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray2dRead - Restores a vector after `VecGetArray2dRead()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. n      - second dimension of the two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- a      - location of pointer to array obtained from VecGetArray2d()

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray2dRead(Vec x, PetscInt m, PetscInt n, PetscInt mstart, PetscInt nstart, PetscScalar **a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 6);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayRead(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray1dRead - Returns a pointer to a 1d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray1dRead()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
- mstart - first index you will use in first coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart` is likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray2d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray1dRead(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscInt N;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 4);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m == N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local array size %" PetscInt_FMT " does not match 1d array dimensions %" PetscInt_FMT, N, m);
  PetscCall(VecGetArrayRead(x, (const PetscScalar **)a));
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray1dRead - Restores a vector after `VecGetArray1dRead()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of two dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray1dRead()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray1dRead()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray2d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray1dRead(Vec x, PetscInt m, PetscInt mstart, PetscScalar *a[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscValidType(x, 1);
  PetscCall(VecRestoreArrayRead(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray3dRead - Returns a pointer to a 3d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray3dRead()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of three dimensional array
. p      - third dimension of three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
- pstart - first index in the third coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: developer

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3dRead()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray3dRead(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  PetscInt           i, N, j;
  const PetscScalar *aa;
  PetscScalar      **b;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 3d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p);
  PetscCall(VecGetArrayRead(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar **) + m * n * sizeof(PetscScalar *), a));
  b = (PetscScalar **)((*a) + m);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = PetscSafePointerPlusOffset((PetscScalar *)aa, i * n * p + j * p - pstart);
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray3dRead - Restores a vector after `VecGetArray3dRead()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of three dimensional array
. n      - second dimension of the three dimensional array
. p      - third dimension of the three dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray3dRead()`

  Level: developer

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray3dRead(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscScalar ***a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 8);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayRead(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecGetArray4dRead - Returns a pointer to a 4d contiguous array that contains this
  processor's portion of the vector data.  You MUST call `VecRestoreArray4dRead()`
  when you no longer need access to the array.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of four dimensional array
. p      - third dimension of four dimensional array
. q      - fourth dimension of four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
- qstart - first index in the fourth coordinate direction (often 0)

  Output Parameter:
. a - location to put pointer to the array

  Level: beginner

  Notes:
  For a vector obtained from `DMCreateLocalVector()` `mstart`, `nstart`, and `pstart` are likely
  obtained from the corner indices obtained from `DMDAGetGhostCorners()` while for
  `DMCreateGlobalVector()` they are the corner indices from `DMDAGetCorners()`. In both cases
  the arguments from `DMDAGet[Ghost]Corners()` are reversed in the call to `VecGetArray3d()`.

  For standard PETSc vectors this is an inexpensive call; it does not copy the vector values.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecGetArrays()`, `VecPlaceArray()`,
          `VecRestoreArray2d()`, `DMDAVecGetarray()`, `DMDAVecRestoreArray()`, `VecGetArray3d()`, `VecRestoreArray3d()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecGetArray4dRead(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  PetscInt           i, N, j, k;
  const PetscScalar *aa;
  PetscScalar     ***b, **c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  PetscCall(VecGetLocalSize(x, &N));
  PetscCheck(m * n * p * q == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local array size %" PetscInt_FMT " does not match 4d array dimensions %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT, N, m, n, p, q);
  PetscCall(VecGetArrayRead(x, &aa));

  PetscCall(PetscMalloc(m * sizeof(PetscScalar ***) + m * n * sizeof(PetscScalar **) + m * n * p * sizeof(PetscScalar *), a));
  b = (PetscScalar ***)((*a) + m);
  c = (PetscScalar **)(b + m * n);
  for (i = 0; i < m; i++) (*a)[i] = b + i * n - nstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++) b[i * n + j] = c + i * n * p + j * p - pstart;
  for (i = 0; i < m; i++)
    for (j = 0; j < n; j++)
      for (k = 0; k < p; k++) c[i * n * p + j * p + k] = (PetscScalar *)aa + i * n * p * q + j * p * q + k * q - qstart;
  *a -= mstart;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  VecRestoreArray4dRead - Restores a vector after `VecGetArray4d()` has been called.

  Logically Collective

  Input Parameters:
+ x      - the vector
. m      - first dimension of four dimensional array
. n      - second dimension of the four dimensional array
. p      - third dimension of the four dimensional array
. q      - fourth dimension of the four dimensional array
. mstart - first index you will use in first coordinate direction (often 0)
. nstart - first index in the second coordinate direction (often 0)
. pstart - first index in the third coordinate direction (often 0)
. qstart - first index in the fourth coordinate direction (often 0)
- a      - location of pointer to array obtained from `VecGetArray4dRead()`

  Level: beginner

  Notes:
  For regular PETSc vectors this routine does not involve any copies. For
  any special vectors that do not store local vector data in a contiguous
  array, this routine will copy the data back into the underlying
  vector data structure from the array obtained with `VecGetArray()`.

  This routine actually zeros out the `a` pointer.

.seealso: [](ch_vectors), `Vec`, `VecGetArray()`, `VecRestoreArray()`, `VecRestoreArrays()`, `VecPlaceArray()`,
          `VecGetArray2d()`, `VecGetArray3d()`, `VecRestoreArray3d()`, `DMDAVecGetArray()`, `DMDAVecRestoreArray()`,
          `VecGetArray1d()`, `VecRestoreArray1d()`, `VecGetArray4d()`, `VecRestoreArray4d()`
@*/
PetscErrorCode VecRestoreArray4dRead(Vec x, PetscInt m, PetscInt n, PetscInt p, PetscInt q, PetscInt mstart, PetscInt nstart, PetscInt pstart, PetscInt qstart, PetscScalar ****a[])
{
  void *dummy;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(a, 10);
  PetscValidType(x, 1);
  dummy = (void *)(*a + mstart);
  PetscCall(PetscFree(dummy));
  PetscCall(VecRestoreArrayRead(x, NULL));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecLockGet - Get the current lock status of a vector

  Logically Collective

  Input Parameter:
. x - the vector

  Output Parameter:
. state - greater than zero indicates the vector is locked for read; less than zero indicates the vector is
           locked for write; equal to zero means the vector is unlocked, that is, it is free to read or write.

  Level: advanced

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecLockReadPush()`, `VecLockReadPop()`
@*/
PetscErrorCode VecLockGet(Vec x, PetscInt *state)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(state, 2);
  *state = x->lock;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecLockGetLocation(Vec x, const char *file[], const char *func[], int *line)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscAssertPointer(file, 2);
  PetscAssertPointer(func, 3);
  PetscAssertPointer(line, 4);
#if PetscDefined(USE_DEBUG) && !PetscDefined(HAVE_THREADSAFETY)
  {
    const int index = x->lockstack.currentsize - 1;

    *file = index < 0 ? NULL : x->lockstack.file[index];
    *func = index < 0 ? NULL : x->lockstack.function[index];
    *line = index < 0 ? 0 : x->lockstack.line[index];
  }
#else
  *file = NULL;
  *func = NULL;
  *line = 0;
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecLockReadPush - Push a read-only lock on a vector to prevent it from being written to

  Logically Collective

  Input Parameter:
. x - the vector

  Level: intermediate

  Notes:
  If this is set then calls to `VecGetArray()` or `VecSetValues()` or any other routines that change the vectors values will generate an error.

  The call can be nested, i.e., called multiple times on the same vector, but each `VecLockReadPush()` has to have one matching
  `VecLockReadPop()`, which removes the latest read-only lock.

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecLockReadPop()`, `VecLockGet()`
@*/
PetscErrorCode VecLockReadPush(Vec x)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscCheck(x->lock++ >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vector is already locked for exclusive write access but you want to read it");
#if PetscDefined(USE_DEBUG) && !PetscDefined(HAVE_THREADSAFETY)
  {
    const char *file, *func;
    int         index, line;

    if ((index = petscstack.currentsize - 2) < 0) {
      // vec was locked "outside" of petsc, either in user-land or main. the error message will
      // now show this function as the culprit, but it will include the stacktrace
      file = "unknown user-file";
      func = "unknown_user_function";
      line = 0;
    } else {
      file = petscstack.file[index];
      func = petscstack.function[index];
      line = petscstack.line[index];
    }
    PetscStackPush_Private(x->lockstack, file, func, line, petscstack.petscroutine[index], PETSC_FALSE);
  }
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecLockReadPop - Pop a read-only lock from a vector

  Logically Collective

  Input Parameter:
. x - the vector

  Level: intermediate

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecLockReadPush()`, `VecLockGet()`
@*/
PetscErrorCode VecLockReadPop(Vec x)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  PetscCheck(--x->lock >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vector has been unlocked from read-only access too many times");
#if PetscDefined(USE_DEBUG) && !PetscDefined(HAVE_THREADSAFETY)
  {
    const char *previous = x->lockstack.function[x->lockstack.currentsize - 1];

    PetscStackPop_Private(x->lockstack, previous);
  }
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecLockWriteSet - Lock or unlock a vector for exclusive read/write access

  Logically Collective

  Input Parameters:
+ x   - the vector
- flg - `PETSC_TRUE` to lock the vector for exclusive read/write access; `PETSC_FALSE` to unlock it.

  Level: intermediate

  Notes:
  The function is useful in split-phase computations, which usually have a begin phase and an end phase.
  One can call `VecLockWriteSet`(x,`PETSC_TRUE`) in the begin phase to lock a vector for exclusive
  access, and call `VecLockWriteSet`(x,`PETSC_FALSE`) in the end phase to unlock the vector from exclusive
  access. In this way, one is ensured no other operations can access the vector in between. The code may like

.vb
       VecGetArray(x,&xdata); // begin phase
       VecLockWriteSet(v,PETSC_TRUE);

       Other operations, which can not access x anymore (they can access xdata, of course)

       VecRestoreArray(x,&vdata); // end phase
       VecLockWriteSet(v,PETSC_FALSE);
.ve

  The call can not be nested on the same vector, in other words, one can not call `VecLockWriteSet`(x,`PETSC_TRUE`)
  again before calling `VecLockWriteSet`(v,`PETSC_FALSE`).

.seealso: [](ch_vectors), `Vec`, `VecRestoreArray()`, `VecGetArrayRead()`, `VecLockReadPush()`, `VecLockReadPop()`, `VecLockGet()`
@*/
PetscErrorCode VecLockWriteSet(Vec x, PetscBool flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(x, VEC_CLASSID, 1);
  if (flg) {
    PetscCheck(x->lock <= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vector is already locked for read-only access but you want to write it");
    PetscCheck(x->lock >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vector is already locked for exclusive write access but you want to write it");
    x->lock = -1;
  } else {
    PetscCheck(x->lock == -1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Vector is not locked for exclusive write access but you want to unlock it from that");
    x->lock = 0;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
