Fix spelling errors in manpages and comments

Merge remote-tracking branch 'origin/maint'

Merge branch 'fix-fortran-DSGetTabulation' into 'maint'

Fix DSGetTabulation for Fortran

See merge request petsc/petsc!2826

typo

Merge branch 'tisaac/feature-dubiner-basis' into 'master'

PetscDT: PKD (Dubiner) basis

See merge request petsc/petsc!2691

Add PetscDTPDKEvalJet(), PetscDTJacobiEvalJet(), PetscDTIndexToGradedOrder(), and PetscDTGradedOrderToIndex()

The Proriol-Koordwinder-Dubiner basis (PKD) is orthonormal on the
reference simplex, so

Add PetscDTPDKEvalJet(), PetscDTJacobiEvalJet(), PetscDTIndexToGradedOrder(), and PetscDTGradedOrderToIndex()

The Proriol-Koordwinder-Dubiner basis (PKD) is orthonormal on the
reference simplex, so we should make it available as a stable basis of
evaluation.

The recursive definition allows for a straightforward and stable
calculation of all derivatives, not just first and second.

`src/dm/dt/tests/ex9.c` tests that the basis is orthonormal
and compares the derivatives against the derivatives computed by
tensor-product Legendre polynomials.

I thought about how to make an interface that would handle that,
and I decided returning the jet in the same kind of graded
representation that makes sense for multivariate polynomial spaces was a
good choice.

To facilitate this, I also added indexing functions for figuring out
where a tuple (either of exponents in a monomial or orders in a partial
derivatives) is in this ordering.

Along the way I made PetscDTStroudConicalQuadrature() handle arbitrary
dimensions instead of just 1--3.

We have a variety of dimensional orderings in PetscDT, related to how we
order points of evaluation, components of the jet, and basis functions.

I thought that:
- downstream users concerned with performance might prefer points of
evaluation as the fastest varying index to facilitate vectorization
of numerical integration, and
- having basis functions as one of the outer dimensions (first or last)
would simplify computing the matrix-matrix product of
a [basis function x evaluation point] matrix with a Vandermonde
inverse matrix

So I ordered the output dimensions of PetscDTPKDEvalJet() as
[basis function, jet component (derivative), evaluation point]. I am
seeking comment as to whether this is good, and whether it might be a
good convention to adopt elsewhere in PetscDT.

undo extern

Fix complex type issue in dm/dt/tests/ex9.c

squashme: fix scaling in PetscDTStroudConicalQuadrature()

squashme: loosen tolerance for single precision

squashme: cast to double before printing

squashme: remove unused static functions

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Merge branch 'tisaac/feature-dual-space-rework' into 'master'

Rework PetscDualSpace

See merge request petsc/petsc!2399

Add PetscDTIndexToBary, PetscDTBaryToIndex, and PetscDTNodeType

Move tests that missed the example excision

Add enum lists for PetscDTNodeTypes

Merge remote-tracking branch 'origin/psanan/docs-fixes-2020-03-25'

Doc fixes (prerequisites for Sphinx docs)

See merge request petsc/petsc!2633

docs: fix sowing list syntax/incomplete man page

Merge branch 'tisaac/feature-unify-quadrature' into 'master'

Unify Jacobi polynomial based computations in PetscDT

See merge request petsc/petsc!2574

Add PetscDTGaussJacobiQuadrature, PetscDTGaussLobattoJacobiQuadrature, PetscDTJacobiEval

Implement the Jacobi recurrence in exactly one place

Add PetscDTJacobiEval

squashme: Fixes to Jacobi polyno

Add PetscDTGaussJacobiQuadrature, PetscDTGaussLobattoJacobiQuadrature, PetscDTJacobiEval

Implement the Jacobi recurrence in exactly one place

Add PetscDTJacobiEval

squashme: Fixes to Jacobi polynomial changes

Use lgamma to determine the scaling coefficient in Newton's method for Gauss-Jacobi quadrature

Fix complex-to-real in postprocessing eigensolve in dt.c

Correctly choose newton for PetscGaussLobattoLegendreQuadrature

Use better initial guess for PetscDTGaussJacobiQuadrature_Newton_Internal

Work around Sun bug (nullus cimex sub sole novus)

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Rename PetscDTGaussJacobiQuadrature to PetscDTStroudConicalQuadrature and consolidate internal quadrature calculations

Revert incorrectly changed quadrature in dmmbfem.cxx

Merge branch 'dalcinl/petscdt-fix-warning' into 'master'

PetscDT: Fix -Wconversion warnings in header file when using 64bit integers

See merge request petsc/petsc!2480

PetscDT: Fix -Wconversion warnings in header file when using 64bit integers

/home/devel/petsc/dev/include/petscdt.h:166:44: \
warning: conversion from ‘PetscInt’ {aka ‘long int’} \
to ‘PetscReal’ {a

PetscDT: Fix -Wconversion warnings in header file when using 64bit integers

/home/devel/petsc/dev/include/petscdt.h:166:44: \
warning: conversion from ‘PetscInt’ {aka ‘long int’} \
to ‘PetscReal’ {aka ‘double’} may change value [-Wconversion]
166 | for (i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1);

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Merge branch 'knepley/feature-project-different-spaces' into 'master'

Knepley/feature project different spaces

See merge request petsc/petsc!2153

FE+DS: Introduce PetscTabulation to hold tabulated function data
- This was created to prevent mismatches in sizes I was getting by just
passing around arrays
- FE+FV+DS now hold tabulations
- GetTab

FE+DS: Introduce PetscTabulation to hold tabulated function data
- This was created to prevent mismatches in sizes I was getting by just
passing around arrays
- FE+FV+DS now hold tabulations
- GetTabulation() --> CreateTabulation() and it creates an object rather
than using DMGetWorkArray(). I put in ComputeTabulation() to reuse
space, but there still may be performance regression.
- Default tabulations are now "cell tabulations"
- The replicas in the tabulation are used to index faces in a face
tabulation

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Merge remote-tracking branch 'origin/knepley/feature-dt-quad-classid'

Knepley/feature dt quad classid

See merge request petsc/petsc!2355

Merge branch 'tisaac/feature-alt-v' into 'master'

Tisaac/feature alt v

See merge request petsc/petsc!2357

Fix uninitialized, C++, and Fortran issues with PetscDTAltV, other small
fixes

Silence compiler Wmaybe-unitialized warnings in petscdt.h

Loosen tolerances for single precision tests

Fix C++ PetscD

Fix uninitialized, C++, and Fortran issues with PetscDTAltV, other small
fixes

Silence compiler Wmaybe-unitialized warnings in petscdt.h

Loosen tolerances for single precision tests

Fix C++ PetscDTAltv test ex7

Fix complex<->real loops in PetscDTJacobianInverse_Internal

Fix -Wmaybe-unitialized errors in ex7

Improve documentation of PetscDTAltV thanks to criticism from Barry Smith

Protect PetscDTFactorial against negative input

Unbracket SETERRQ

Make "the" -> "a"/"an" more input argument documentation in PetscDTAltV

Rename formIndex to formDegree for consistent notation

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Add PetscQuadraturePushForward to make it easier to use arbitrary node sets in mixed elements

Use getri in PetscDTJacobianInverse_Internal

Remove unneeded header from dt.c that was introduced in fe

Add PetscQuadraturePushForward to make it easier to use arbitrary node sets in mixed elements

Use getri in PetscDTJacobianInverse_Internal

Remove unneeded header from dt.c that was introduced in feature development

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Add PetscDTPermIndex that inverts PetscDTEnumPerm

Document static inlines in petscdt.h

Expose PetscDTFactorial and PetscDTFactorialInt, match with PetscDTBinomial and PetscDTBinomialInt

Document PetscDTAltV

Add PetscDTAltVInteriorPattern that is reusable for multiple inputs

Fix PetscDTAltVInteriorPattern

PetscDTAltV: added interior product pattern check

Update PetscDTAltV tests with interior product

Add PetscDTAltVInteriorPattern that is reusable for multiple inputs

Fix PetscDTAltVInteriorPattern

PetscDTAltV: added interior product pattern check

Update PetscDTAltV tests with interior product output

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Start PetscDTAltV

Added reference implementation of alternating multilinear forms

But I'm going to clean up the interface. I don't think an actual object is necessary
and we want to optimize the c

Start PetscDTAltV

Added reference implementation of alternating multilinear forms

But I'm going to clean up the interface. I don't think an actual object is necessary
and we want to optimize the cases N = 2, 3

PetscDTAltV: change representation order

so that when k != N / 2, there is no reordering in hodge star

PetscDTAltv: New basis for alterting multilinear forms.

For $k$-forms with $2 k \leq N$, the standard lexicographic
basis of $\{dx_{\sigma(1)} \wedge \dots \wedge dx_{\sigma(k)}\}$
is used.

For $2 k > N$, we modify this by first reversing the lexicographic
order, and then swapping $\sigma(1)$ and $\sigma(k)$ if $\sigma$ is odd.
While this involves more sign flips than the basic approach, it has two
good properties:

- it preserves the case as before that the dofs of a row vector /
covector are the dofs of the equivalent 1-form, but now
- the dofs of a contravariant vector (like an H(div)-conforming flux)
are the dofs of the equivalent (N-1)-form (importantly, this means
that the contravariant pullback is the same as the alternating form
pullback)

The only exception is 2D, for which the case is the same as before: the
1-form pullback is the covariant pullback, the contravariant pullback
can be obtained by Hodge star isometry before and afer the pullback.

Remove bad file from rename during merge

PetscDTAltV: interface simplifaction, undo specialized basis.

The fact that the N=2 case wasn't handle bothered me. Now I think the
thing to do is to let PetscDTAltVPullback() and PetscDTAltVInterior() take
negative form degrees, indicating that the pullback/interior product should be
conjugated with the hodge star.

Fix c++ PetscBool issues with PetscDT static inlines

PetscDTAltV: negative form index in pullback...

indicates $\star^{-1} \circ L* \circ$. This gives the contravariant
pullback by $ k=-(N-1)$ in all dimensions.

PetscDTAltV: stop using altv data structures

I'm going to remove the object

PetscDTAltV: Remove object

PetscDTAltV: avoid mallocs/frees for N <= 3

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