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Magicl NG (quil-lang#63)

* Add initial version of magicl high-level rewrite

* Add *derive-function-types* to asdf project

* Add random, fix multiplication, add lapack, make things work

* Fix idenetity typo

* Fix empty and deye documentation and fix assert-square-matrix printing whole matrix

* Remove FASL in high-level dir (Why was that there?)

* Fix indentation in matrix.lisp and clean up trace

* Add macro to generate blas mult boilerplate

* Remove old version of matrix/double-float

* Add lapack macros to make mult work

* Fix from-*-major-index and add tests for util file

* Move lapack method definitions into macros for ease of use

* Add square restriction to qr/ql/rq/lq

* Remove magicl from :use on packages to avoid shadowing errors

* Add support for calling PPRINT-MATRIX within FORMAT

* Add distribution as function to RAND and add tests

* Add lapack inverse to high level and finish updating examples to new interface

* Remove debug message from lapack-inv

* Update TEST-RANDOM-UNITARY and TEST-LOGM to new interface

* Fix TEST-KRON

* Gave it some throught. It should work.

* Add p-norm to vector type

* Add slice to ABSTRACT-TENSOR

- Slice implemented for abstract-tensor
- Docstrings cleaned up
- TODOs TODONE

* Remove TODO regarding if it makes sense. It makes sense.

* Fix tests not calling all the tests

* Fix constant redefinition in magicl-tests caused by incorrect test predicate

* Extract function for type inferring in tensor constructors

* Clean up TODOs in high-level

* Reduce oddity in abstract-tensor-tests and include dim=1 case

* Fix TEST-TENSOR-SHAPE and TEST-TENSOR-RANK with more advanced loops

* Remove unneeded multiplication of shape in FROM-DIAG constructor

* Update high-level docstrings to be more uniform and descriptive and add order parameters to map and into

* Implement VALID-INDEX-P properly and use in high-level

* Fix teh typo and bad indentation in high-level-tests

* Fix indentation in INFER-TENSOR-TYPE

* Fix VALID-INDEX-P to allow for not specifying shape

* Make map and into functions more readable

* Change high-level constructors to functions from generic functions

* Make DEFVECTOR/DEFMATRIX macros more expandable

* Add HERMITIAN-EIG to new high-level interface

* Fix appleby's nitpicks

* Add policy-cond for performance when speed > safety and directly construct classes

* Switch from CLOS to structs for tensor objects

This gives a significant performance improvement due to avoiding generics
at the cost of some flexibility and my sanity.

* Remove freeze on tensor struct causing type error

* Fix pretty printing for matrix and tensor types and remove old methods

* Remove accidentally committed log files

* Add (SETF SHAPE) and optimize matrix TREF

* Remove warnings from unused arguments and load order

* Add basic documentation for high-level interface

* Fix bug in transpose on matrix with dimension of 1

* Add integer printing to matrix and vector pretty printers

* Change from dynamic to static symbols in INFER-TENSOR-TYPE and move to appropriate file

* Add CAST, a replacement for CHANGE-CLASS on tensors

* Clean up util and comments

* Add subtypes and straggling symbols to package

* Add reduced svd interface and tests (quil-lang#65)

* Add CSD-2X2-BASIC (quil-lang#67)

* Use use-expectations in the expected way

* Change ABSTRACT-TENSOR to not allow for construction or copying

* Move magicl high-level into module in ASDF

* Clean up documentation for ABSTRACT-TENSOR

* Replace POLICY-IF with WITH-EXPECTATIONS in constructors

* Fix mistake in abstract-tensor docstring

* Use COPY-SEQ for copying tensor storage and add copiers to vector

* Remove funky comma in ASSERT-SQUARE-SHAPE

* Move lapack bindings to lapack-bindings.lisp and switch to functions to generate lapack code

* Update docstrings for DEFTENSOR, DEFMATRIX, DEFVECTOR, and DEFCOMPATIBLE

* Fix other library equivalents table errors

Co-Authored-By: Juan M. Bello-Rivas <jbellorivas@rigetti.com>

* Change def- to generate- in lapack-templates to reflect change from macro to func

* Add numpy rq to high-level doc

* Change terminology regarding indexing and number of dimensions of tensors

ORDER is now LAYOUT
RANK is now ORDER

* Remove LAYOUT arg from INTO! and FOREACH in abstract tensor interface

These fields do not make sense to have on a method which is calling a function independent of the ordering of the elements

* Add ZEROS and ONES constructors for convenience

* Remove square requirement from DEYE constructor

* Remove ORDER 2 requirement from DEYE

* Rename DEYE to EYE

* Add TRIL and TRIU synonyms and change DAGGER(!) to synonyms

* Add TRIL/TRIU to package

* Add issue number to ZUNCSD shim

* Replace = with := in LOOPs

* Allow for FIXNUM in EYE shape and remove SHAPE requirement from FROM-DIAG

* Update tests to refelect change in FROM-DIAG interface

* Add BINARY-OPERATOR method and add '.' prefix to element-wise operators

* Update documentation for elementwise operators

* Remove unwanted argument on FROM-DIAG

* Fix typo, represening how bad I am at speling

* Fix RAND docstring to be more documenting

* Allow for multiple tensors in every, any, notevery, notany

* Fix bug in hermitian-eig caused by copying/resetting layout slot on return and export method

* Export slice and mult from high-level

* Fix expm returning incorrect layout for result

* Bump version to 0.7.0

* Symbol case invariance. Drop unused declarations (quil-lang#74)

* Add optimizations for MATRIX class

Add matrix-{row,column}-major-index
Add specialized INTO! for MATRIX class
Add make-storage for matrix class

* Update documentation to be more correct

Apply suggestions from code review

Co-Authored-By: appleby <mappleby@rigetti.com>

* Change INVERSE -> INV

* Change POLICY-IF to POLICY-COND

herminitan-matrix-p has a strict epsilon added to avoid test failures

* Fix LAYOUT->ORDER in high-level docs

* Fix indentation in high-level docs

* Fix deye->eye in high-level docs

* Add check for valid index to tref and setf tref in vector and tensor classes

* Change default tensor type to var to allow for rebinding

* Remove unneeded variable in hermitian-eig

* Force square shape for upper and lower triangular of matrix

* Update element-wise exponentiation in high-level docs to be consistent

* Update examples.lisp

Co-Authored-By: Erik Davis <erik@rigetti.com>

* Remove layout from ARANGE constructor

layout is not needed because it returns a vector

* Fix tensor equality errors and add corresponding tests

* Add equality for float vectors and fix error in high-level tests

* Overhaul p-norm for vectors and add tests

* Update documentation for numpy hermitian transpose

* Fix p-norm for infinite norm of negative single element vectors

* Change float comparison thresholds to variables

* Change *-MATRIX-P to functions

* Fix incorrect assertion in p-norm of vector

* Apply suggestions from code review

Co-Authored-By: Erik Davis <erik@rigetti.com>

* Remove ORTHONORMALIZE methods for matrices (just use QR)

* Add check for singular matrices in INV folllowing call to LU

* Remove old note about LU requried for INV.

INV now calls the LU LAPACK routine directly and does not require LU to be defined.

* Add P-NORM-TYPE and modify vector norm to use type and to disallow negative infinity

Co-authored-by: Juan M. Bello-Rivas <jmbr@superadditive.com>
Co-authored-by: appleby <mappleby@rigetti.com>
Co-authored-by: Erik Davis <erik@cadlag.org>

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