Float32 support

[delta-leader]

Template the following classes (with hardcoded "double" in the rest of the code):

• Dense
• LowRank
• Hierarchical
• MatrixProxy, Matrix? (should not be necessary)
• IndexRange (split_like function)
• MatrixInitializer (no template necessary, can fill any type of matrix)
• MatrixInitializerFile (no template necessary, reads doubles and can fill any type of matrix)
• MatrixInitializerBlock (template for the datatype of the matrix to be copied from, can fill any type of matrix)
• MatrixInitializerFunction(template for the matrix kernel, can only fill double matrix from double function
• MatrixKernel (removed for now)

Template functions so that they can support both double and float:

• Initialization:
• Functions (kernels for filling matrices - currently limited to double params)
• Find a better solution for filling from functions/kernels
• Misc:
• split (Hierarchical; note that his calls an omm that does not work for float yet)
• get_dim
• misc
• morton_index (not templated because currently not in use)
• norm
• resize
• transpose
• randomized:
• rid
• rsvd
• operations:
• addition (plus operator finished - extend to OMM?)
• multiplication (what happens in case of float*double?)
• subtraction

Extend classes to "float" - OMM:

• Dense - Constructor from MatrixProxy (If MatrixProxy is not of the same Type a bad_cast exception is thrown instead of omm_error and aborting; EDIT: found a solution that works with YOMM)
• Dense - Constructor from Matrix (no float types for Hierarchical and LowRank yet)
• Dense - implicit type conversion? (currently only explicit conversion allowed)
• Matrix Proxy (both clone and move_clone)

Extend functions to "float" - OMM:

• Misc:
• get_dim
• resize
• norm
• BLAS (What to do with double parameters for BLAS calls?):
• gemm (alpha, beta remain double, template type is deduced depending on the type of Matrix passed in)
• trmm
• trsm
• LAPACK:
• gepq3
• geqrt
• id
• larfb
• lartms
• qr
• svd (template specialization for float and double)
• tpmqrt
• tpqrt
• Util:
• experiment_setup
• geometry_file (not templated since parameters remain double)
• get_memory_usage
• global_key_value (no template needed)
• l2_error
• omm_error_handler (no template needed)
• print
• timer (no template needed)
• Arithmetic:
• subtraction
• addition
• merge_col_basis
• merge_row_basis

Write test functions:

• Initialization:
• ClusterTree
• IndexRange
• MatrixFunctions
• MatrixInitializer (except coordinate based admissibility for Kernel)
• Dense:
• Standard Constructor, Construct from dimensions and Copy-Constructor
• Construct from Kernel
• Construct from other Matrix types
• Construct from MatrixProxy
• Construct from File?
• Assignment (currently only allowed for identical datatypes)
• split function (currently only for double)
• LowRank:
• Standard Constructor, Construct from 3 matrices
• Construct from Dense
• Hierarchical:
• Constructors (except from file)
• operations:
• addition (currently only for dense)
• subtraction?
• scalar multiply?
• BLAS:
• gemm
• trmm
• trsm
• LAPACK:
• gepq3
• geqrt
• id
• larfb
• lartms
• qr
• svd
• tpmqrt
• tpqrt
• Misc:
• get_dim
• misc
• morton_index
• norm
• resize
• transpose
• randomized:
• rid
• rsvd
• util:
• experiment_setup
• geometry_file (not templated since parameters remain double)
• get_memory_usage
• global_key_value (no template needed)
• l2_error
• omm_error_handler (no template needed)
• print
• timer (no template needed)

Requires addition of the corresponding float functions from BLAS/LAPACK:

• BLAS - float
• LAPACK - float
• Define operations between double and float?

Notes:
Prioritize getting a working single-precision implementation with a hierarchical LU test-case. Other test cases can be added later and the limitations described below should only be addressed if there is an actual need for their functionality.

Initialization from Kernel-Functions is still considerably restricted. The following limitations apply:

• Geometry information can only be
• Random number generators can only be
• Seed for the random number generators can not be set
• Admissibility can not be passed as a function
• Only pre-defined kernel-functions are available

There are also some shortcomings in arithmetics:

• Addition operator += is defined for all matrix types while operator + is only defined for dense
• Subtraction operator -= is not defined
• Multiplication (Scalar) is only defined for double (restrict? allow for mixed precision?)
• Multiplication (Scalar) operator * is not defined

Investigate how a MatrixProxy is conerted into a Matrix (i.e. is that template safe?)
Automatic template deduction does not work for return type, in some cases old C style might be better (include return type as argument)
Shall we change the return value of functions that return a double to float?