lapack_base.fs is the main user Application Program Interface (API). It uses F# Power Pack's Microsoft.FSharp.Math matrix and vector extensively.
The lapack_bas.fs API wraps the existing LAPACK API, but how completely I am not sure. Let's answer that question here.
LAPACK divides its functions into three types: drivers, computational, auxilary.
http://www.netlib.org/lapack/lug/node22.html
LAPACK handles 4 types of data primitives :
S 
REAL 
D 
DOUBLE PRECISION 
C 
COMPLEX 
Z 
COMPLEX*16 or DOUBLE COMPLEX 
But lapack_base.fs seems to ignore all but double. Thus all the functions begin with "d". It seems that complex numbers are not handled by lapack_base. Microsoft.FSharp.Math.Complex exists, so MathProvider could handle complex someday.
LAPACK handles these types of matrices:
BD 
bidiagonal 
DI 
diagonal 
GB 
general band 
GE 
general (i.e., unsymmetric, in some cases rectangular) 
GG 
general matrices, generalized problem (i.e., a pair of general matrices) 
GT 
general tridiagonal 
HB 
(complex) Hermitian band 
HE 
(complex) Hermitian 
HG 
upper Hessenberg matrix, generalized problem (i.e a Hessenberg and a 

triangular matrix) 
HP 
(complex) Hermitian, packed storage 
HS 
upper Hessenberg 
OP 
(real) orthogonal, packed storage 
OR 
(real) orthogonal 
PB 
symmetric or Hermitian positive definite band 
PO 
symmetric or Hermitian positive definite 
PP 
symmetric or Hermitian positive definite, packed storage 
PT 
symmetric or Hermitian positive definite tridiagonal 
SB 
(real) symmetric band 
SP 
symmetric, packed storage 
ST 
(real) symmetric tridiagonal 
SY 
symmetric 
TB 
triangular band 
TG 
triangular matrices, generalized problem (i.e., a pair of triangular matrices) 
TP 
triangular, packed storage 
TR 
triangular (or in some cases quasitriangular) 
TZ 
trapezoidal 
UN 
(complex) unitary 
UP 
(complex) unitary, packed storage 
lapack_base.fs exposes the following subset: GE,PO,TR,SY,GG
Let's look at the drivers (high level functions). LAPACK has these:
Linear Equations Driver
SV Simple
SVX Expert
lapack_base.fs exposes: SV
Least Squares Driver
LS Least Squares
LSE Least Squares Equalityconstrained
GLM General Linear Model
lapack_base.fs exposes: LS, LSE
EigenValue/Vector Driver
EV Computes eigenvalues and eigenvalues simply
EVX Computes eigenvectors and eigenvalues expertly
EVD Divide and conquer
EVR Relatively Robust Representation
ES Schur factorization
lapack_base.fs exposes EV
Singular Value Decomposition
SVD Simple Singular Value Decomposition
SDD Improved SVD
lapack_base.fs exposes: SVD, SDD
There are a few more areas to cover, but...
To conclude: lapack_base.fs exposes about onehalf of the calls of LAPACK (no doubt the most important ones!).
