# bend-blas: LAPACK routines on Array<F32>, one def per routine, the
# Fortran names without the trailing underscore. Generated by
# gen/effs.py: edit the table there, not this file.
#
# The same conventions as blas.bend: sizes U32, matrices row-major and
# consumed, answers fresh; a general operand is copied to column major
# for LAPACK and back, a symmetric one as it is. A failure is
# Fail{(code, message)} with the routine's info as the code (the pivot
# or minor at fault, from 1); the .try twin dies on it. A routine with
# several answers hands back a pair (Sigma), opened by matching in a
# def of its own.
#
# The symbols (sgesv_ and so on) come from the same library as the BLAS
# (Accelerate, OpenBLAS), or from liblapack beside a plain system BLAS.
# On the interpreter the JS twins run: LU with pivoting, Cholesky, and
# Jacobi for the SVD and the symmetric eigenproblem, correct and slow.
import Base

# X = A^-1 B: A is n x n, B is n x nrhs, both row-major, both consumed;
# answers X (n x nrhs). Fails with code i when U(i, i) of the LU
# factorization is exactly zero (A singular).
def Lapack.sgesv(n: U32, nrhs: U32, a: Array<F32>, b: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32>>):
  import "./effs/lapack_sgesv.c"
  import "./effs/lapack_sgesv.js"

def Lapack.sgesv.try(n: U32, nrhs: U32, a: Array<F32>, b: Array<F32>) -> IO(Array<F32>):
  IO.try(Array<F32>, Lapack.sgesv(n, nrhs, a, b))

# The Cholesky factor of a symmetric positive definite n x n matrix:
# answers L, row-major, lower triangular with zeros above, A = L L^T.
# Fails with code i when the leading minor of order i is not positive.
def Lapack.spotrf(n: U32, a: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32>>):
  import "./effs/lapack_spotrf.c"
  import "./effs/lapack_spotrf.js"

def Lapack.spotrf.try(n: U32, a: Array<F32>) -> IO(Array<F32>):
  IO.try(Array<F32>, Lapack.spotrf(n, a))

# X = A^-1 B given the Cholesky factor L of A from spotrf (n x n, lower,
# row-major) and B (n x nrhs, row-major); both consumed, answers X.
def Lapack.spotrs(n: U32, nrhs: U32, l: Array<F32>, b: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32>>):
  import "./effs/lapack_spotrs.c"
  import "./effs/lapack_spotrs.js"

def Lapack.spotrs.try(n: U32, nrhs: U32, l: Array<F32>, b: Array<F32>) -> IO(Array<F32>):
  IO.try(Array<F32>, Lapack.spotrs(n, nrhs, l, b))

# The singular values of an m x n row-major matrix (consumed), largest
# first, min(m, n) of them.
def Lapack.sgesvd_s(m: U32, n: U32, a: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32>>):
  import "./effs/lapack_sgesvd_s.c"
  import "./effs/lapack_sgesvd_s.js"

def Lapack.sgesvd_s.try(m: U32, n: U32, a: Array<F32>) -> IO(Array<F32>):
  IO.try(Array<F32>, Lapack.sgesvd_s(m, n, a))

# The thin SVD of an m x n row-major matrix (consumed): answers
# (s, (u, vt)) with s the min(m, n) singular values largest first, u
# m x k and vt k x n row-major, A = u diag(s) vt.
def Lapack.sgesvd(m: U32, n: U32, a: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32> & (Array<F32> & Array<F32>)>):
  import "./effs/lapack_sgesvd.c"
  import "./effs/lapack_sgesvd.js"

def Lapack.sgesvd.try(m: U32, n: U32, a: Array<F32>) -> IO(Array<F32> & (Array<F32> & Array<F32>)):
  IO.try(Array<F32> & (Array<F32> & Array<F32>), Lapack.sgesvd(m, n, a))

# The eigenvalues and eigenvectors of a symmetric n x n row-major matrix
# (consumed, its lower triangle read): answers (w, v) with w the n
# eigenvalues ascending and v n x n row-major, row i the unit eigenvector
# of w[i].
def Lapack.ssyev(n: U32, a: Array<F32>) -> IO(Result<&1, &1, U32 & String, Array<F32> & Array<F32>>):
  import "./effs/lapack_ssyev.c"
  import "./effs/lapack_ssyev.js"

def Lapack.ssyev.try(n: U32, a: Array<F32>) -> IO(Array<F32> & Array<F32>):
  IO.try(Array<F32> & Array<F32>, Lapack.ssyev(n, a))