Mitchell Documentation

Copyright 2019 Systems & Technology Research, LLC and other contributors.

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Linear Algebra (GSL Bindings)

Mitchell includes bindings to a portion of the GNU Scientific Library (GSL) for performing linear algebra computations. The provided bindings are listed below. Documentation on the behavior of these procedures can be found at the GSL documentation page.

Specific documentation for the dense linear algebra bindings can be found at

Specific documentation for the sparse linear algebra bindings can be found at

Interface

Types

  • type Vector
  • type Matrix
  • type VectorComplex
  • type EigenGenWorkspace
  • type EigenGenSymmvWorkspace
  • Flag used for blas_dgemv, blas_dgemm, and spblas_dgemv. 
      datatype CblasTranspose =
           CblasNoTrans
           | CblasTrans
           | CblasConjTrans
  • Flag used for spmatrix_alloc_nzmax. 
      datatype SpType =
           SpMatrixTriplet
           | SpMatrixCcs
           | SpMatrixCrs

Methods

Dense

  • val error : string * string * Int32.int * Int32.int -> unit
  • val stream_printf : string * string * Int32.int * string -> unit
  • val strerror : Int32.int -> string
  • val error_handler_t : string * string * Int32.int * Int32.int -> unit
  • val stream_handler_t : string * string * Int32.int * string -> unit
  • val vector_alloc : Int64.int -> Vector
  • val vector_calloc : Int64.int -> Vector
  • val vector_alloc_from_vector : Vector * Int64.int * Int64.int * Int64.int -> Vector
  • val vector_free : Vector -> unit
  • val vector_set_zero : Vector -> unit
  • val vector_set_all : Vector * Real64.real -> unit
  • val vector_set_basis : Vector * Int64.int -> Int32.int
  • val vector_memcpy : Vector * Vector -> Int32.int
  • val vector_reverse : Vector -> Int32.int
  • val vector_swap : Vector * Vector -> Int32.int
  • val vector_swap_elements : Vector * Int64.int * Int64.int -> Int32.int
  • val vector_max : Vector -> Real64.real
  • val vector_min : Vector -> Real64.real
  • val vector_minmax : Vector * Real64.real vector * Real64.real vector -> unit
  • val vector_max_index : Vector -> Int64.int
  • val vector_min_index : Vector -> Int64.int
  • val vector_add : Vector * Vector -> Int32.int
  • val vector_sub : Vector * Vector -> Int32.int
  • val vector_mul : Vector * Vector -> Int32.int
  • val vector_div : Vector * Vector -> Int32.int
  • val vector_scale : Vector * Real64.real -> Int32.int
  • val vector_add_constant : Vector * Real64.real -> Int32.int
  • val vector_equal : Vector * Vector -> Int32.int
  • val vector_isnull : Vector -> Int32.int
  • val vector_ispos : Vector -> Int32.int
  • val vector_isneg : Vector -> Int32.int
  • val vector_isnonneg : Vector -> Int32.int
  • val vector_get : Vector * Int64.int -> Real64.real
  • val vector_set : Vector * Int64.int * Real64.real -> unit
  • val vector_ptr : Vector * Int64.int -> Real64.real vector
  • val vector_const_ptr : Vector * Int64.int -> Real64.real vector
  • val vector_complex_alloc : Int64.int -> VectorComplex
  • val vector_complex_calloc : Int64.int -> VectorComplex
  • val vector_complex_alloc_from_vector : VectorComplex * Int64.int * Int64.int * Int64.int -> VectorComplex
  • val vector_complex_free : VectorComplex -> unit
  • val vector_complex_set_zero : VectorComplex -> unit
  • val vector_complex_set_basis : VectorComplex * Int64.int -> Int32.int
  • val vector_complex_memcpy : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_reverse : VectorComplex -> Int32.int
  • val vector_complex_swap : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_swap_elements : VectorComplex * Int64.int * Int64.int -> Int32.int
  • val vector_complex_equal : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_isnull : VectorComplex -> Int32.int
  • val vector_complex_ispos : VectorComplex -> Int32.int
  • val vector_complex_isneg : VectorComplex -> Int32.int
  • val vector_complex_isnonneg : VectorComplex -> Int32.int
  • val vector_complex_add : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_sub : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_mul : VectorComplex * VectorComplex -> Int32.int
  • val vector_complex_div : VectorComplex * VectorComplex -> Int32.int
  • val matrix_alloc : Int64.int * Int64.int -> Matrix
  • val matrix_calloc : Int64.int * Int64.int -> Matrix
  • val matrix_alloc_from_matrix : Matrix * Int64.int * Int64.int * Int64.int * Int64.int -> Matrix
  • val vector_alloc_row_from_matrix : Matrix * Int64.int -> Vector
  • val vector_alloc_col_from_matrix : Matrix * Int64.int -> Vector
  • val matrix_free : Matrix -> unit
  • val matrix_set_zero : Matrix -> unit
  • val matrix_set_identity : Matrix -> unit
  • val matrix_set_all : Matrix * Real64.real -> unit
  • val matrix_memcpy : Matrix * Matrix -> Int32.int
  • val matrix_swap : Matrix * Matrix -> Int32.int
  • val matrix_swap_rows : Matrix * Int64.int * Int64.int -> Int32.int
  • val matrix_swap_columns : Matrix * Int64.int * Int64.int -> Int32.int
  • val matrix_swap_rowcol : Matrix * Int64.int * Int64.int -> Int32.int
  • val matrix_transpose : Matrix -> Int32.int
  • val matrix_transpose_memcpy : Matrix * Matrix -> Int32.int
  • val matrix_max : Matrix -> Real64.real
  • val matrix_min : Matrix -> Real64.real
  • val matrix_minmax : Matrix * Real64.real vector * Real64.real vector -> unit
  • val matrix_equal : Matrix * Matrix -> Int32.int
  • val matrix_isnull : Matrix -> Int32.int
  • val matrix_ispos : Matrix -> Int32.int
  • val matrix_isneg : Matrix -> Int32.int
  • val matrix_isnonneg : Matrix -> Int32.int
  • val matrix_add : Matrix * Matrix -> Int32.int
  • val matrix_sub : Matrix * Matrix -> Int32.int
  • val matrix_mul_elements : Matrix * Matrix -> Int32.int
  • val matrix_div_elements : Matrix * Matrix -> Int32.int
  • val matrix_scale : Matrix * Real64.real -> Int32.int
  • val matrix_add_constant : Matrix * Real64.real -> Int32.int
  • val matrix_add_diagonal : Matrix * Real64.real -> Int32.int
  • val matrix_get_row : Vector * Matrix * Int64.int -> Int32.int
  • val matrix_get_col : Vector * Matrix * Int64.int -> Int32.int
  • val matrix_set_row : Matrix * Int64.int * Vector -> Int32.int
  • val matrix_set_col : Matrix * Int64.int * Vector -> Int32.int
  • val matrix_get : Matrix * Int64.int * Int64.int -> Real64.real
  • val matrix_set : Matrix * Int64.int * Int64.int * Real64.real -> unit
  • val matrix_ptr : Matrix * Int64.int * Int64.int -> Real64.real vector
  • val matrix_const_ptr : Matrix * Int64.int * Int64.int -> Real64.real vector
  • val log1p : Real64.real -> Real64.real
  • val expm1 : Real64.real -> Real64.real
  • val hypot : Real64.real * Real64.real -> Real64.real
  • val hypot3 : Real64.real * Real64.real * Real64.real -> Real64.real
  • val acosh : Real64.real -> Real64.real
  • val asinh : Real64.real -> Real64.real
  • val atanh : Real64.real -> Real64.real
  • val isnan : Real64.real -> Int32.int
  • val isinf : Real64.real -> Int32.int
  • val finite : Real64.real -> Int32.int
  • val nan : unit -> Real64.real
  • val posinf : unit -> Real64.real
  • val neginf : unit -> Real64.real
  • val fdiv : Real64.real * Real64.real -> Real64.real
  • val coerce_double : Real64.real -> Real64.real
  • val ldexp : Real64.real * Int32.int -> Real64.real
  • val fcmp : Real64.real * Real64.real * Real64.real -> Int32.int
  • val pow_2 : Real64.real -> Real64.real
  • val pow_3 : Real64.real -> Real64.real
  • val pow_4 : Real64.real -> Real64.real
  • val pow_5 : Real64.real -> Real64.real
  • val pow_6 : Real64.real -> Real64.real
  • val pow_7 : Real64.real -> Real64.real
  • val pow_8 : Real64.real -> Real64.real
  • val pow_9 : Real64.real -> Real64.real
  • val pow_int : Real64.real * Int32.int -> Real64.real
  • val max : Real64.real * Real64.real -> Real64.real
  • val min : Real64.real * Real64.real -> Real64.real
  • val cblas_ddot : Int32.int * Real64.real vector * Int32.int * Real64.real vector * Int32.int -> Real64.real
  • val cblas_dnrm2 : Int32.int * Real64.real vector * Int32.int -> Real64.real
  • val cblas_dasum : Int32.int * Real64.real vector * Int32.int -> Real64.real
  • val cblas_idamax : Int32.int * Real64.real vector * Int32.int -> Int64.int
  • val cblas_dswap : Int32.int * Real64.real vector * Int32.int * Real64.real vector * Int32.int -> unit
  • val cblas_dcopy : Int32.int * Real64.real vector * Int32.int * Real64.real vector * Int32.int -> unit
  • val cblas_daxpy : Int32.int * Real64.real * Real64.real vector * Int32.int * Real64.real vector * Int32.int -> unit
  • val cblas_drotg : Real64.real vector * Real64.real vector * Real64.real vector * Real64.real vector -> unit
  • val cblas_drotmg : Real64.real vector * Real64.real vector * Real64.real vector * Real64.real * Real64.real vector -> unit
  • val cblas_drot : Int32.int * Real64.real vector * Int32.int * Real64.real vector * Int32.int * Real64.real * Real64.real -> unit
  • val cblas_drotm : Int32.int * Real64.real vector * Int32.int * Real64.real vector * Int32.int * Real64.real vector -> unit
  • val cblas_dscal : Int32.int * Real64.real * Real64.real vector * Int32.int -> unit
  • val blas_ddot : Vector * Vector * Real64.real vector -> Int32.int
  • val blas_dnrm2 : Vector -> Real64.real
  • val blas_dasum : Vector -> Real64.real
  • val blas_dznrm2 : VectorComplex -> Real64.real
  • val blas_dzasum : VectorComplex -> Real64.real
  • val blas_dswap : Vector * Vector -> Int32.int
  • val blas_dcopy : Vector * Vector -> Int32.int
  • val blas_daxpy : Real64.real * Vector * Vector -> Int32.int
  • val blas_zswap : VectorComplex * VectorComplex -> Int32.int
  • val blas_zcopy : VectorComplex * VectorComplex -> Int32.int
  • val blas_drot : Vector * Vector * Real64.real * Real64.real -> Int32.int
  • val blas_dscal : Real64.real * Vector -> unit
  • val blas_zdscal : Real64.real * VectorComplex -> unit
  • val blas_dger : Real64.real * Vector * Vector * Matrix -> Int32.int
  • val linalg_matmult : Matrix * Matrix * Matrix -> Int32.int
  • val linalg_householder_transform : Vector -> Real64.real
  • val linalg_householder_hm : Real64.real * Vector * Matrix -> Int32.int
  • val linalg_householder_mh : Real64.real * Vector * Matrix -> Int32.int
  • val linalg_householder_hv : Real64.real * Vector * Vector -> Int32.int
  • val linalg_householder_hm1 : Real64.real * Matrix -> Int32.int
  • val linalg_hessenberg_decomp : Matrix * Vector -> Int32.int
  • val linalg_hessenberg_unpack : Matrix * Vector * Matrix -> Int32.int
  • val linalg_hessenberg_unpack_accum : Matrix * Vector * Matrix -> Int32.int
  • val linalg_hessenberg_set_zero : Matrix -> Int32.int
  • val linalg_hessenberg_submatrix : Matrix * Matrix * Int64.int * Vector -> Int32.int
  • val linalg_hesstri_decomp : Matrix * Matrix * Matrix * Matrix * Vector -> Int32.int
  • val linalg_SV_decomp : Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_SV_decomp_mod : Matrix * Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_SV_decomp_jacobi : Matrix * Matrix * Vector -> Int32.int
  • val linalg_SV_solve : Matrix * Matrix * Vector * Vector * Vector -> Int32.int
  • val linalg_SV_leverage : Matrix * Vector -> Int32.int
  • val linalg_LU_det : Matrix * Int32.int -> Real64.real
  • val linalg_LU_lndet : Matrix -> Real64.real
  • val linalg_LU_sgndet : Matrix * Int32.int -> Int32.int
  • val linalg_QR_decomp : Matrix * Vector -> Int32.int
  • val linalg_QR_solve : Matrix * Vector * Vector * Vector -> Int32.int
  • val linalg_QR_svx : Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_lssolve : Matrix * Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_QR_QRsolve : Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_Rsolve : Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_Rsvx : Matrix * Vector -> Int32.int
  • val linalg_QR_update : Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_QTvec : Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_Qvec : Matrix * Vector * Vector -> Int32.int
  • val linalg_QR_QTmat : Matrix * Vector * Matrix -> Int32.int
  • val linalg_QR_matQ : Matrix * Vector * Matrix -> Int32.int
  • val linalg_QR_unpack : Matrix * Vector * Matrix * Matrix -> Int32.int
  • val linalg_R_solve : Matrix * Vector * Vector -> Int32.int
  • val linalg_R_svx : Matrix * Vector -> Int32.int
  • val linalg_QRPT_rank : Matrix * Real64.real -> Int64.int
  • val linalg_QRPT_rcond : Matrix * Real64.real vector * Vector -> Int32.int
  • val linalg_COD_unpack : Matrix * Vector * Vector * Int64.int * Matrix * Matrix * Matrix -> Int32.int
  • val linalg_COD_matZ : Matrix * Vector * Int64.int * Matrix * Vector -> Int32.int
  • val linalg_LQ_decomp : Matrix * Vector -> Int32.int
  • val linalg_LQ_solve_T : Matrix * Vector * Vector * Vector -> Int32.int
  • val linalg_LQ_svx_T : Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_lssolve_T : Matrix * Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_LQ_Lsolve_T : Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_Lsvx_T : Matrix * Vector -> Int32.int
  • val linalg_L_solve_T : Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_vecQ : Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_vecQT : Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_unpack : Matrix * Vector * Matrix * Matrix -> Int32.int
  • val linalg_LQ_update : Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_LQ_LQsolve : Matrix * Matrix * Vector * Vector -> Int32.int
  • val linalg_cholesky_decomp : Matrix -> Int32.int
  • val linalg_cholesky_decomp1 : Matrix -> Int32.int
  • val linalg_cholesky_solve : Matrix * Vector * Vector -> Int32.int
  • val linalg_cholesky_svx : Matrix * Vector -> Int32.int
  • val linalg_cholesky_invert : Matrix -> Int32.int
  • val linalg_cholesky_decomp_unit : Matrix * Vector -> Int32.int
  • val linalg_cholesky_scale : Matrix * Vector -> Int32.int
  • val linalg_cholesky_scale_apply : Matrix * Vector -> Int32.int
  • val linalg_cholesky_decomp2 : Matrix * Vector -> Int32.int
  • val linalg_cholesky_svx2 : Matrix * Vector * Vector -> Int32.int
  • val linalg_cholesky_solve2 : Matrix * Vector * Vector * Vector -> Int32.int
  • val linalg_cholesky_rcond : Matrix * Real64.real vector * Vector -> Int32.int
  • val linalg_symmtd_decomp : Matrix * Vector -> Int32.int
  • val linalg_symmtd_unpack : Matrix * Vector * Matrix * Vector * Vector -> Int32.int
  • val linalg_symmtd_unpack_T : Matrix * Vector * Vector -> Int32.int
  • val linalg_HH_solve : Matrix * Vector * Vector -> Int32.int
  • val linalg_HH_svx : Matrix * Vector -> Int32.int
  • val linalg_solve_symm_tridiag : Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_solve_tridiag : Vector * Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_solve_symm_cyc_tridiag : Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_solve_cyc_tridiag : Vector * Vector * Vector * Vector * Vector -> Int32.int
  • val linalg_bidiag_decomp : Matrix * Vector * Vector -> Int32.int
  • val linalg_bidiag_unpack : Matrix * Vector * Matrix * Vector * Matrix * Vector * Vector -> Int32.int
  • val linalg_bidiag_unpack2 : Matrix * Vector * Vector * Matrix -> Int32.int
  • val linalg_bidiag_unpack_B : Matrix * Vector * Vector -> Int32.int
  • val linalg_balance_matrix : Matrix * Vector -> Int32.int
  • val linalg_balance_accum : Matrix * Vector -> Int32.int
  • val linalg_balance_columns : Matrix * Vector -> Int32.int
  • val linalg_tri_upper_rcond : Matrix * Real64.real vector * Vector -> Int32.int
  • val linalg_tri_lower_rcond : Matrix * Real64.real vector * Vector -> Int32.int
  • val linalg_tri_upper_invert : Matrix -> Int32.int
  • val linalg_tri_lower_invert : Matrix -> Int32.int
  • val linalg_tri_upper_unit_invert : Matrix -> Int32.int
  • val linalg_tri_lower_unit_invert : Matrix -> Int32.int
  • val linalg_givens : Real64.real * Real64.real * Real64.real vector * Real64.real vector -> unit
  • val linalg_givens_gv : Vector * Int64.int * Int64.int * Real64.real * Real64.real -> unit
  • val eigen_gensymm_standardize : Matrix * Matrix -> Int32.int
  • val eigen_gensymmv_alloc : Int64.int -> EigenGenSymmvWorkspace
  • val eigen_gensymmv_free : EigenGenSymmvWorkspace -> unit
  • val eigen_gensymmv : Matrix * Matrix * Vector * Matrix * EigenGenSymmvWorkspace -> Int32.int
  • val eigen_gen_alloc : Int64.int -> EigenGenWorkspace
  • val eigen_gen_free : EigenGenWorkspace -> unit
  • val eigen_gen_params : Int32.int * Int32.int * Int32.int * EigenGenWorkspace -> unit
  • val eigen_gen : Matrix * Matrix * VectorComplex * Vector * EigenGenWorkspace -> Int32.int
  • val eigen_gen_QZ : Matrix * Matrix * VectorComplex * Vector * Matrix * Matrix * EigenGenWorkspace -> Int32.int
  • val schur_gen_eigvals : Matrix * Matrix * Real64.real vector * Real64.real vector * Real64.real vector * Real64.real vector * Real64.real vector -> Int32.int
  • val schur_solve_equation : Real64.real * Matrix * Real64.real * Real64.real * Real64.real * Vector * Vector * Real64.real vector * Real64.real vector * Real64.real -> Int32.int
  • val blas_dgemv : CblasTranspose * Real64.real * Matrix * Vector * Real64.real * Vector -> Int32.int
  • val blas_dgemm : CblasTranspose * CblasTranspose * Real64.real * Matrix * Matrix * Real64.real * Matrix -> Int32.int

Sparse

  • val spmatrix_alloc : Int64.int * Int64.int -> SpMatrix
  • val spmatrix_alloc_nzmax : Int64.int * Int64.int * Int64.int * SpType -> SpMatrix
  • val spmatrix_free : SpMatrix -> unit
  • val spmatrix_get : SpMatrix * Int64.int * Int64.int -> Real64.real
  • val spmatrix_set : SpMatrix * Int64.int * Int64.int * Real64.real -> Int32.int
  • val spmatrix_set_zero : SpMatrix -> Int32.int
  • val spmatrix_memcpy : SpMatrix * SpMatrix -> Int32.int
  • val spmatrix_transpose_memcpy : SpMatrix * SpMatrix -> Int32.int
  • val spmatrix_transpose : SpMatrix -> Int32.int
  • val spmatrix_transpose2 : SpMatrix -> Int32.int
  • val spmatrix_add : SpMatrix * SpMatrix * SpMatrix -> Int32.int
  • val spmatrix_scale : SpMatrix * Real64.real -> Int32.int
  • val spmatrix_nnz : SpMatrix -> Int64.int
  • val spmatrix_d2sp : SpMatrix * Matrix -> Int32.int
  • val spmatrix_sp2d : Matrix * SpMatrix -> Int32.int
  • val spblas_gemv : CblasTranspose * Real64.real * SpMatrix * Vector * Real64.real * Vector -> Int32.int
  • val spblas_dgemm : Real64.real * SpMatrix * SpMatrix * SpMatrix -> Int32.int