mplinsolve

mplinsolve(A, b, solver, opt)

mplinsolve() - Solve A * x = b using specified solver.

x = mplinsolve(A, b)
x = mplinsolve(A, b, solver)
x = mplinsolve(A, b, solver, opt)
x = mplinsolve(factors, b, ...)
factors = mplinsolve(A)
factors = mplinsolve(A, [], ...)
[x, factors] = mplinsolve(A, b, 'lu' ...)

Solves the linear system of equations A * x == b for x using the selected solver.

Inputs:

  • A (double) – sparse matrix

  • factors (struct) – contains (e.g. LU) factors of A from previous call to mplinsolve(), with a type field to identify which of the following sets of additional fields are included:

    type

    add’l fields

    description

    1

    L, U, p, qa

    3 output Gilbert-Peierls, permutation vectors

    2

    L, U, P, Qa

    3 output Gilbert-Peierls, permutation matrices

    3

    L, U, p, q

    4 output UMFPACK, permutation vectors

    4

    L, U, P, Q

    4 output UMFPACK, permutation matrices

    5

    L, U, p, q, R

    same as 3, with row scaling

    6

    L, U, P, Q, R

    same as 4, with row scaling

  • b (double) – RHS vector (or full matrix)

  • solver (char array) – (optional, default '' ) selected linear system solver

    • '' – use default solver, currently this is always the built-in backslash operator

    • '\' – built-in backslash operator

    • 'LU' – use explicit LU decomposition and back substitution

      The following are also provided as short-cuts, with less overhead and thus better performance on small systems, as alternatives for 'LU' with the following options:

      solver

      opt.lu.nout

      opt.lu.vec

      opt.lu.thresh

      'LU3'

      3

      1

      1.0

      'LU3a'

      3

      1

      'LU4'

      4

      1

      'LU5'

      5

      1

      'LU3m'

      3

      0

      1.0

      'LU3am'

      3

      0

      'LU4m'

      4

      0

      'LU5m'

      5

      0

    • 'PARDISO' – PARDISO

  • opt (struct) – options for certain solvers (e.g. lu() and PARDISO), with fields:

    • lu : struct of options to determine form of call to lu() solver, with the following possible fields (default value in parens):

      • nout (4) - number of output args for call to lu(), UMFPACK is used for 4 or 5 output args, Gilbert-Peierls algorithm with AMD ordering for 3 output args.

      • vec (1) - use permutation vectors instead of matrices (permutation matrices used by default for MATLAB < 7.3)

      • thresh - pivot threshold, see help lu for details

    • pardiso : struct of PARDISO options (default shown in parens), see PARDISO documentation for details

      • verbose (0) - true or false

      • mtype (11, i.e. real and nonsymmetric) - matrix type

      • solver (0, i.e. sparse direct) - solver method

      • iparm ([]) - \(n \by 2\) matrix of integer parameters 1st, 2nd columns are index, value of parameter respectively

      • dparm ([]) - \(n \by 2\) matrix of double parameters 1st, 2nd columns are index, value of parameter respectively

    • tr (0) : if true, solve transposed system A' * x = b

Outputs:

  • x – solution vector (or matrix) satisfying A * x == b

  • factors – see description under Inputs