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mat: clarify docs for Dense.Solve and VecDense.SolveVec

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This commit is contained in:
Vladimir Chalupecky
2020-06-30 12:23:38 +02:00
committed by Vladimír Chalupecký
parent 4605b656e4
commit 0f360d3c36
1 changed files with 35 additions and 11 deletions
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46
mat/solve.go
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@@ -10,14 +10,25 @@ import (
"gonum.org/v1/gonum/lapack/lapack64"
)
// Solve finds a minimum-norm solution to a system of linear equations defined
// by the matrices A and B. If A is singular or near-singular, a Condition error
// is returned. See the documentation for Condition for more information.
// Solve solves the linear least squares problem
// minimize over x |b - A*x|_2
// where A is an m×n matrix A, b is a given m element vector and x is n element
// solution vector. Solve assumes that A has full rank, that is
// rank(A) = min(m,n)
//
// The minimization problem solved depends on the input parameters:
// - if m >= n, find X such that ||A*X - B||_2 is minimized,
// - if m < n, find the minimum norm solution of A * X = B.
// The solution matrix, X, is stored in-place into the receiver.
// If m >= n, Solve finds the unique least squares solution of an overdetermined
// system.
//
// If m < n, there is an infinite number of solutions that satisfy b-A*x=0. In
// this case Solve finds the unique solution of an underdetermined system that
// minimizes |x|_2.
//
// Several right-hand side vectors b and solution vectors x can be handled in a
// single call. Vectors b are stored in the columns of the m×k matrix B. Vectors
// x will be stored in-place into the n×k receiver.
//
// If A does not have full rank, a Condition error is returned. See the
// documentation for Condition for more information.
func (m *Dense) Solve(a, b Matrix) error {
ar, ac := a.Dims()
br, bc := b.Dims()
@@ -103,10 +114,23 @@ func (m *Dense) Solve(a, b Matrix) error {
}
}
// SolveVec finds a minimum-norm solution to a system of linear equations defined
// by the matrix a and the right-hand side column vector b. If A is singular or
// near-singular, a Condition error is returned. See the documentation for
// Dense.Solve for more information.
// SolveVec solves the linear least squares problem
// minimize over x |b - A*x|_2
// where A is an m×n matrix A, b is a given m element vector and x is n element
// solution vector. Solve assumes that A has full rank, that is
// rank(A) = min(m,n)
//
// If m >= n, Solve finds the unique least squares solution of an overdetermined
// system.
//
// If m < n, there is an infinite number of solutions that satisfy b-A*x=0. In
// this case Solve finds the unique solution of an underdetermined system that
// minimizes |x|_2.
//
// The solution vector x will be stored in-place into the receiver.
//
// If A does not have full rank, a Condition error is returned. See the
// documentation for Condition for more information.
func (v *VecDense) SolveVec(a Matrix, b Vector) error {
if _, bc := b.Dims(); bc != 1 {
panic(ErrShape)