feat: add solve_triangular module function to TinyLinalg

lib/numo/tiny_linalg.rb

@@ -399,6 +399,47 @@ def solve(a, b, driver: 'gen', uplo: 'U') # rubocop:disable Lint/UnusedMethodArg
       Numo::TinyLinalg::Lapack.send(gesv, a.dup, b.dup)[1]
     end
 
+    # Solves linear equation `A * x = b` or `A * X = B` for `x` assuming `A` is a triangular matrix.
+    #
+    # @example
+    #   require 'numo/tiny_linalg'
+    #
+    #   Numo::Linalg = Numo::TinyLinalg unless defined?(Numo::Linalg)
+    #
+    #   a = Numo::DFloat.new(3, 3).rand.triu
+    #   b = Numo::DFloat.eye(3)
+    #
+    #   x = Numo::Linalg.solve(a, b)
+    #
+    #   pp x
+    #   # =>
+    #   # Numo::DFloat#shape=[3,3]
+    #   # [[16.1932, -52.0604, 30.5283],
+    #   #  [0, 8.61765, -17.9585],
+    #   #  [0, 0, 6.05735]]
+    #
+    #   pp (b - a.dot(x)).abs.max
+    #   # => 4.071100642430302e-16
+    #
+    # @param a [Numo::NArray] The n-by-n triangular matrix.
+    # @param b [Numo::NArray] The n right-hand side vector, or n-by-nrhs right-hand side matrix.
+    # @param lower [Boolean] The flag indicating whether to use the lower-triangular part of `a`.
+    # @return [Numo::NArray] The solusion vector / matrix `X`.
+    def solve_triangular(a, b, lower: false)
+      raise ArgumentError, 'input array a must be 2-dimensional' if a.ndim != 2
+      raise ArgumentError, 'input array a must be square' if a.shape[0] != a.shape[1]
+
+      bchr = blas_char(a, b)
+      raise ArgumentError, "invalid array type: #{a.class}, #{b.class}" if bchr == 'n'
+
+      trtrs = :"#{bchr}trtrs"
+      uplo = lower ? 'L' : 'U'
+      x, info = Numo::TinyLinalg::Lapack.send(trtrs, a, b.dup, uplo: uplo)
+      raise "wrong value is given to the #{info}-th argument of #{trtrs} used internally" if info.negative?
+
+      x
+    end
+
     # Computes the Singular Value Decomposition (SVD) of a matrix: `A = U * S * V^T`
     #
     # @example

test/test_tiny_linalg.rb

@@ -208,6 +208,15 @@ def test_solve
     assert(error_ab < 1e-7)
   end
 
+  def test_solve_triangular
+    a = Numo::SFloat.new(3, 3).rand.triu
+    b = Numo::DComplex.new(3).rand
+    x = Numo::TinyLinalg.solve_triangular(a, b)
+    error_ab = (b - a.dot(x)).abs.max
+
+    assert(error_ab < 1e-7)
+  end
+
   def test_svd
     x = Numo::DFloat.new(5, 3).rand.dot(Numo::DFloat.new(3, 2).rand)
     s, u, vt, = Numo::TinyLinalg.svd(x, driver: 'sdd', job: 'S')