feat: Added tridiagonal_solve in tensorflow frontend (ivy-llc#23279)

Co-authored-by: NripeshN <nripesh14@gmail.com>

ivy/functional/frontends/tensorflow/linalg.py

@@ -458,3 +458,52 @@ def tensorsolve(a, b, axes):
 @to_ivy_arrays_and_back
 def trace(x, name=None):
     return ivy.trace(x, axis1=-2, axis2=-1)
+
+
+@to_ivy_arrays_and_back
+@with_supported_dtypes(
+    {
+        "2.13.0 and below": (
+            "float32",
+            "float64",
+            "complex64",
+            "complex128",
+        )
+    },
+    "tensorflow",
+)
+def tridiagonal_solve(
+    diagonals,
+    rhs,
+    diagonals_format="compact",
+    transpose_rhs=False,
+    conjugate_rhs=False,
+    name=None,
+    partial_pivoting=True,
+    perturb_singular=False,
+):
+    if transpose_rhs is True:
+        rhs_copy = ivy.matrix_transpose(rhs)
+    if conjugate_rhs is True:
+        rhs_copy = ivy.conj(rhs)
+    if not transpose_rhs and not conjugate_rhs:
+        rhs_copy = ivy.array(rhs)
+
+    if diagonals_format == "matrix":
+        return ivy.solve(diagonals, rhs_copy)
+    elif diagonals_format in ["sequence", "compact"]:
+        diagonals = ivy.array(diagonals)
+        dim = diagonals[0].shape[0]
+        diagonals[[0, -1], [-1, 0]] = 0
+        dummy_idx = [0, 0]
+        indices = ivy.array([
+            [(i, i + 1) for i in range(dim - 1)] + [dummy_idx],
+            [(i, i) for i in range(dim)],
+            [dummy_idx] + [(i + 1, i) for i in range(dim - 1)],
+        ])
+        constructed_matrix = ivy.scatter_nd(
+            indices, diagonals, shape=ivy.array([dim, dim])
+        )
+        return ivy.solve(constructed_matrix, rhs_copy)
+    else:
+        raise "Unexpected diagonals_format"

ivy_tests/test_ivy/test_frontends/test_tensorflow/test_linalg.py

@@ -153,6 +153,41 @@ def _get_second_matrix(draw):
     )
 
 
+@st.composite
+def _get_tridiagonal_dtype_matrix_format(draw):
+    input_dtype_strategy = st.shared(
+        st.sampled_from(draw(helpers.get_dtypes("float_and_complex"))),
+        key="shared_dtype",
+    )
+    input_dtype = draw(input_dtype_strategy)
+    shared_size = draw(
+        st.shared(helpers.ints(min_value=2, max_value=4), key="shared_size")
+    )
+    diagonals_format = draw(st.sampled_from(["compact", "sequence", "matrix"]))
+    if diagonals_format == "matrix":
+        matrix = draw(
+            helpers.array_values(
+                dtype=input_dtype,
+                shape=tuple([shared_size, shared_size]),
+                min_value=2,
+                max_value=5,
+            ).filter(tridiagonal_matrix_filter)
+        )
+    elif diagonals_format in ["compact", "sequence"]:
+        matrix = draw(
+            helpers.array_values(
+                dtype=input_dtype,
+                shape=tuple([3, shared_size]),
+                min_value=2,
+                max_value=5,
+            ).filter(tridiagonal_compact_filter)
+        )
+        if diagonals_format == "sequence":
+            matrix = list(matrix)
+
+    return input_dtype, matrix, diagonals_format
+
+
 # --- Main --- #
 # ------------ #
 
@@ -1207,3 +1242,74 @@ def test_tensorflow_trace(
         fn_tree=fn_tree,
         x=x[0],
     )
+
+
+# tridiagonal_solve
+@handle_frontend_test(
+    fn_tree="tensorflow.linalg.tridiagonal_solve",
+    x=_get_tridiagonal_dtype_matrix_format(),
+    y=_get_second_matrix(),
+    transpose_rhs=st.just(False),
+    conjugate_rhs=st.booleans(),
+)
+def test_tensorflow_tridiagonal_solve(
+    *,
+    x,
+    y,
+    transpose_rhs,
+    conjugate_rhs,
+    frontend,
+    backend_fw,
+    test_flags,
+    fn_tree,
+    on_device,
+):
+    input_dtype1, x1, diagonals_format = x
+    input_dtype2, x2 = y
+    helpers.test_frontend_function(
+        input_dtypes=[input_dtype1, input_dtype2],
+        backend_to_test=backend_fw,
+        frontend=frontend,
+        test_flags=test_flags,
+        fn_tree=fn_tree,
+        on_device=on_device,
+        rtol=1e-3,
+        atol=1e-3,
+        diagonals=x1,
+        rhs=x2,
+        diagonals_format=diagonals_format,
+        transpose_rhs=transpose_rhs,
+        conjugate_rhs=conjugate_rhs,
+    )
+
+
+def tridiagonal_compact_filter(x):
+    diagonals = ivy.array(x)
+    dim = diagonals[0].shape[0]
+    diagonals[[0, -1], [-1, 0]] = 0
+    dummy_idx = [0, 0]
+    indices = ivy.array([
+        [(i, i + 1) for i in range(dim - 1)] + [dummy_idx],
+        [(i, i) for i in range(dim)],
+        [dummy_idx] + [(i + 1, i) for i in range(dim - 1)],
+    ])
+    matrix = ivy.scatter_nd(
+        indices, diagonals, ivy.array([dim, dim]), reduction="replace"
+    )
+    return tridiagonal_matrix_filter(matrix)
+
+
+def tridiagonal_matrix_filter(x):
+    dim = x.shape[0]
+    if ivy.abs(ivy.det(x)) < 1e-3:
+        return False
+    for i in range(dim):
+        for j in range(dim):
+            cell = x[i][j]
+            if i == j or i == j - 1 or i == j + 1:
+                if cell == 0:
+                    return False
+            else:
+                if cell != 0:
+                    return False
+    return True