# pgr_bdAstarCostMatrix¶

pgr_bdAstarCostMatrix - Calculates the a cost matrix using pgr_aStar.

Availability

• Version 3.0.0
• Official function
• Version 2.5.0
• New Proposed function

Support

## Description¶

The main characteristics are:

• Using internaly the pgr_bdAstar algorithm
• Returns a cost matrix.
• No ordering is performed
• let v and u are nodes on the graph:
• when there is no path from v to u:
• no corresponding row is returned
• cost from v to u is $$\inf$$
• when $$v = u$$ then
• no corresponding row is returned
• cost from v to u is $$0$$
• When the graph is undirected the cost matrix is symmetric

## Signatures¶

Summary

pgr_bdAstarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)


Using defaults

pgr_bdAstarCostMatrix(edges_sql, vids)
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example: Cost matrix for vertices $$\{1, 2, 3, 4\}$$ on a directed graph
SELECT * FROM pgr_bdAstarCostMatrix(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
(SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5)
);
start_vid | end_vid | agg_cost
-----------+---------+----------
1 |       2 |        1
1 |       3 |        6
1 |       4 |        5
2 |       1 |        1
2 |       3 |        5
2 |       4 |        4
3 |       1 |        2
3 |       2 |        1
3 |       4 |        3
4 |       1 |        3
4 |       2 |        2
4 |       3 |        1
(12 rows)



### Complete Signature¶

pgr_bdAstarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example: Symmetric cost matrix for vertices $$\{1, 2, 3, 4\}$$ on an undirected graph using heuristic $$2$$
SELECT * FROM pgr_bdAstarCostMatrix(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
(SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5),
false
);
start_vid | end_vid | agg_cost
-----------+---------+----------
1 |       2 |        1
1 |       3 |        2
1 |       4 |        3
2 |       1 |        1
2 |       3 |        1
2 |       4 |        2
3 |       1 |        2
3 |       2 |        1
3 |       4 |        1
4 |       1 |        3
4 |       2 |        2
4 |       3 |        1
(12 rows)



## Parameters¶

Parameter Type Description
edges_sql TEXT edges_sql inner query.
vids ARRAY[ANY-INTEGER] Array of vertices identifiers.

### Optional Parameters¶

Parameter Type Default Description
directed BOOLEAN true
• When true the graph is considered as Directed.
• When false the graph is considered as Undirected.
heuristic INTEGER 5

Heuristic number. Current valid values 0~5. Default 5

• 0: h(v) = 0 (Use this value to compare with pgr_dijkstra)
• 1: h(v) abs(max(dx, dy))
• 2: h(v) abs(min(dx, dy))
• 3: h(v) = dx * dx + dy * dy
• 4: h(v) = sqrt(dx * dx + dy * dy)
• 5: h(v) = abs(dx) + abs(dy)
factor FLOAT 1 For units manipulation. $$factor > 0$$. See Factor
epsilon FLOAT 1 For less restricted results. $$epsilon >= 1$$.

## Inner query¶

### edges_sql¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
cost ANY-NUMERICAL

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
x1 ANY-NUMERICAL   X coordinate of source vertex.
y1 ANY-NUMERICAL   Y coordinate of source vertex.
x2 ANY-NUMERICAL   X coordinate of target vertex.
y2 ANY-NUMERICAL   Y coordinate of target vertex.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Result Columns¶

Returns SET OF (start_vid, end_vid, agg_cost)

Column Type Description
start_vid BIGINT Identifier of the starting vertex.
end_vid BIGINT Identifier of the ending vertex.
agg_cost FLOAT Aggregate cost from start_vid to end_vid.

Example: Use with pgr_TSP
SELECT * FROM pgr_TSP(
$$SELECT * FROM pgr_bdAstarCostMatrix( 'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table', (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5), false )$$,
randomize := false
);
seq | node | cost | agg_cost
-----+------+------+----------
1 |    1 |    1 |        0
2 |    2 |    1 |        1
3 |    3 |    1 |        2
4 |    4 |    3 |        3
5 |    1 |    0 |        6
(5 rows)