# pgr_aStarCostMatrix¶

pgr_aStarCostMatrix - Calculates the a cost matrix using pgr_aStar.

Availability

• Version 3.0.0

• Official function

• Version 2.4.0

• New proposed function

## Description¶

The main characteristics are:

• Using internaly the pgr_aStar 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_aStarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)


Using defaults

pgr_aStarCostMatrix(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_aStarCostMatrix(
'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_aStarCostMatrix(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_aStarCostMatrix(
'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),
directed := false, heuristic := 2
);
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

ANY-NUMERICAL

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(
$$SELECT * FROM pgr_aStarCostMatrix( 'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table', (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5), directed:= false, heuristic := 2 )$$,
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)