Find missing element SQL - sql

Question

I have a couple of tables of a database where one defines a set of matrices and the other the data in the matrices
Matrices
Id Name
1 M1
2 M2
3 M3
4 M4
MatrixElements
Matrix_Id ElementKey Value
1 1 234
1 2 234
1 3 4432
2 1 234
2 2 13
2 3 123
3 1 34
3 3 345
4 1 234
4 2 11
4 3 344
So the Matrix_Id column is a foreign key back to the Id of the Matrices table. The ElementKey reprents an ij pair. The matrices are sparse, so there may or may not be an element with a specific key. However, if one matrix has a particular ElementKey, then the ElementKey with that ID must be defined in ALL matrices.
Is there some SQL that I can run that will find Matrix_Id and ElementKey combinations for any offending entries, i.e. one that is not defined for all matrices? So for the example above, ElementKey = 2 is defined for Matrix 1, 2 and 4 but not 3, so I would expect [Matrix = 3, ElementKey = 2] back.

Answer 1

This will get the missing elements and the matrices they are in:
select m.id, me.element_key
from matrices m cross join
(select distinct element_key from matrix_elements me) e left join
matrix_elements me
on me.matrix_id = m.id and me.element_key = e.element_key
where me.matrix_id is null;
The cross join generates all combinations of matrices with known element keys. The left join and where then find the ones that are missing.

Answer 2

First we make a list of all live elements, then cross join to all active matrices. With this list, we left join the active elements and use a case to determine if they exist.
I've used ANSI, but a CTE would be better if SQL server or Oracle.
select c.id, c.ElementKey, case when b.MatrixID is null then 0 else 1 end as InPlace
from
(
select id, a.ElementKey
from Matrices
cross join
(
select distinct ElementKey
from MatrixElements
) a
) c
left join Matrices b
on b.Matrix_id = c.id
and b.ElementKey = c.ElementKey

Answer 3

Thanks to the responses I have had. I haven't been able to implement it effectively because I am using Entity Framework and it is hard to translate the code given to a query statement that will give me back the results. I did take inspiration from the samples given and this is what I came up with.
public class Matrix
{
[Key]
public int Id { get; set; }
public virtual List<MatrixElement> Data { get; set; }
}
public class MatrixElement
{
[Key]
public int Id { get; set; }
public int OdPairKey { get; set; }
public double Value { get; set; }
}
public class EngineDataContext : DbContext
{
public virtual DbSet<Matrix> MatrixFiles { get; set; }
public virtual DbSet<MatrixElement> MatrixData { get; set; }
}
public class SqliteRepository
{
private readonly EngineDataContext _dataContext;
public SqliteRepository(EngineDataContext dataContext)
{
_dataContext = dataContext;
}
public IEnumerable<Tuple<Matrix, int>> FindMissingODPairs(IEnumerable<Matrix> matrices)
{
IEnumerable<Matrix> matricesWithData =
matrices.Select(m => _dataContext.MatrixFiles
.Include("Data").First(mf => mf.Id == m.Id));
// Do the cross join on matrices and OD pairs
IEnumerable<dynamic> combinations =
from m in matrices
from od in matricesWithData.SelectMany(mat => mat.Data.Select(md => md.OdPairKey)).Distinct()
select new { M = m.Id, O = od };
// Find all the used matrix / OD pair combinations
IEnumerable<dynamic> used =
from m in matricesWithData
from od in m.Data
select new { M = m.Id, O = od.OdPairKey };
// Find the missing combinations with a simple "Except" query
return combinations
.Except(used)
.Select(c => new Tuple<Matrix, int>(matrices.First(m => m.Id == c.M), c.O));
}
}