add docs

Author: perazz

doc/specs/stdlib_linalg.md

@@ -595,3 +595,76 @@ Specifically, upper Hessenberg matrices satisfy `a_ij = 0` when `j < i-1`, and l
 ```fortran
 {!example/linalg/example_is_hessenberg.f90!}
 ```
+
+## `det` - Computes the determinant of a square matrix
+
+### Status
+
+Experimental
+
+### Description
+
+This function computes the determinant of a real square matrix.
+
+This interface comes with a `pure` version `det(a)`, and a non-pure version `det(a,overwrite_a,err)` that
+allows for more expert control.
+
+### Syntax
+
+`c = ` [[stdlib_linalg(module):det(interface)]] `(a,overwrite_a,err)`
+
+### Arguments
+
+`a`: Shall be a rank-2 square array
+
+`overwrite_a` (optional): Shall be an input `logical` flag. if `.true.`, input matrix `a` will be used as temporary storage and overwritten. This avoids internal data allocation.  
+
+`err` (optional): Shall be a `type(linalg_state_type)` return value. 
+
+### Return value
+
+Returns a real scalar value that represents the determinnt of the matrix.
+
+Raises `LINALG_ERROR` if the matrix is singular.
+Raises `LINALG_VALUE_ERROR` if the matrix is non-square.
+Exceptions are returned to the `err` argument if provided; an `error stop` is triggered otherwise.
+
+### Example
+
+```fortran
+{!example/linalg/example_determinant.f90!}
+```
+
+## `.det.` - Determinant operator of a square matrix
+
+### Status
+
+Experimental
+
+### Description
+
+This operator returns the determinant of a real square matrix.
+
+This interface is equivalent to the `pure` version of determinant [[stdlib_linalg(module):det(interface)]]. 
+
+### Syntax
+
+`c = ` [[stdlib_linalg(module):operator(.det.)(interface)]] `(a)`
+
+### Arguments
+
+`a`: Shall be a rank-2 square array
+
+### Return value
+
+Returns a real scalar value that represents the determinnt of the matrix.
+
+Raises `LINALG_ERROR` if the matrix is singular.
+Raises `LINALG_VALUE_ERROR` if the matrix is non-square.
+Exceptions trigger an `error stop`.
+
+### Example
+
+```fortran
+{!example/linalg/example_determinant2.f90!}
+```

example/linalg/CMakeLists.txt

@@ -19,4 +19,5 @@ ADD_EXAMPLE(state2)
 ADD_EXAMPLE(blas_gemv)
 ADD_EXAMPLE(lapack_getrf)
 ADD_EXAMPLE(determinant)
+ADD_EXAMPLE(determinant2)
 

example/linalg/example_determinant2.f90

@@ -0,0 +1,13 @@
+program example_determinant2
+  use stdlib_kinds, only: dp
+  use stdlib_linalg, only: operator(.det.)
+  implicit none
+
+  real(dp) :: d
+
+  ! Compute determinate of a real matrix
+  d = .det.reshape([real(dp)::1,2,3,4],[2,2])
+
+  print *, d ! a*d-b*c = -2.0
+
+end program example_determinant2