document eig

Author: perazz

doc/specs/stdlib_linalg.md

@@ -987,20 +987,30 @@ Stable
 
 ### Description
 
-This subroutine computes the solution to the eigenproblem \( A \cdot \bar{v} - \lambda \cdot \bar{v} \), where \( A \) is a square, full-rank, `real` or `complex` matrix.
+This subroutine computes the solution to the eigenproblem \( A \cdot \bar{v} - \lambda \cdot \bar{v} \), 
+where \( A \) is a square, full-rank, `real` or `complex` matrix, or to the generalized eigenproblem \( A \cdot \bar{v} - \lambda \cdot B \cdot \bar{v} \), 
+where \( B \) is a square matrix with the same type and kind as \( A \).
 
 Result array `lambda` returns the eigenvalues of \( A \). The user can request eigenvectors to be returned: if provided, on output `left` will contain the left eigenvectors, `right` the right eigenvectors of \( A \).
 Both `left` and `right` are rank-2 arrays, where eigenvectors are stored as columns.
-The solver is based on LAPACK's `*GEEV` backends.
+The solver is based on LAPACK's `*GEEV` and `*GGEV` backends.
 
 ### Syntax
 
+For the standard eigenproblem: 
+
 `call ` [[stdlib_linalg(module):eig(interface)]] `(a, lambda [, right] [,left] [,overwrite_a] [,err])`
 
+For the generalized eigenproblem: 
+
+`call ` [[stdlib_linalg(module):eig(interface)]] `(a, b, lambda [, right] [, left] [, overwrite_a] [, overwrite_b] [, err])
+
 ### Arguments
 
 `a` : `real` or `complex` square array containing the coefficient matrix. If `overwrite_a=.false.`, it is an `intent(in)` argument. Otherwise, it is an `intent(inout)` argument and is destroyed by the call. 
 
+`b`: `real` or `complex` square array containing the second coefficient matrix. If `overwrite_b=.false.`, it is an intent(in) argument.  Otherwise, it is an `intent(inout)` argument and is destroyed by the call. 
+
 `lambda`: Shall be a `complex` or `real` rank-1 array of the same kind as `a`, containing the eigenvalues, or their `real` component only. It is an `intent(out)` argument.
 
 `right` (optional): Shall be a `complex` rank-2 array of the same size and kind as `a`, containing the right eigenvectors of `a`. It is an `intent(out)` argument.
@@ -1009,6 +1019,8 @@ The solver is based on LAPACK's `*GEEV` backends.
 
 `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. This is an `intent(in)` argument.
 
+`overwrite_b` (optional): Shall be an input logical flag. If `.true.`, input matrix `b` will be used as temporary storage and overwritten. This avoids internal data allocation. This is an `intent(in)` argument.
+
 `err` (optional): Shall be a `type(linalg_state_type)` value. This is an `intent(out)` argument.
 
 ### Return value