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‎src/stdlib_linalg_determinant.fypp‎

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#:include "common.fypp"
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#:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
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!> Determinant of a rectangular matrix
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module stdlib_linalg_determinant
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!! Determinant of a rectangular matrix
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use stdlib_linalg_constants
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use stdlib_linalg_lapack, only: getrf
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use stdlib_linalg_state, only: linalg_state_type, linalg_error_handling, LINALG_ERROR, &
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LINALG_INTERNAL_ERROR, LINALG_VALUE_ERROR
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implicit none(type,external)
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private
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!> Function interface
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! Function interface
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public :: det
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public :: operator(.det.)
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character(*), parameter :: this = 'determinant'
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! Numpy: det(a)
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! Scipy: det(a, overwrite_a=False, check_finite=True)
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! IMSL: DET(a)
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interface det
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!!### Summary
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!! Interface for computing matrix determinant.
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!!
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!!### Description
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!!
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!! This interface provides methods for computing the determinant of a matrix.
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!! Supported data types include real and complex.
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!!
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!!@note The provided functions are intended for square matrices.
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!!
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!!### Example
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!!
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!!```fortran
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!!
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!! real(sp) :: a(3,3), d
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!! type(linalg_state_type) :: state
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!! a = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
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!!
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!! d = det(a,err=state)
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!! if (state%ok()) then
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!! print *, 'Success! det=',d
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!! else
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!! print *, state%print()
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!! endif
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!!
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!!```
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!!
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#:for rk,rt in RC_KINDS_TYPES
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#:if rk!="xdp"
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! Interface with error control
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module procedure stdlib_linalg_${rt[0]}$${rk}$determinant
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! Pure interface
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module procedure stdlib_linalg_${rt[0]}$${rk}$determinant
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module procedure stdlib_linalg_pure_${rt[0]}$${rk}$determinant
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#:endif
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#:endfor
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end interface det
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! Pure Operator interface
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interface operator(.det.)
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!!### Summary
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!! Pure operator interface for computing matrix determinant.
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!!
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!!### Description
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!!
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!! This pure operator interface provides a convenient way to compute the determinant of a matrix.
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!! Supported data types include real and complex.
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!!
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!!@note The provided functions are intended for square matrices.
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!!
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!!### Example
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!!
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!!```fortran
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!!
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!! real(sp) :: matrix(3,3), d
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!! matrix = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
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!! d = .det.matrix
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!!
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!!```
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!
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#:for rk,rt in RC_KINDS_TYPES
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#:if rk!="xdp"
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module procedure stdlib_linalg_pure_${rt[0]}$${rk}$determinant
@@ -43,20 +83,39 @@ module stdlib_linalg_determinant
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#:for rk,rt in RC_KINDS_TYPES
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#:if rk!="xdp"
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! Compute determinant of a square matrix A: pure interface
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pure function stdlib_linalg_pure_${rt[0]}$${rk}$determinant(a) result(det)
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pure function stdlib_linalg_pure_${rt[0]}$${rk}$determinant(a) result(det)
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!!### Summary
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!! Compute determinant of a real square matrix (pure interface).
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!!
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!!### Description
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!!
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!! This function computes the determinant of a real square matrix.
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!!
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!! param: a Input matrix of size [m,n].
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!! return: det Matrix determinant.
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!!
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!!### Example
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!!
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!!```fortran
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!!
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!! ${rt}$ :: matrix(3,3)
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!! ${rt}$ :: determinant
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!! matrix = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
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!! determinant = det(matrix)
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!!
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!!```
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!> Input matrix a[m,n]
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${rt}$, intent(in) :: a(:,:)
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!> Result: matrix determinant
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!> Matrix determinant
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${rt}$ :: det
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!> Local variables
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!! Local variables
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type(linalg_state_type) :: err0
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integer(ilp) :: m,n,info,perm,k
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integer(ilp), allocatable :: ipiv(:)
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${rt}$, allocatable :: amat(:,:)
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!> Matrix determinant size
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! Matrix determinant size
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m = size(a,1,kind=ilp)
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n = size(a,2,kind=ilp)
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@@ -121,25 +180,47 @@ module stdlib_linalg_determinant
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end function stdlib_linalg_pure_${rt[0]}$${rk}$determinant
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! Compute determinant of a square matrix A, with error control
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function stdlib_linalg_${rt[0]}$${rk}$determinant(a,overwrite_a,err) result(det)
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!!### Summary
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!! Compute determinant of a square matrix (with error control).
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!!
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!!### Description
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!!
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!! This function computes the determinant of a square matrix with error control.
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!!
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!! param: a Input matrix of size [m,n].
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!! param: overwrite_a [optional] Flag indicating if the input matrix can be overwritten.
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!! param: err State return flag.
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!! return: det Matrix determinant.
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!!
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!!### Example
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!!
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!!```fortran
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!!
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!! ${rt}$ :: matrix(3,3)
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!! ${rt}$ :: determinant
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!! matrix = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
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!! determinant = det(matrix, err=err)
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!!
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!!```
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!
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!> Input matrix a[m,n]
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${rt}$, intent(inout), target :: a(:,:)
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!> [optional] Can A data be overwritten and destroyed?
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logical(lk), optional, intent(in) :: overwrite_a
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!> [optional] state return flag. On error if not requested, the code will stop
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!> State return flag.
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type(linalg_state_type), intent(out) :: err
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!> Result: matrix determinant
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!> Matrix determinant
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${rt}$ :: det
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!> Local variables
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!! Local variables
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type(linalg_state_type) :: err0
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integer(ilp) :: m,n,info,perm,k
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integer(ilp), allocatable :: ipiv(:)
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logical(lk) :: copy_a
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${rt}$, pointer :: amat(:,:)
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!> Matrix determinant size
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! Matrix determinant size
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m = size(a,1,kind=ilp)
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n = size(a,2,kind=ilp)
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