Re: Determinant of Matrix

Thanks Dennis. Tested and implemented.

On 5/7/14, 11:44 MDT, "Dennis Shea" <shea@ucar.edu> wrote:

>To my knowledge, there is no NCL function that explicitly or
>implicitly (ie, an attribute) returns the determinant.
>
>===
>
>Some NCL functions do calculate a determinant internally
>(eg, 'solve_linsys') however these are not returned as part of solution.
>
>https://www.ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml
>
>===
>An untested double precision f77 subroutine is attached. You could
>alter to handle float if you wish.
>+++
>NOTE:
>
>LAPACK, which is used by NCL functions, does not have an explicit
>subroutine to calculate the determinant. If there was, NCL would
>provide a function.
>
>That said, a double precision LAPACK library is (silently)
>distributed with NCL. You could use LAPACK's DGETRF
>to compute an LU factorization of a real general M-by-N matrix.
>Documentation is appended. The following URL shows how to use
>the complex form of DGETRF (ZGETRF) to calculate a determinant.
>I'm sure you could modify to handle double.
>
>http://dualm.wordpress.com/2012/01/06/computing-determinant-in-fortran/
>
>***
>
> SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
>*
>* -- LAPACK routine (version 3.2) --
>* -- LAPACK is a software package provided by Univ. of Tennessee, --
>* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG
>Ltd..--
>* November 2006
>*
>* .. Scalar Arguments ..
> INTEGER INFO, LDA, M, N
>* ..
>* .. Array Arguments ..
> INTEGER IPIV( * )
> DOUBLE PRECISION A( LDA, * )
>* ..
>*
>* Purpose
>* =======
>*
>* DGETRF computes an LU factorization of a general M-by-N matrix A
>* using partial pivoting with row interchanges.
>*
>* The factorization has the form
>* A = P * L * U
>* where P is a permutation matrix, L is lower triangular with unit
>* diagonal elements (lower trapezoidal if m > n), and U is upper
>* triangular (upper trapezoidal if m < n).
>*
>* This is the right-looking Level 3 BLAS version of the algorithm.
>*
>* Arguments
>* =========
>*
>* M (input) INTEGER
>* The number of rows of the matrix A. M >= 0.
>*
>* N (input) INTEGER
>* The number of columns of the matrix A. N >= 0.
>*
>* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
>* On entry, the M-by-N matrix to be factored.
>* On exit, the factors L and U from the factorization
>* A = P*L*U; the unit diagonal elements of L are not stored.
>*
>* LDA (input) INTEGER
>* The leading dimension of the array A. LDA >= max(1,M).
>*
>* IPIV (output) INTEGER array, dimension (min(M,N))
>* The pivot indices; for 1 <= i <= min(M,N), row i of the
>* matrix was interchanged with row IPIV(i).
>*
>* INFO (output) INTEGER
>* = 0: successful exit
>* < 0: if INFO = -i, the i-th argument had an illegal value
>* > 0: if INFO = i, U(i,i) is exactly zero. The factorization
>* has been completed, but the factor U is exactly
>* singular, and division by zero will occur if it is used
>* to solve a system of equations.
>*
>* =====================================================================
>*
>
>On 5/7/14, 8:53 AM, Capehart, William J wrote:
>> Hi All:
>>
>> Is there a Determinant of a Matrix deeply hidden in side of of the
>>"return attributes" of an existing function or do I have to "WRAPIT" one
>>myself.
>>
>> Just wonderin'
>>
>> Bill
>>
>>
>>
>> ================================================================
>> Bill Capehart
>><William.Capehart@sdsmt.edu<mailto:William.Capehart@sdsmt.edu>>
>>Associate Professor
>> Department of Atmospheric & Envir. Sciences AES PhD Coordinator
>> 213 Mineral Industries Building Skype/EVO: wcapehart
>> South Dakota School of Mines and Technology Ph: +1-605-394-1994
>> 501 East Saint Joseph Street Fax: +1-605-394-6061
>> Rapid City, SD 57701-3995 Mobile: +1-605-484-5692
>> =================== http://capehart.sdsmt.edu ==================
>>
>>
>>
>>
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Received on Wed May 7 15:17:00 2014