Visible to Intel only — GUID: GUID-6627C65C-C5F0-4DD2-8DED-7D9451CE9B8C
Visible to Intel only — GUID: GUID-6627C65C-C5F0-4DD2-8DED-7D9451CE9B8C
?sptri
Computes the inverse of a symmetric matrix using U*D*UT or L*D*LT Bunch-Kaufman factorization of matrix in packed storage.
Syntax
call ssptri( uplo, n, ap, ipiv, work, info )
call dsptri( uplo, n, ap, ipiv, work, info )
call csptri( uplo, n, ap, ipiv, work, info )
call zsptri( uplo, n, ap, ipiv, work, info )
call sptri( ap, ipiv [,uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the inverse inv(A) of a packed symmetric matrix A. Before calling this routine, call ?sptrf to factorize A.
Input Parameters
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', the array ap stores the Bunch-Kaufman factorization A = U*D*UT. If uplo = 'L', the array ap stores the Bunch-Kaufman factorization A = L*D*LT. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
ap, work |
REAL for ssptri DOUBLE PRECISION for dsptri COMPLEX for csptri DOUBLE COMPLEX for zsptri. Arrays: ap(*) contains the factorization of the matrix A, as returned by ?sptrf. The dimension of ap must be at least max(1,n(n+1)/2). work(*) is a workspace array. The dimension of work must be at least max(1,n). |
ipiv |
INTEGER. Array, size at least max(1, n). The ipiv array, as returned by ?sptrf. |
Output Parameters
ap |
Overwritten by the matrix inv(A) in packed form. |
info |
INTEGER. If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value. If info = i, the i-th diagonal element of D is zero, D is singular, and the inversion could not be completed. |
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine sptri interface are as follows:
ap |
Holds the array A of size (n*(n+1)/2). |
ipiv |
Holds the vector of length n. |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |
Application Notes
The computed inverse X satisfies the following error bounds:
|D*UT*PT*X*P*U - I| ≤ c(n)ε(|D||UT|PT|X|P|U| + |D||D-1|)
for uplo = 'U', and
|D*LT*PT*X*P*L - I| ≤ c(n)ε(|D||LT|PT|X|P|L| + |D||D-1|)
for uplo = 'L'. Here c(n) is a modest linear function of n, and ε is the machine precision; I denotes the identity matrix.
The total number of floating-point operations is approximately (2/3)n3 for real flavors and (8/3)n3 for complex flavors.