Visible to Intel only — GUID: GUID-932B0A5D-D7A0-4AB1-8CC0-70F67F2EBC2A
Visible to Intel only — GUID: GUID-932B0A5D-D7A0-4AB1-8CC0-70F67F2EBC2A
?sytri
Computes the inverse of a symmetric matrix using U*D*UT or L*D*LT Bunch-Kaufman factorization.
Syntax
call ssytri( uplo, n, a, lda, ipiv, work, info )
call dsytri( uplo, n, a, lda, ipiv, work, info )
call csytri( uplo, n, a, lda, ipiv, work, info )
call zsytri( uplo, n, a, lda, ipiv, work, info )
call sytri( a, ipiv [,uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the inverse inv(A) of a symmetric matrix A. Before calling this routine, call ?sytrf 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 a stores the Bunch-Kaufman factorization A = U*D*UT. If uplo = 'L', the array a stores the Bunch-Kaufman factorization A = L*D*LT. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
a, work |
REAL for ssytri DOUBLE PRECISION for dsytri COMPLEX for csytri DOUBLE COMPLEX for zsytri. Arrays: a(size lda by *) contains the factorization of the matrix A, as returned by ?sytrf. The second dimension of a must be at least max(1,n). work(*) is a workspace array. The dimension of work must be at least max(1,2*n). |
lda |
INTEGER. The leading dimension of a; lda≥ max(1, n). |
ipiv |
INTEGER. Array, size at least max(1, n). The ipiv array, as returned by ?sytrf. |
Output Parameters
a |
Overwritten by the n-by-n matrix inv(A). |
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 sytri interface are as follows:
a |
Holds the matrix A of size (n,n). |
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.