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Visible to Intel only — GUID: GUID-C2AA1F15-D2C5-425B-90BD-1012163DA3EE
?trtri
Computes the inverse of a triangular matrix.
Syntax
call strtri( uplo, diag, n, a, lda, info )
call dtrtri( uplo, diag, n, a, lda, info )
call ctrtri( uplo, diag, n, a, lda, info )
call ztrtri( uplo, diag, n, a, lda, info )
call trtri( a [,uplo] [,diag] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the inverse inv(A) of a triangular matrix A.
Input Parameters
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates whether A is upper or lower triangular: If uplo = 'U', then A is upper triangular. If uplo = 'L', then A is lower triangular. |
diag |
CHARACTER*1. Must be 'N' or 'U'. If diag = 'N', then A is not a unit triangular matrix. If diag = 'U', A is unit triangular: diagonal elements of A are assumed to be 1 and not referenced in the array a. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
a |
REAL for strtri DOUBLE PRECISION for dtrtri COMPLEX for ctrtri DOUBLE COMPLEX for ztrtri. Array: size lda by *size max(1,lda*n). Contains the matrix A. The second dimension of a must be at least max(1,n). |
lda |
INTEGER. The first dimension of a; lda≥ max(1, n). |
Output Parameters
a |
Overwritten by the 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 A is zero, A 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 trtri interface are as follows:
a |
Holds the matrix A of size (n,n). |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |
diag |
Must be 'N' or 'U'. The default value is 'N'. |
Application Notes
The computed inverse X satisfies the following error bounds:
|XA - I| ≤ c(n)ε |X||A|
|XA - I| ≤ c(n)ε |A-1||A||X|,
where c(n) is a modest linear function of n; ε is the machine precision; I denotes the identity matrix.
The total number of floating-point operations is approximately (1/3)n3 for real flavors and (4/3)n3 for complex flavors.