Visible to Intel only — GUID: GUID-BD8C8134-65F7-4A08-9576-5204D6F9F58B
Visible to Intel only — GUID: GUID-BD8C8134-65F7-4A08-9576-5204D6F9F58B
?pftri
Computes the inverse of a symmetric (Hermitian) positive-definite matrix in RFP format using the Cholesky factorization.
Syntax
call spftri( transr, uplo, n, a, info )
call dpftri( transr, uplo, n, a, info )
call cpftri( transr, uplo, n, a, info )
call zpftri( transr, uplo, n, a, info )
Include Files
- mkl.fi, mkl_lapack.f90
Description
The routine computes the inverse inv(A) of a symmetric positive definite or, for complex data, Hermitian positive-definite matrix A using the Cholesky factorization:
A = UT*U for real data, A = UH*U for complex data | if uplo='U' |
A = L*LT for real data, A = L*LH for complex data | if uplo='L' |
Before calling this routine, call ?pftrf to factorize A.
The matrix A is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.
Input Parameters
transr |
CHARACTER*1. Must be 'N', 'T' (for real data) or 'C' (for complex data). If transr = 'N', the Normal transr of RFP U (if uplo = 'U') or L (if uplo = 'L') is stored. If transr = 'T', the Transpose transr of RFP U (if uplo = 'U') or L (if uplo = 'L' is stored. If transr = 'C', the Conjugate-Transpose transr of RFP U (if uplo = 'U') or L (if uplo = 'L' is stored. |
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', A = UT*U for real data or A = UH*U for complex data, and U is stored. If uplo = 'L', A = L*LT for real data or A = L*LH for complex data, and L is stored. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
a |
REAL for spftri DOUBLE PRECISION for dpftri COMPLEX for cpftri DOUBLE COMPLEX for zpftri. Array, size (n*(n+1)/2). The array a contains the factor U or L matrix A in the RFP format. |
Output Parameters
a |
The symmetric/Hermitian inverse of the original matrix in the same storage format. |
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,i) element of the factor U or L is zero, and the inverse could not be computed. |