Visible to Intel only — GUID: GUID-674C9C39-E08F-4C9C-865A-AA3D8881D974
Visible to Intel only — GUID: GUID-674C9C39-E08F-4C9C-865A-AA3D8881D974
?pftrs
Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix using the Rectangular Full Packed (RFP) format.
Syntax
call spftrs( transr, uplo, n, nrhs, a, b, ldb, info )
call dpftrs( transr, uplo, n, nrhs, a, b, ldb, info )
call cpftrs( transr, uplo, n, nrhs, a, b, ldb, info )
call zpftrs( transr, uplo, n, nrhs, a, b, ldb, info )
Include Files
- mkl.fi, mkl_lapack.f90
Description
The routine solves a system of linear equations A*X = B with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix A using the Cholesky factorization of A:
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 ?pftrs, you must call ?pftrf to compute the Cholesky factorization of A. L stands for a lower triangular matrix and U for an upper triangular matrix.
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 untransposed factor of Ais stored in RFP format. If transr = 'T', the transposed factor of Ais stored in RFP format. If transr = 'C', the conjugate-transposed factor of Ais stored in RFP format. |
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', U is stored, where A = UT*U for real data, A = UH*U for complex data. If uplo = 'L', L is stored, where A = L*LT for real data, A = L*LH for complex data |
n |
INTEGER. The order of the matrix A; n≥ 0. |
nrhs |
INTEGER. The number of right-hand sides, that is, the number of columns of the matrix B; nrhs≥ 0. |
a, b |
REAL for spftrs DOUBLE PRECISION for dpftrs COMPLEX for cpftrs DOUBLE COMPLEX for zpftrs. Arrays: a(n*(n + 1)/2), b(ldb,nrhs). The array a contains, in the RFP format, the factor U or L obtained by factorization of matrix A. The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. |
ldb |
INTEGER. The leading dimension of b; ldb≥ max(1, n). |
Output Parameters
b |
The solution matrix X. |
info |
INTEGER. If info=0, the execution is successful. If info = -i, the i-th parameter had an illegal value. |