
NAMEzpftrs.f SYNOPSISFunctions/Subroutinessubroutine zpftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO) Function/Subroutine Documentationsubroutine zpftrs (characterTRANSR, characterUPLO, integerN, integerNRHS, complex*16, dimension( 0: * )A, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)ZPFTRS Purpose:ZPFTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPFTRF. TRANSR
Author:
TRANSR is CHARACTER*1 = 'N': The Normal TRANSR of RFP A is stored; = 'C': The Conjugatetranspose TRANSR of RFP A is stored.UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of RFP A is stored; = 'L': Lower triangle of RFP A is stored.N N is INTEGER The order of the matrix A. N >= 0.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.A A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); The triangular factor U or L from the Cholesky factorization of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF. See note below for more details about RFP A.B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
We first consider Standard Packed Format when N is even. We give an example where N = 6. AP is Upper AP is Lower 00 01 02 03 04 05 00 11 12 13 14 15 10 11 22 23 24 25 20 21 22 33 34 35 30 31 32 33 44 45 40 41 42 43 44 55 50 51 52 53 54 55 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last three columns of AP upper. The lower triangle A(4:6,0:2) consists of conjugatetranspose of the first three columns of AP upper. For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns of AP lower. The upper triangle A(0:2,0:2) consists of conjugatetranspose of the last three columns of AP lower. To denote conjugate we place  above the element. This covers the case N even and TRANSR = 'N'. RFP A RFP A    03 04 05 33 43 53   13 14 15 00 44 54  23 24 25 10 11 55 33 34 35 20 21 22  00 44 45 30 31 32   01 11 55 40 41 42    02 12 22 50 51 52 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate transpose of RFP A above. One therefore gets: RFP A RFP A           03 13 23 33 00 01 02 33 00 10 20 30 40 50           04 14 24 34 44 11 12 43 44 11 21 31 41 51           05 15 25 35 45 55 22 53 54 55 22 32 42 52 We next consider Standard Packed Format when N is odd. We give an example where N = 5. AP is Upper AP is Lower 00 01 02 03 04 00 11 12 13 14 10 11 22 23 24 20 21 22 33 34 30 31 32 33 44 40 41 42 43 44 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last three columns of AP upper. The lower triangle A(3:4,0:1) consists of conjugatetranspose of the first two columns of AP upper. For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns of AP lower. The upper triangle A(0:1,1:2) consists of conjugatetranspose of the last two columns of AP lower. To denote conjugate we place  above the element. This covers the case N odd and TRANSR = 'N'. RFP A RFP A   02 03 04 00 33 43  12 13 14 10 11 44 22 23 24 20 21 22  00 33 34 30 31 32   01 11 44 40 41 42 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate transpose of RFP A above. One therefore gets: RFP A RFP A          02 12 22 00 01 00 10 20 30 40 50          03 13 23 33 11 33 11 21 31 41 51          04 14 24 34 44 43 44 22 32 42 52 AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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