LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  spftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO) 
SPFTRS 
subroutine spftrs  (  character  TRANSR, 
character  UPLO,  
integer  N,  
integer  NRHS,  
real, dimension( 0: * )  A,  
real, dimension( ldb, * )  B,  
integer  LDB,  
integer  INFO  
) 
SPFTRS
Download SPFTRS + dependencies [TGZ] [ZIP] [TXT]SPFTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPFTRF.
[in]  TRANSR  TRANSR is CHARACTER*1 = 'N': The Normal TRANSR of RFP A is stored; = 'T': The Transpose TRANSR of RFP A is stored. 
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of RFP A is stored; = 'L': Lower triangle of RFP A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  NRHS  NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 
[in]  A  A is REAL 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**T, as computed by SPFTRF. See note below for more details about RFP A. 
[in,out]  B  B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
We first consider Rectangular Full Packed (RFP) 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 the transpose 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 the transpose of the last three columns of AP lower. 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 = 'T'. RFP A in both UPLO cases is just the 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 then consider Rectangular Full Packed (RFP) 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 the transpose 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 the transpose of the last two columns of AP lower. 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 = 'T'. RFP A in both UPLO cases is just the 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
Definition at line 200 of file spftrs.f.