dpftrs (l)  Linux Man Pages
dpftrs: 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 DPFTRF
NAME
DPFTRS  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 DPFTRFSYNOPSIS
 SUBROUTINE DPFTRS(
 TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
 CHARACTER TRANSR, UPLO
 INTEGER INFO, LDB, N, NRHS
 DOUBLE PRECISION A( 0: * ), B( LDB, * )
PURPOSE
DPFTRS 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 DPFTRF.ARGUMENTS
 TRANSR (input) CHARACTER

= aqNaq: The Normal TRANSR of RFP A is stored;
= aqTaq: The Transpose TRANSR of RFP A is stored.  UPLO (input) CHARACTER

= aqUaq: Upper triangle of RFP A is stored;
= aqLaq: Lower triangle of RFP A is stored.  N (input) INTEGER
 The order of the matrix A. N >= 0.
 NRHS (input) INTEGER
 The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
 A (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
 The triangular factor U or L from the Cholesky factorization of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF. See note below for more details about RFP A.
 B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 On entry, the right hand side matrix B. On exit, the solution matrix X.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,N).
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
We first consider Rectangular Full Packed (RFP) Format when N is even. We give an example where N = 6.Let TRANSR = aqNaq. RFP holds AP as follows:
For UPLO = aqUaq 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 = aqLaq 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 = aqNaq.
03 04 05
13 14 15
23 24 25
33 34 35
00 44 45
01 11 55
02 12 22
Now let TRANSR = aqTaq. RFP A in both UPLO cases is just the transpose of RFP A above. One therefore gets:
03 13 23 33 00 01 02
04 14 24 34 44 11 12
05 15 25 35 45 55 22
We first consider Rectangular Full Packed (RFP) Format when N is odd. We give an example where N = 5.
AP is Upper