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zpftrs.f(3) LAPACK zpftrs.f(3)

zpftrs.f -


subroutine zpftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO)
 
ZPFTRS

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.
Parameters:
TRANSR
          TRANSR is CHARACTER*1
          = 'N':  The Normal TRANSR of RFP A is stored;
          = 'C':  The Conjugate-transpose 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 i-th argument had an illegal value
Author:
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 conjugate-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 conjugate-transpose 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 conjugate-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 conjugate-transpose 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
Definition at line 221 of file zpftrs.f.

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