SRC/zpftrs.f(3) Library Functions Manual SRC/zpftrs.f(3)
NAME
SRC/zpftrs.f
SYNOPSIS
Functions/Subroutines
subroutine zpftrs (transr, uplo, n, nrhs, a, b, ldb, info)
ZPFTRS
Function/Subroutine Documentation
subroutine zpftrs (character transr, character uplo, integer n, integer
nrhs, complex*16, dimension( 0: * ) a, complex*16, dimension( ldb, * )
b, integer ldb, integer info)
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.
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 219 of file zpftrs.f.
Author
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