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zpftri.f(3) LAPACK zpftri.f(3)

zpftri.f -


subroutine zpftri (TRANSR, UPLO, N, A, INFO)
 
ZPFTRI

ZPFTRI
Purpose:
 ZPFTRI computes the inverse of a complex 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 A is stored;
          = 'L':  Lower triangle of A is stored.
N
          N is INTEGER
          The order of the matrix A.  N >= 0.
A
          A is COMPLEX*16 array, dimension ( N*(N+1)/2 );
          On entry, the Hermitian matrix A in RFP format. RFP format is
          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
          the Conjugate-transpose of RFP A as defined when
          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
          follows: If UPLO = 'U' the RFP A contains the nt elements of
          upper packed A. If UPLO = 'L' the RFP A contains the elements
          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
          'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N
          is odd. See the Note below for more details.
On exit, the Hermitian inverse of the original matrix, in the same storage format.
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the (i,i) element of the factor U or L is
                zero, and the inverse could not be computed.
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 213 of file zpftri.f.

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