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cpftri-f(3)

cpftri.f –

Synopsis

Functions/Subroutines

subroutine cpftri (TRANSR, UPLO, N, A, INFO)
CPFTRI

Function/Subroutine Documentation

subroutine cpftri (characterTRANSR, characterUPLO, integerN, complex, dimension( 0: * )A, integerINFO)

CPFTRI

Purpose:

 CPFTRI 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 CPFTRF.

 

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 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 cpftri.f.

Author

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