zpftrf (l)  Linux Man Pages
zpftrf: computes the Cholesky factorization of a complex Hermitian positive definite matrix A
NAME
ZPFTRF  computes the Cholesky factorization of a complex Hermitian positive definite matrix ASYNOPSIS
 SUBROUTINE ZPFTRF(
 TRANSR, UPLO, N, A, INFO )
 CHARACTER TRANSR, UPLO
 INTEGER N, INFO
 COMPLEX*16 A( 0: * )
PURPOSE
ZPFTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. The factorization has the formA
A
where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS.
ARGUMENTS
 TRANSR (input) CHARACTER

= aqNaq: The Normal TRANSR of RFP A is stored;
= aqCaq: The Conjugatetranspose 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.
 A (input/output) 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 = aqNaq
then RFP A is (0:N,0:k1) when N is even; k=N/2. RFP A is
(0:N1,0:k) when N is odd; k=N/2. IF TRANSR = aqCaq then RFP is the Conjugatetranspose of RFP A as defined when TRANSR = aqNaq. The contents of RFP A are defined by UPLO as follows: If UPLO = aqUaq the RFP A contains the nt elements of upper packed A. If UPLO = aqLaq the RFP A contains the elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = aqCaq. When TRANSR is aqNaq the LDA is N+1 when N is even and N is odd. See the Note below for more details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization RFP A = U**H*U or RFP A = L*L**H.  INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed. Further Notes on RFP Format: ============================ 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 = 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 conjugatetranspose 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 conjugatetranspose of the last three columns of AP lower. To denote conjugate we place  above the element. This covers the case N even and TRANSR = aqNaq. 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 = aqCaq. 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 = aqNaq. RFP holds AP as follows: For UPLO = aqUaq 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 conjugatetranspose of the first two columns of AP upper. For UPLO = aqLaq 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 conjugatetranspose of the last two columns of AP lower. To denote conjugate we place  above the element. This covers the case N odd and TRANSR = aqNaq. 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 = aqCaq. 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