---
name: "cpftrf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cpftrf/3lapack"
---

# cpftrf(3lapack)

computes the Cholesky factorization of a complex Hermitian positive definite matrix A

## NAME

CPFTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A

## SYNOPSIS

- SUBROUTINE CPFTRF(

  TRANSR, UPLO, N, A, INFO )

- CHARACTER

  TRANSR, UPLO

- INTEGER

  N, INFO

- COMPLEX

  A( 0: \* )

## PURPOSE

CPFTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. The factorization has the form\
\
    A = U\*\*H \* U,  if UPLO = 'U', or\
\
    A = L  \* L\*\*H,  if UPLO = 'L',\
 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

  \= 'N':  The Normal TRANSR of RFP A is stored;\
   \= 'C':  The Conjugate-transpose TRANSR of RFP A is stored.

- UPLO (input) CHARACTER

  \= 'U':  Upper triangle of RFP A is stored;\
   \= 'L':  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 = '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, 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 i-th 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 = '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