cpftrf man page on Scientific

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```CPFTRF(1LAPACK routine (version 3.2)				     CPFTRF(1)

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 posi‐
tive 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.  Fur‐
ther 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) con‐
sists 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)  con‐
sists  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)  con‐
sists  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) con‐
sists 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-	trans‐
pose   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

LAPACK routine (version 3.2)	 November 2008			     CPFTRF(1)
```
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