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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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