CPFTRS man page on Oracle

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```cpftrs.f(3)			    LAPACK			   cpftrs.f(3)

NAME
cpftrs.f -

SYNOPSIS
Functions/Subroutines
subroutine cpftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO)
CPFTRS

Function/Subroutine Documentation
subroutine cpftrs (characterTRANSR, characterUPLO, integerN, integerNRHS,
complex, dimension( 0: * )A, complex, dimension( ldb, * )B, integerLDB,
integerINFO)
CPFTRS

Purpose:

CPFTRS solves a system of linear equations A*X = B with a 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 RFP A is stored;
= 'L':  Lower triangle of RFP A is stored.

N

N is INTEGER
The order of the matrix A.	 N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

A

A is COMPLEX array, dimension ( N*(N+1)/2 );
The triangular factor U or L from the Cholesky factorization
of RFP A = U**H*U or RFP A = L*L**H, as computed by CPFTRF.
See note below for more details about RFP A.

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

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 221 of file cpftrs.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			   cpftrs.f(3)
```
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