# ztfttp.f(3) [debian man page]

```ztfttp.f(3)							      LAPACK							       ztfttp.f(3)

NAME
ztfttp.f -

SYNOPSIS
Functions/Subroutines
subroutine ztfttp (TRANSR, UPLO, N, ARF, AP, INFO)
ZTFTTP

Function/Subroutine Documentation
subroutine ztfttp (characterTRANSR, characterUPLO, integerN, complex*16, dimension( 0: * )ARF, complex*16, dimension( 0: * )AP, integerINFO)
ZTFTTP

Purpose:

ZTFTTP copies a triangular matrix A from rectangular full packed
format (TF) to standard packed format (TP).

Parameters:
TRANSR

TRANSR is CHARACTER*1
= 'N':  ARF is in Normal format;
= 'C':  ARF is in Conjugate-transpose format;

UPLO

UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.

N

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

ARF

ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
On entry, the upper or lower triangular matrix A stored in
RFP format. For a further discussion see Notes below.

AP

AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
On exit, the upper or lower triangular matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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 209 of file ztfttp.f.

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

Version 3.4.1							  Sun May 26 2013						       ztfttp.f(3)```
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