# ctpttf (l) - Linux Manuals

## NAME

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

## SYNOPSIS

SUBROUTINE CTPTTF(
TRANSR, UPLO, N, AP, ARF, INFO )

CHARACTER TRANSR, UPLO

INTEGER INFO, N

COMPLEX AP( 0: * ), ARF( 0: * )

## PURPOSE

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

## ARGUMENTS

TRANSR (input) CHARACTER
= aqNaq: ARF in Normal format is wanted;
= aqCaq: ARF in Conjugate-transpose format is wanted.
UPLO (input) CHARACTER

= aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) COMPLEX array, dimension ( N*(N+1)/2 ),
On entry, 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 = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
ARF (output) COMPLEX array, dimension ( N*(N+1)/2 ),
On exit, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

## 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 = aqNaq. RFP holds AP as follows:
For UPLO = aqUaq 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 = aqLaq 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 = aqNaq.

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 = aqCaq. 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 = aqNaq. RFP holds AP as follows:
For UPLO = aqUaq 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 = aqLaq 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 = aqNaq.

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 = aqCaq. 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