ctfttr (l) - Linux Manuals

ctfttr: copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR)

Command to display ctfttr manual in Linux: $ man l ctfttr

NAME

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

SYNOPSIS

SUBROUTINE CTFTTR(: TRANSR, UPLO, N, ARF, A, LDA, INFO )
: CHARACTER TRANSR, UPLO
: INTEGER INFO, N, LDA
: COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )

PURPOSE

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

ARGUMENTS

TRANSR (input) CHARACTER: = aqNaq: ARF is in Normal format;
= aqCaq: ARF is in Conjugate-transpose format;
UPLO (input) CHARACTER: = aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.
N (input) INTEGER: The order of the matrix A. N >= 0.
ARF (input) COMPLEX 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.
A (output) COMPLEX array, dimension ( LDA, N ): On exit, the triangular matrix A. If UPLO = aqUaq, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = aqLaq, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
LDA (input) INTEGER: The leading dimension of the array A. LDA >= max(1,N).
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