ctfttr - mat (TF) to the standard full format (TR)
SUBROUTINE CTFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO) CHARACTER*1 TRANSR, UPLO INTEGER INFO, N, LDA COMPLEX A(0:LDA-1,0:*), ARF(0:*) SUBROUTINE CTFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 INFO, N, LDA COMPLEX A(0:LDA-1,0:*), ARF(0:*) F95 INTERFACE SUBROUTINE TFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO) INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:,:) :: A COMPLEX, DIMENSION(:) :: ARF SUBROUTINE TFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:,:) :: A COMPLEX, DIMENSION(:) :: ARF C INTERFACE #include <sunperf.h> void ctfttr (char transr, char uplo, int n, floatcomplex *arf, float- complex *a, int lda, int *info); void ctfttr_64 (char transr, char uplo, long n, floatcomplex *arf, floatcomplex *a, long lda, long *info);
Oracle Solaris Studio Performance Library ctfttr(3P)
NAME
ctfttr - copy a triangular matrix from the rectangular full packed for-
mat (TF) to the standard full format (TR)
SYNOPSIS
SUBROUTINE CTFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER INFO, N, LDA
COMPLEX A(0:LDA-1,0:*), ARF(0:*)
SUBROUTINE CTFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER*8 INFO, N, LDA
COMPLEX A(0:LDA-1,0:*), ARF(0:*)
F95 INTERFACE
SUBROUTINE TFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO)
INTEGER :: N, LDA, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX, DIMENSION(:,:) :: A
COMPLEX, DIMENSION(:) :: ARF
SUBROUTINE TFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO)
INTEGER(8) :: N, LDA, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX, DIMENSION(:,:) :: A
COMPLEX, DIMENSION(:) :: ARF
C INTERFACE
#include <sunperf.h>
void ctfttr (char transr, char uplo, int n, floatcomplex *arf, float-
complex *a, int lda, int *info);
void ctfttr_64 (char transr, char uplo, long n, floatcomplex *arf,
floatcomplex *a, long lda, long *info);
PURPOSE
ctfttr copies a triangular matrix A from rectangular full packed format
(TF) to standard full format (TR).
ARGUMENTS
TRANSR (input)
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'C': ARF is in Conjugate-transpose format;
UPLO (input)
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
N (input)
N is INTEGER
The order of the matrix A. N >= 0.
ARF (input)
ARF is 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)
A is COMPLEX array, dimension ( LDA, N )
On exit, the triangular matrix A. If UPLO = 'U', 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 = 'L', 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)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output)
INFO is 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 = '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
7 Nov 2015 ctfttr(3P)