dtfttr - mat (TF) to the standard full format (TR)
SUBROUTINE DTFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO) CHARACTER*1 TRANSR, UPLO INTEGER INFO, N, LDA DOUBLE PRECISION A(0:LDA-1,0:*), ARF(0:*) SUBROUTINE DTFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 INFO, N, LDA DOUBLE PRECISION 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 REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: ARF SUBROUTINE TFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: TRANSR, UPLO REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: ARF C INTERFACE #include <sunperf.h> void dtfttr (char transr, char uplo, int n, double *arf, double *a, int lda, int *info); void dtfttr_64 (char transr, char uplo, long n, double *arf, double *a, long lda, long *info);
Oracle Solaris Studio Performance Library dtfttr(3P)
NAME
dtfttr - copy a triangular matrix from the rectangular full packed for-
mat (TF) to the standard full format (TR)
SYNOPSIS
SUBROUTINE DTFTTR(TRANSR, UPLO, N, ARF, A, LDA, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER INFO, N, LDA
DOUBLE PRECISION A(0:LDA-1,0:*), ARF(0:*)
SUBROUTINE DTFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER*8 INFO, N, LDA
DOUBLE PRECISION 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
REAL(8), DIMENSION(:,:) :: A
REAL(8), DIMENSION(:) :: ARF
SUBROUTINE TFTTR_64(TRANSR, UPLO, N, ARF, A, LDA, INFO)
INTEGER(8) :: N, LDA, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
REAL(8), DIMENSION(:,:) :: A
REAL(8), DIMENSION(:) :: ARF
C INTERFACE
#include <sunperf.h>
void dtfttr (char transr, char uplo, int n, double *arf, double *a, int
lda, int *info);
void dtfttr_64 (char transr, char uplo, long n, double *arf, double *a,
long lda, long *info);
PURPOSE
dtfttr 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;
= 'T': ARF is in 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 matrices ARF and A. N >= 0.
ARF (input)
ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2).
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
matrix A in RFP format. See the "Notes" below for more
details.
A (output)
A is DOUBLE PRECISION 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 NOTES ON RFP FORMAT
We first consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last three columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the 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 then consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last two columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the 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 dtfttr(3P)