ztfttp - mat (TF) to the standard packed format (TP)
SUBROUTINE ZTFTTP(TRANSR, UPLO, N, ARF, AP, INFO) CHARACTER*1 TRANSR, UPLO INTEGER INFO, N DOUBLE COMPLEX AP(0:*), ARF(0:*) SUBROUTINE ZTFTTP_64(TRANSR, UPLO, N, ARF, AP, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 INFO, N DOUBLE COMPLEX AP(0:*), ARF(0:*) F95 INTERFACE SUBROUTINE TFTTP(TRANSR, UPLO, N, ARF, AP, INFO) INTEGER :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: ARF, AP SUBROUTINE TFTTP_64(TRANSR, UPLO, N, ARF, AP, INFO) INTEGER(8) :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: ARF, AP C INTERFACE #include <sunperf.h> void ztfttp (char transr, char uplo, int n, doublecomplex *arf, double- complex *ap, int *info); void ztfttp_64 (char transr, char uplo, long n, doublecomplex *arf, doublecomplex *ap, long *info);
Oracle Solaris Studio Performance Library ztfttp(3P)
NAME
ztfttp - copy a triangular matrix from the rectangular full packed for-
mat (TF) to the standard packed format (TP)
SYNOPSIS
SUBROUTINE ZTFTTP(TRANSR, UPLO, N, ARF, AP, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER INFO, N
DOUBLE COMPLEX AP(0:*), ARF(0:*)
SUBROUTINE ZTFTTP_64(TRANSR, UPLO, N, ARF, AP, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER*8 INFO, N
DOUBLE COMPLEX AP(0:*), ARF(0:*)
F95 INTERFACE
SUBROUTINE TFTTP(TRANSR, UPLO, N, ARF, AP, INFO)
INTEGER :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: ARF, AP
SUBROUTINE TFTTP_64(TRANSR, UPLO, N, ARF, AP, INFO)
INTEGER(8) :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: ARF, AP
C INTERFACE
#include <sunperf.h>
void ztfttp (char transr, char uplo, int n, doublecomplex *arf, double-
complex *ap, int *info);
void ztfttp_64 (char transr, char uplo, long n, doublecomplex *arf,
doublecomplex *ap, long *info);
PURPOSE
ztfttp copies a triangular matrix A from rectangular full packed format
(TF) to standard packed format (TP).
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*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 (output)
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 (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 ztfttp(3P)