ztpttf - copy a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF)
SUBROUTINE ZTPTTF(TRANSR, UPLO, N, AP, ARF, INFO) CHARACTER*1 TRANSR, UPLO INTEGER INFO, N DOUBLE COMPLEX AP(0:*), ARF(0:*) SUBROUTINE ZTPTTF_64(TRANSR, UPLO, N, AP, ARF, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 INFO, N DOUBLE COMPLEX AP(0:*), ARF(0:*) F95 INTERFACE SUBROUTINE TPTTF(TRANSR, UPLO, N, AP, ARF, INFO) INTEGER :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: AP, ARF SUBROUTINE TPTTF_64(TRANSR, UPLO, N, AP, ARF, INFO) INTEGER(8) :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: AP, ARF C INTERFACE #include <sunperf.h> void ztpttf (char transr, char uplo, int n, doublecomplex *ap, double- complex *arf, int *info); void ztpttf_64 (char transr, char uplo, long n, doublecomplex *ap, dou- blecomplex *arf, long *info);
Oracle Solaris Studio Performance Library ztpttf(3P)
NAME
ztpttf - copy a triangular matrix from the standard packed format (TP)
to the rectangular full packed format (TF)
SYNOPSIS
SUBROUTINE ZTPTTF(TRANSR, UPLO, N, AP, ARF, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER INFO, N
DOUBLE COMPLEX AP(0:*), ARF(0:*)
SUBROUTINE ZTPTTF_64(TRANSR, UPLO, N, AP, ARF, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER*8 INFO, N
DOUBLE COMPLEX AP(0:*), ARF(0:*)
F95 INTERFACE
SUBROUTINE TPTTF(TRANSR, UPLO, N, AP, ARF, INFO)
INTEGER :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: AP, ARF
SUBROUTINE TPTTF_64(TRANSR, UPLO, N, AP, ARF, INFO)
INTEGER(8) :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: AP, ARF
C INTERFACE
#include <sunperf.h>
void ztpttf (char transr, char uplo, int n, doublecomplex *ap, double-
complex *arf, int *info);
void ztpttf_64 (char transr, char uplo, long n, doublecomplex *ap, dou-
blecomplex *arf, long *info);
PURPOSE
ztpttf copies a triangular matrix A from standard packed format (TP) to
rectangular full packed format (TF).
ARGUMENTS
TRANSR (input)
TRANSR is CHARACTER*1
= 'N': ARF in Normal format is wanted;
= 'C': ARF in Conjugate-transpose format is wanted.
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.
AP (input)
AP is COMPLEX*16 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 = '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.
ARF (output)
ARF is COMPLEX*16 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)
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 ztpttf(3P)