ZTFTTR - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)
NAMEZTFTTR - copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR)
SYNOPSISSUBROUTINE ZTFTTR(  TRANSR, UPLO, N, ARF, A, LDA, INFO )  CHARACTER TRANSR, UPLO  INTEGER INFO, N, LDA  COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
PURPOSEZTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR).
ARGUMENTSTRANSR (input) CHARACTER  = 'N': ARF is in Normal format;
= 'C': ARF is in Conjugate-transpose format; UPLO (input) CHARACTER  
= 'U': A is upper triangular;
= 'L': A is lower triangular. N (input) INTEGER  The order of the matrix A. N >= 0. ARF (input) 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. A (output) COMPLEX*16 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) 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 DETAILSWe 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
0
Johanes Gumabo
Data Size   :   14,066 byte
man-ztfttr.lBuild   :   2025-03-22, 13:26   :  
Visitor Screen   :   x
Visitor Counter ( page / site )   :   2 / 1,209,923
Visitor ID   :     :  
Visitor IP   :   3.135.246.28   :  
Visitor Provider   :   AMAZON-02   :  
Provider Position ( lat x lon )   :   37.751000 x -97.822000   :   x
Provider Accuracy Radius ( km )   :   1000   :  
Provider City   :     :  
Provider Province   :   ,   :   ,
Provider Country   :   United States   :  
Provider Continent   :   North America   :  
Visitor Recorder   :   Version   :  
Visitor Recorder   :   Library   :  
Online Linux Manual Page   :   Version   :   Online Linux Manual Page - Fedora.40 - march=x86-64 - mtune=generic - 25.03.22
Online Linux Manual Page   :   Library   :   lib_c - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Online Linux Manual Page   :   Library   :   lib_m - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Data Base   :   Version   :   Online Linux Manual Page Database - 24.04.13 - march=x86-64 - mtune=generic - fedora-38
Data Base   :   Library   :   lib_c - 23.02.07 - march=x86-64 - mtune=generic - fedora.36
Very long time ago, I have the best tutor, Wenzel Svojanovsky. If someone knows the email address of Wenzel Svojanovsky, please send an email to johanesgumabo@gmail.com.
Help me, linux0001.com will expire on July 16, 2025. I have no money to renew it. View detail
If error, please print screen and send to johanes_gumabo@yahoo.co.id
Under development. Support me via PayPal.