Library Functions Manual

NAME¶

tpttf - tpttf: triangular matrix, packed (tp) to RFP (tf)

SYNOPSIS¶

Functions¶

subroutine CTPTTF (transr, uplo, n, ap, arf, info)
CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). subroutine DTPTTF (transr, uplo, n, ap, arf, info)
DTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). subroutine STPTTF (transr, uplo, n, ap, arf, info)
STPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). subroutine ZTPTTF (transr, uplo, n, ap, arf, info)
ZTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Detailed Description¶

Function Documentation¶

subroutine CTPTTF (character transr, character uplo, integer n, complex, dimension( 0: * ) ap, complex, dimension( 0: * ) arf, integer info)¶

CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Purpose:

!>
!> CTPTTF copies a triangular matrix A from standard packed format (TP)
!> to rectangular full packed format (TF).
!>

Parameters

TRANSR

!>          TRANSR is CHARACTER*1
!>          = 'N':  ARF in Normal format is wanted;
!>          = 'C':  ARF in Conjugate-transpose format is wanted.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          AP is COMPLEX 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

!>          ARF is COMPLEX 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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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
!>

Definition at line 206 of file ctpttf.f.

subroutine DTPTTF (character transr, character uplo, integer n, double precision, dimension( 0: * ) ap, double precision, dimension( 0: * ) arf, integer info)¶

DTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Purpose:

!>
!> DTPTTF copies a triangular matrix A from standard packed format (TP)
!> to rectangular full packed format (TF).
!>

Parameters

TRANSR

!>          TRANSR is CHARACTER*1
!>          = 'N':  ARF in Normal format is wanted;
!>          = 'T':  ARF in Conjugate-transpose format is wanted.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          AP is DOUBLE PRECISION 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

!>          ARF is DOUBLE PRECISION 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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  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
!>

Definition at line 185 of file dtpttf.f.

subroutine STPTTF (character transr, character uplo, integer n, real, dimension( 0: * ) ap, real, dimension( 0: * ) arf, integer info)¶

STPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Purpose:

!>
!> STPTTF copies a triangular matrix A from standard packed format (TP)
!> to rectangular full packed format (TF).
!>

Parameters

TRANSR

!>          TRANSR is CHARACTER*1
!>          = 'N':  ARF in Normal format is wanted;
!>          = 'T':  ARF in Conjugate-transpose format is wanted.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          AP is REAL 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

!>          ARF is REAL 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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  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
!>

Definition at line 185 of file stpttf.f.

subroutine ZTPTTF (character transr, character uplo, integer n, complex16, dimension( 0: ) ap, complex16, dimension( 0: ) arf, integer info)¶

ZTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Purpose:

!>
!> ZTPTTF copies a triangular matrix A from standard packed format (TP)
!> to rectangular full packed format (TF).
!>

Parameters

TRANSR

!>          TRANSR is CHARACTER*1
!>          = 'N':  ARF in Normal format is wanted;
!>          = 'C':  ARF in Conjugate-transpose format is wanted.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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

!>          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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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
!>

Definition at line 206 of file ztpttf.f.

Author¶

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NAME¶

SYNOPSIS¶

Functions¶

Detailed Description¶

Function Documentation¶

subroutine CTPTTF (character transr, character uplo, integer n, complex, dimension( 0: * ) ap, complex, dimension( 0: * ) arf, integer info)¶

subroutine DTPTTF (character transr, character uplo, integer n, double precision, dimension( 0: * ) ap, double precision, dimension( 0: * ) arf, integer info)¶

subroutine STPTTF (character transr, character uplo, integer n, real, dimension( 0: * ) ap, real, dimension( 0: * ) arf, integer info)¶

subroutine ZTPTTF (character transr, character uplo, integer n, complex*16, dimension( 0: * ) ap, complex*16, dimension( 0: * ) arf, integer info)¶

Author¶

subroutine ZTPTTF (character transr, character uplo, integer n, complex16, dimension( 0: ) ap, complex16, dimension( 0: ) arf, integer info)¶