table of contents
| trttf(3) | Library Functions Manual | trttf(3) |
NAME¶
trttf - trttf: triangular matrix, full (tr) to RFP (tf)
SYNOPSIS¶
Functions¶
subroutine CTRTTF (transr, uplo, n, a, lda, arf, info)
CTRTTF copies a triangular matrix from the standard full format (TR) to
the rectangular full packed format (TF). subroutine DTRTTF (transr,
uplo, n, a, lda, arf, info)
DTRTTF copies a triangular matrix from the standard full format (TR) to
the rectangular full packed format (TF). subroutine STRTTF (transr,
uplo, n, a, lda, arf, info)
STRTTF copies a triangular matrix from the standard full format (TR) to
the rectangular full packed format (TF). subroutine ZTRTTF (transr,
uplo, n, a, lda, arf, info)
ZTRTTF copies a triangular matrix from the standard full format (TR) to
the rectangular full packed format (TF).
Detailed Description¶
Function Documentation¶
subroutine CTRTTF (character transr, character uplo, integer n, complex, dimension( 0: lda-1, 0: * ) a, integer lda, complex, dimension( 0: * ) arf, integer info)¶
CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Purpose:
!> !> CTRTTF copies a triangular matrix A from standard full format (TR) !> to rectangular full packed format (TF) . !>
Parameters
TRANSR
!> TRANSR is CHARACTER*1 !> = 'N': ARF in Normal mode is wanted; !> = 'C': ARF in Conjugate Transpose mode is wanted; !>
UPLO
!> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
A
!> A is COMPLEX array, dimension ( LDA, N ) !> On entry, 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
!> LDA is INTEGER !> The leading dimension of the matrix A. LDA >= max(1,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 215 of file ctrttf.f.
subroutine DTRTTF (character transr, character uplo, integer n, double precision, dimension( 0: lda-1, 0: * ) a, integer lda, double precision, dimension( 0: * ) arf, integer info)¶
DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Purpose:
!> !> DTRTTF copies a triangular matrix A from standard full format (TR) !> to rectangular full packed format (TF) . !>
Parameters
TRANSR
!> TRANSR is CHARACTER*1 !> = 'N': ARF in Normal form is wanted; !> = 'T': ARF in Transpose form is wanted. !>
UPLO
!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
A
!> A is DOUBLE PRECISION array, dimension (LDA,N). !> On entry, 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
!> LDA is INTEGER !> The leading dimension of the matrix A. LDA >= max(1,N). !>
ARF
!> ARF is DOUBLE PRECISION array, dimension (NT). !> NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. !>
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 193 of file dtrttf.f.
subroutine STRTTF (character transr, character uplo, integer n, real, dimension( 0: lda-1, 0: * ) a, integer lda, real, dimension( 0: * ) arf, integer info)¶
STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Purpose:
!> !> STRTTF copies a triangular matrix A from standard full format (TR) !> to rectangular full packed format (TF) . !>
Parameters
TRANSR
!> TRANSR is CHARACTER*1 !> = 'N': ARF in Normal form is wanted; !> = 'T': ARF in Transpose form is wanted. !>
UPLO
!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
A
!> A is REAL array, dimension (LDA,N). !> On entry, 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
!> LDA is INTEGER !> The leading dimension of the matrix A. LDA >= max(1,N). !>
ARF
!> ARF is REAL array, dimension (NT). !> NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. !>
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 193 of file strttf.f.
subroutine ZTRTTF (character transr, character uplo, integer n, complex*16, dimension( 0: lda-1, 0: * ) a, integer lda, complex*16, dimension( 0: * ) arf, integer info)¶
ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Purpose:
!> !> ZTRTTF copies a triangular matrix A from standard full format (TR) !> to rectangular full packed format (TF) . !>
Parameters
TRANSR
!> TRANSR is CHARACTER*1 !> = 'N': ARF in Normal mode is wanted; !> = 'C': ARF in Conjugate Transpose mode is wanted; !>
UPLO
!> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
A
!> A is COMPLEX*16 array, dimension ( LDA, N ) !> On entry, 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
!> LDA is INTEGER !> The leading dimension of the matrix A. LDA >= max(1,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 215 of file ztrttf.f.
Author¶
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