table of contents
| tfttr(3) | LAPACK | tfttr(3) |
NAME¶
tfttr - tfttr: triangular matrix, RFP (tf) to full (tr)
SYNOPSIS¶
Functions¶
subroutine ctfttr (transr, uplo, n, arf, a, lda, info)
CTFTTR copies a triangular matrix from the rectangular full packed
format (TF) to the standard full format (TR). subroutine dtfttr
(transr, uplo, n, arf, a, lda, info)
DTFTTR copies a triangular matrix from the rectangular full packed
format (TF) to the standard full format (TR). subroutine stfttr
(transr, uplo, n, arf, a, lda, info)
STFTTR copies a triangular matrix from the rectangular full packed
format (TF) to the standard full format (TR). subroutine ztfttr
(transr, uplo, n, arf, a, lda, info)
ZTFTTR copies a triangular matrix from the rectangular full packed
format (TF) to the standard full format (TR).
Detailed Description¶
Function Documentation¶
subroutine ctfttr (character transr, character uplo, integer n, complex, dimension( 0: * ) arf, complex, dimension( 0: lda-1, 0: * ) a, integer lda, integer info)¶
CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
Purpose:
CTFTTR copies a triangular matrix A from rectangular full packed
format (TF) to standard full format (TR).
Parameters
TRANSR
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'C': ARF is in Conjugate-transpose format;
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.
ARF
ARF is COMPLEX 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
A is COMPLEX 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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
subroutine dtfttr (character transr, character uplo, integer n, double precision, dimension( 0: * ) arf, double precision, dimension( 0: lda-1, 0: * ) a, integer lda, integer info)¶
DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
Purpose:
DTFTTR copies a triangular matrix A from rectangular full packed
format (TF) to standard full format (TR).
Parameters
TRANSR
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'T': ARF is in Transpose format.
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
N
N is INTEGER
The order of the matrices ARF and A. N >= 0.
ARF
ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2).
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
matrix A in RFP format. See the 'Notes' below for more
details.
A
A is DOUBLE PRECISION 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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
subroutine stfttr (character transr, character uplo, integer n, real, dimension( 0: * ) arf, real, dimension( 0: lda-1, 0: * ) a, integer lda, integer info)¶
STFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
Purpose:
STFTTR copies a triangular matrix A from rectangular full packed
format (TF) to standard full format (TR).
Parameters
TRANSR
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'T': ARF is in Transpose format.
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
N
N is INTEGER
The order of the matrices ARF and A. N >= 0.
ARF
ARF is REAL array, dimension (N*(N+1)/2).
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
matrix A in RFP format. See the 'Notes' below for more
details.
A
A is REAL 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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
subroutine ztfttr (character transr, character uplo, integer n, complex*16, dimension( 0: * ) arf, complex*16, dimension( 0: lda-1, 0: * ) a, integer lda, integer info)¶
ZTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
Purpose:
ZTFTTR copies a triangular matrix A from rectangular full packed
format (TF) to standard full format (TR).
Parameters
TRANSR
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'C': ARF is in Conjugate-transpose format;
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.
ARF
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.
A
A is 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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
Author¶
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