phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
ea86668bfcbc6dd9aa56477ec2dae9cd79e2fe8a
lapack/SRC/ctrttf.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

535 lines
15 KiB
FortranFixed
Raw Blame History

*> \brief \b CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CTRTTF + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctrttf.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctrttf.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctrttf.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANSR, UPLO
* INTEGER INFO, N, LDA
* ..
* .. Array Arguments ..
* COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> TRANSR is CHARACTER*1
*> = 'N': ARF in Normal mode is wanted;
*> = 'C': ARF in Conjugate Transpose mode is wanted;
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': A is upper triangular;
*> = 'L': A is lower triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the matrix A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] ARF
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER TRANSR, UPLO
INTEGER INFO, N, LDA
* ..
* .. Array Arguments ..
COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
* =====================================================================
*
* .. Parameters ..
* ..
* .. Local Scalars ..
LOGICAL LOWER, NISODD, NORMALTRANSR
INTEGER I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, MOD
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NORMALTRANSR = LSAME( TRANSR, 'N' )
LOWER = LSAME( UPLO, 'L' )
IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
INFO = -1
ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTRTTF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 ) THEN
IF( NORMALTRANSR ) THEN
ARF( 0 ) = A( 0, 0 )
ELSE
ARF( 0 ) = CONJG( A( 0, 0 ) )
END IF
END IF
RETURN
END IF
*
* Size of array ARF(1:2,0:nt-1)
*
NT = N*( N+1 ) / 2
*
* set N1 and N2 depending on LOWER: for N even N1=N2=K
*
IF( LOWER ) THEN
N2 = N / 2
N1 = N - N2
ELSE
N1 = N / 2
N2 = N - N1
END IF
*
* If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
* If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
* N--by--(N+1)/2.
*
IF( MOD( N, 2 ).EQ.0 ) THEN
K = N / 2
NISODD = .FALSE.
IF( .NOT.LOWER )
$ NP1X2 = N + N + 2
ELSE
NISODD = .TRUE.
IF( .NOT.LOWER )
$ NX2 = N + N
END IF
*
IF( NISODD ) THEN
*
* N is odd
*
IF( NORMALTRANSR ) THEN
*
* N is odd and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
* T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
*
IJ = 0
DO J = 0, N2
DO I = N1, N2 + J
ARF( IJ ) = CONJG( A( N2+J, I ) )
IJ = IJ + 1
END DO
DO I = J, N - 1
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
* T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
*
IJ = NT - N
DO J = N - 1, N1, -1
DO I = 0, J
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
DO L = J - N1, N1 - 1
ARF( IJ ) = CONJG( A( J-N1, L ) )
IJ = IJ + 1
END DO
IJ = IJ - NX2
END DO
*
END IF
*
ELSE
*
* N is odd and TRANSR = 'C'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, TRANSPOSE and N is odd
* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
* T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
*
IJ = 0
DO J = 0, N2 - 1
DO I = 0, J
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
DO I = N1 + J, N - 1
ARF( IJ ) = A( I, N1+J )
IJ = IJ + 1
END DO
END DO
DO J = N2, N - 1
DO I = 0, N1 - 1
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is odd
* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
* T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
*
IJ = 0
DO J = 0, N1
DO I = N1, N - 1
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
END DO
DO J = 0, N1 - 1
DO I = 0, J
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
DO L = N2 + J, N - 1
ARF( IJ ) = CONJG( A( N2+J, L ) )
IJ = IJ + 1
END DO
END DO
*
END IF
*
END IF
*
ELSE
*
* N is even
*
IF( NORMALTRANSR ) THEN
*
* N is even and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
* T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
*
IJ = 0
DO J = 0, K - 1
DO I = K, K + J
ARF( IJ ) = CONJG( A( K+J, I ) )
IJ = IJ + 1
END DO
DO I = J, N - 1
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
* T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
*
IJ = NT - N - 1
DO J = N - 1, K, -1
DO I = 0, J
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
DO L = J - K, K - 1
ARF( IJ ) = CONJG( A( J-K, L ) )
IJ = IJ + 1
END DO
IJ = IJ - NP1X2
END DO
*
END IF
*
ELSE
*
* N is even and TRANSR = 'C'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
* T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
* T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
*
IJ = 0
J = K
DO I = K, N - 1
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
DO J = 0, K - 2
DO I = 0, J
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
DO I = K + 1 + J, N - 1
ARF( IJ ) = A( I, K+1+J )
IJ = IJ + 1
END DO
END DO
DO J = K - 1, N - 1
DO I = 0, K - 1
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
* T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
* T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
*
IJ = 0
DO J = 0, K
DO I = K, N - 1
ARF( IJ ) = CONJG( A( J, I ) )
IJ = IJ + 1
END DO
END DO
DO J = 0, K - 2
DO I = 0, J
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
DO L = K + 1 + J, N - 1
ARF( IJ ) = CONJG( A( K+1+J, L ) )
IJ = IJ + 1
END DO
END DO
*
* Note that here J = K-1
*
DO I = 0, J
ARF( IJ ) = A( I, J )
IJ = IJ + 1
END DO
*
END IF
*
END IF
*
END IF
*
RETURN
*
* End of CTRTTF
*
END
Reference in New Issue View Git Blame Copy Permalink