*> \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
*>
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*>
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*>
*> [TXT]
*> \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*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.
*> \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.
*
*> \date September 2012
*
*> \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 (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. 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