*> \brief \b DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTFTTP + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANSR, UPLO
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> TRANSR is CHARACTER*1
*> = 'N': ARF is in Normal format;
*> = 'T': ARF is in Transpose format;
*> \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] ARF
*> \verbatim
*> ARF is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[out] AP
*> \verbatim
*> AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
*> On exit, 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.
*> \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 December 2016
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER TRANSR, UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
* ..
*
* =====================================================================
*
* .. Parameters ..
* ..
* .. Local Scalars ..
LOGICAL LOWER, NISODD, NORMALTRANSR
INTEGER N1, N2, K, NT
INTEGER I, J, IJ
INTEGER IJP, JP, LDA, JS
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NORMALTRANSR = LSAME( TRANSR, 'N' )
LOWER = LSAME( UPLO, 'L' )
IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
INFO = -1
ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTFTTP', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
IF( NORMALTRANSR ) THEN
AP( 0 ) = ARF( 0 )
ELSE
AP( 0 ) = ARF( 0 )
END IF
RETURN
END IF
*
* Size of array ARF(0:NT-1)
*
NT = N*( N+1 ) / 2
*
* Set N1 and N2 depending on LOWER
*
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.
* If N is even, set K = N/2 and NISODD = .FALSE.
*
* set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
* where noe = 0 if n is even, noe = 1 if n is odd
*
IF( MOD( N, 2 ).EQ.0 ) THEN
K = N / 2
NISODD = .FALSE.
LDA = N + 1
ELSE
NISODD = .TRUE.
LDA = N
END IF
*
* ARF^C has lda rows and n+1-noe cols
*
IF( .NOT.NORMALTRANSR )
$ LDA = ( N+1 ) / 2
*
* start execution: there are eight cases
*
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
*
IJP = 0
JP = 0
DO J = 0, N2
DO I = J, N - 1
IJ = I + JP
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JP = JP + LDA
END DO
DO I = 0, N2 - 1
DO J = 1 + I, N2
IJ = I + J*LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 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)
*
IJP = 0
DO J = 0, N1 - 1
IJ = N2 + J
DO I = 0, J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
IJ = IJ + LDA
END DO
END DO
JS = 0
DO J = N1, N - 1
IJ = JS
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
*
END IF
*
ELSE
*
* N is odd and TRANSR = 'T'
*
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
*
IJP = 0
DO I = 0, N2
DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
JS = 1
DO J = 0, N2 - 1
DO IJ = JS, JS + N2 - J - 1
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA + 1
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
*
IJP = 0
JS = N2*LDA
DO J = 0, N1 - 1
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
DO I = 0, N1
DO IJ = I, I + ( N1+I )*LDA, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 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)
*
IJP = 0
JP = 0
DO J = 0, K - 1
DO I = J, N - 1
IJ = 1 + I + JP
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JP = JP + LDA
END DO
DO I = 0, K - 1
DO J = I, K - 1
IJ = I + J*LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 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)
*
IJP = 0
DO J = 0, K - 1
IJ = K + 1 + J
DO I = 0, J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
IJ = IJ + LDA
END DO
END DO
JS = 0
DO J = K, N - 1
IJ = JS
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
*
END IF
*
ELSE
*
* N is even and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, TRANSPOSE and N is even (see paper)
* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
*
IJP = 0
DO I = 0, K - 1
DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
JS = 0
DO J = 0, K - 1
DO IJ = JS, JS + K - J - 1
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA + 1
END DO
*
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is even (see paper)
* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
*
IJP = 0
JS = ( K+1 )*LDA
DO J = 0, K - 1
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
DO I = 0, K - 1
DO IJ = I, I + ( K+I )*LDA, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
*
END IF
*
END IF
*
END IF
*
RETURN
*
* End of DTFTTP
*
END