SUBROUTINE DTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* -- LAPACK routine (version 3.2.1) --
*
* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
* -- April 2009 --
*
* -- 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 ..
DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
* Purpose
* =======
*
* DTRTTF copies a triangular matrix A from standard full format (TR)
* to rectangular full packed format (TF) .
*
* Arguments
* =========
*
* TRANSR (input) CHARACTER
* = 'N': ARF in Normal form is wanted;
* = 'T': ARF in Transpose form is wanted.
*
* UPLO (input) CHARACTER
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input) 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 (input) INTEGER
* The leading dimension of the matrix A. LDA >= max(1,N).
*
* ARF (output) DOUBLE PRECISION array, dimension (NT).
* NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* 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 first 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
*
* Reference
* =========
*
* =====================================================================
*
* ..
* .. 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 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, 'T' ) ) 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( 'DTRTTF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 ) THEN
ARF( 0 ) = A( 0, 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: 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
*
* N is odd, TRANSR = 'N', and UPLO = 'L'
*
IJ = 0
DO J = 0, N2
DO I = N1, N2 + J
ARF( IJ ) = 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
*
* N is odd, TRANSR = 'N', and UPLO = 'U'
*
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 ) = A( J-N1, L )
IJ = IJ + 1
END DO
IJ = IJ - NX2
END DO
*
END IF
*
ELSE
*
* N is odd and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* N is odd, TRANSR = 'T', and UPLO = 'L'
*
IJ = 0
DO J = 0, N2 - 1
DO I = 0, J
ARF( IJ ) = 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 ) = A( J, I )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* N is odd, TRANSR = 'T', and UPLO = 'U'
*
IJ = 0
DO J = 0, N1
DO I = N1, N - 1
ARF( IJ ) = 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 ) = 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
*
* N is even, TRANSR = 'N', and UPLO = 'L'
*
IJ = 0
DO J = 0, K - 1
DO I = K, K + J
ARF( IJ ) = 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
*
* N is even, TRANSR = 'N', and UPLO = 'U'
*
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 ) = A( J-K, L )
IJ = IJ + 1
END DO
IJ = IJ - NP1X2
END DO
*
END IF
*
ELSE
*
* N is even and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* N is even, TRANSR = 'T', and UPLO = 'L'
*
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 ) = 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 ) = A( J, I )
IJ = IJ + 1
END DO
END DO
*
ELSE
*
* N is even, TRANSR = 'T', and UPLO = 'U'
*
IJ = 0
DO J = 0, K
DO I = K, N - 1
ARF( IJ ) = 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 ) = A( K+1+J, L )
IJ = IJ + 1
END DO
END DO
* Note that here, on exit of the loop, 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 DTRTTF
*
END