*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [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 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 June 2016 * *> \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 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. 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