SUBROUTINE STFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO ) * * -- LAPACK routine (version 3.2) -- * * -- Contributed by Fred Gustavson of the IBM Watson Research Center -- * -- November 2008 -- * * -- 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 .. REAL A( 0: LDA-1, 0: * ), ARF( 0: * ) * .. * * Purpose * ======= * * STFTTR copies a triangular matrix A from rectangular full packed * format (TF) to standard full format (TR). * * Arguments * ========= * * TRANSR (input) CHARACTER * = 'N': ARF is in Normal format; * = 'T': ARF is in Transpose format. * * UPLO (input) CHARACTER * = 'U': A is upper triangular; * = 'L': A is lower triangular. * * N (input) INTEGER * The order of the matrices ARF and A. N >= 0. * * ARF (input) REAL array, dimension (N*(N+1)/2). * On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') * matrix A in RFP format. See the "Notes" below for more * details. * * A (output) REAL array, dimension (LDA,N) * On exit, 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 array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * Notes * ===== * * 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 N1, N2, K, NT, NX2, NP1X2 INTEGER I, J, L, IJ * .. * .. 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 = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STFTTR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.1 ) THEN IF( N.EQ.1 ) THEN A( 0, 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: 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 A( N2+J, I ) = ARF( IJ ) IJ = IJ + 1 END DO DO I = J, N - 1 A( I, J ) = ARF( IJ ) 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 A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO DO L = J - N1, N1 - 1 A( J-N1, L ) = ARF( IJ ) 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 A( J, I ) = ARF( IJ ) IJ = IJ + 1 END DO DO I = N1 + J, N - 1 A( I, N1+J ) = ARF( IJ ) IJ = IJ + 1 END DO END DO DO J = N2, N - 1 DO I = 0, N1 - 1 A( J, I ) = ARF( IJ ) 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 A( J, I ) = ARF( IJ ) IJ = IJ + 1 END DO END DO DO J = 0, N1 - 1 DO I = 0, J A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO DO L = N2 + J, N - 1 A( N2+J, L ) = ARF( IJ ) 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 A( K+J, I ) = ARF( IJ ) IJ = IJ + 1 END DO DO I = J, N - 1 A( I, J ) = ARF( IJ ) 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 A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO DO L = J - K, K - 1 A( J-K, L ) = ARF( IJ ) 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 A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO DO J = 0, K - 2 DO I = 0, J A( J, I ) = ARF( IJ ) IJ = IJ + 1 END DO DO I = K + 1 + J, N - 1 A( I, K+1+J ) = ARF( IJ ) IJ = IJ + 1 END DO END DO DO J = K - 1, N - 1 DO I = 0, K - 1 A( J, I ) = ARF( IJ ) 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 A( J, I ) = ARF( IJ ) IJ = IJ + 1 END DO END DO DO J = 0, K - 2 DO I = 0, J A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO DO L = K + 1 + J, N - 1 A( K+1+J, L ) = ARF( IJ ) IJ = IJ + 1 END DO END DO * Note that here, on exit of the loop, J = K-1 DO I = 0, J A( I, J ) = ARF( IJ ) IJ = IJ + 1 END DO * END IF * END IF * END IF * RETURN * * End of STFTTR * END