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SUBROUTINE STPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
* * -- LAPACK routine (version 3.3.1) -- * * -- Contributed by Fred Gustavson of the IBM Watson Research Center -- * -- April 2011 -- * * -- 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 * .. * .. Array Arguments .. REAL AP( 0: * ), ARF( 0: * ) * * Purpose * ======= * * STPTTF copies a triangular matrix A from standard packed format (TP) * to rectangular full packed format (TF). * * Arguments * ========= * * TRANSR (input) CHARACTER*1 * = 'N': ARF in Normal format is wanted; * = 'T': ARF in Conjugate-transpose format is wanted. * * UPLO (input) CHARACTER*1 * = 'U': A is upper triangular; * = 'L': A is lower triangular. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input) REAL array, dimension ( N*(N+1)/2 ), * On entry, 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. * * ARF (output) REAL 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. * * 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 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 * * ===================================================================== * * .. 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 * .. * .. Intrinsic Functions .. INTRINSIC 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 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STPTTF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN IF( NORMALTRANSR ) THEN ARF( 0 ) = AP( 0 ) ELSE ARF( 0 ) = AP( 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 * * N is odd, TRANSR = 'N', and UPLO = 'L' * IJP = 0 JP = 0 DO J = 0, N2 DO I = J, N - 1 IJ = I + JP ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JP = JP + LDA END DO DO I = 0, N2 - 1 DO J = 1 + I, N2 IJ = I + J*LDA ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO END DO * ELSE * * N is odd, TRANSR = 'N', and UPLO = 'U' * IJP = 0 DO J = 0, N1 - 1 IJ = N2 + J DO I = 0, J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 IJ = IJ + LDA END DO END DO JS = 0 DO J = N1, N - 1 IJ = JS DO IJ = JS, JS + J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA END DO * END IF * ELSE * * N is odd and TRANSR = 'T' * IF( LOWER ) THEN * * N is odd, TRANSR = 'T', and UPLO = 'L' * IJP = 0 DO I = 0, N2 DO IJ = I*( LDA+1 ), N*LDA - 1, LDA ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO END DO JS = 1 DO J = 0, N2 - 1 DO IJ = JS, JS + N2 - J - 1 ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA + 1 END DO * ELSE * * N is odd, TRANSR = 'T', and UPLO = 'U' * IJP = 0 JS = N2*LDA DO J = 0, N1 - 1 DO IJ = JS, JS + J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA END DO DO I = 0, N1 DO IJ = I, I + ( N1+I )*LDA, LDA ARF( IJ ) = AP( IJP ) 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 * * N is even, TRANSR = 'N', and UPLO = 'L' * IJP = 0 JP = 0 DO J = 0, K - 1 DO I = J, N - 1 IJ = 1 + I + JP ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JP = JP + LDA END DO DO I = 0, K - 1 DO J = I, K - 1 IJ = I + J*LDA ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO END DO * ELSE * * N is even, TRANSR = 'N', and UPLO = 'U' * IJP = 0 DO J = 0, K - 1 IJ = K + 1 + J DO I = 0, J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 IJ = IJ + LDA END DO END DO JS = 0 DO J = K, N - 1 IJ = JS DO IJ = JS, JS + J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA END DO * END IF * ELSE * * N is even and TRANSR = 'T' * IF( LOWER ) THEN * * N is even, TRANSR = 'T', and UPLO = 'L' * IJP = 0 DO I = 0, K - 1 DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO END DO JS = 0 DO J = 0, K - 1 DO IJ = JS, JS + K - J - 1 ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA + 1 END DO * ELSE * * N is even, TRANSR = 'T', and UPLO = 'U' * IJP = 0 JS = ( K+1 )*LDA DO J = 0, K - 1 DO IJ = JS, JS + J ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO JS = JS + LDA END DO DO I = 0, K - 1 DO IJ = I, I + ( K+I )*LDA, LDA ARF( IJ ) = AP( IJP ) IJP = IJP + 1 END DO END DO * END IF * END IF * END IF * RETURN * * End of STPTTF * END |