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author | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
commit | ff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch) | |
tree | a386cad907bcaefd6893535c31d67ec9468e693e /SRC/ctfttr.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) | |
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Diffstat (limited to 'SRC/ctfttr.f')
-rw-r--r-- | SRC/ctfttr.f | 470 |
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diff --git a/SRC/ctfttr.f b/SRC/ctfttr.f new file mode 100644 index 00000000..bc23d16d --- /dev/null +++ b/SRC/ctfttr.f @@ -0,0 +1,470 @@ + SUBROUTINE CTFTTR( 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 .. + COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * ) +* .. +* +* Purpose +* ======= +* +* CTFTTR 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; +* = 'C': ARF is in Conjugate-transpose format; +* +* UPLO (input) CHARACTER +* = 'U': A is upper triangular; +* = 'L': A is lower triangular. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* ARF (input) COMPLEX 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. +* +* A (output) COMPLEX 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 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 +* +* ===================================================================== +* +* .. Parameters .. +* .. +* .. 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 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 = -6 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CTFTTR', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.LE.1 ) THEN + IF( N.EQ.1 ) THEN + IF( NORMALTRANSR ) THEN + A( 0, 0 ) = ARF( 0 ) + ELSE + A( 0, 0 ) = CONJG( ARF( 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 + A( N2+J, I ) = CONJG( 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 +* +* 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 + A( I, J ) = ARF( IJ ) + IJ = IJ + 1 + END DO + DO L = J - N1, N1 - 1 + A( J-N1, L ) = CONJG( ARF( IJ ) ) + 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 + A( J, I ) = CONJG( 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 ) = CONJG( ARF( IJ ) ) + 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 + A( J, I ) = CONJG( 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 ) = CONJG( 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 +* +* 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 + A( K+J, I ) = CONJG( 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 +* +* 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 + A( I, J ) = ARF( IJ ) + IJ = IJ + 1 + END DO + DO L = J - K, K - 1 + A( J-K, L ) = CONJG( ARF( IJ ) ) + 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 + A( I, J ) = ARF( IJ ) + IJ = IJ + 1 + END DO + DO J = 0, K - 2 + DO I = 0, J + A( J, I ) = CONJG( 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 ) = CONJG( ARF( IJ ) ) + 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 + A( J, I ) = CONJG( 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 ) = CONJG( ARF( IJ ) ) + IJ = IJ + 1 + END DO + END DO +* +* Note that here 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 CTFTTR +* + END |