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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/ztpttf.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) | |
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Diffstat (limited to 'SRC/ztpttf.f')
-rw-r--r-- | SRC/ztpttf.f | 476 |
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diff --git a/SRC/ztpttf.f b/SRC/ztpttf.f new file mode 100644 index 00000000..9e49eae6 --- /dev/null +++ b/SRC/ztpttf.f @@ -0,0 +1,476 @@ + SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, 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 +* .. +* .. Array Arguments .. + COMPLEX*16 AP( 0: * ), ARF( 0: * ) +* +* Purpose +* ======= +* +* ZTPTTF copies a triangular matrix A from standard packed format (TP) +* to rectangular full packed format (TF). +* +* Arguments +* ========= +* +* TRANSR (input) CHARACTER +* = 'N': ARF in Normal format is wanted; +* = 'C': ARF in Conjugate-transpose format is wanted. +* +* UPLO (input) CHARACTER +* = 'U': A is upper triangular; +* = 'L': A is lower triangular. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* AP (input) COMPLEX*16 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) COMPLEX*16 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 +* +* 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 + INTEGER I, J, IJ + INTEGER IJP, JP, LDA, JS +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG, 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 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZTPTTF', -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 ) = DCONJG( 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 +* +* 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 +* + 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 ) = DCONJG( AP( IJP ) ) + IJP = IJP + 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) +* + IJP = 0 + DO J = 0, N1 - 1 + IJ = N2 + J + DO I = 0, J + ARF( IJ ) = DCONJG( 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 = '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 +* + IJP = 0 + DO I = 0, N2 + DO IJ = I*( LDA+1 ), N*LDA - 1, LDA + ARF( IJ ) = DCONJG( 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 +* +* 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 +* + 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 ) = DCONJG( 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 +* +* 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) +* + 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 ) = DCONJG( AP( IJP ) ) + IJP = IJP + 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) +* + IJP = 0 + DO J = 0, K - 1 + IJ = K + 1 + J + DO I = 0, J + ARF( IJ ) = DCONJG( 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 = 'C' +* + IF( LOWER ) THEN +* +* SRPA for LOWER, TRANSPOSE and N is even (see paper) +* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) +* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k +* + IJP = 0 + DO I = 0, K - 1 + DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA + ARF( IJ ) = DCONJG( 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 +* +* SRPA for UPPER, TRANSPOSE and N is even (see paper) +* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) +* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k +* + 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 ) = DCONJG( AP( IJP ) ) + IJP = IJP + 1 + END DO + END DO +* + END IF +* + END IF +* + END IF +* + RETURN +* +* End of ZTPTTF +* + END |