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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/dtftri.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) | |
download | lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.gz lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.bz2 lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.zip |
Diffstat (limited to 'SRC/dtftri.f')
-rw-r--r-- | SRC/dtftri.f | 407 |
1 files changed, 407 insertions, 0 deletions
diff --git a/SRC/dtftri.f b/SRC/dtftri.f new file mode 100644 index 00000000..60eecdd9 --- /dev/null +++ b/SRC/dtftri.f @@ -0,0 +1,407 @@ + SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, 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, DIAG + INTEGER INFO, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( 0: * ) +* .. +* +* Purpose +* ======= +* +* DTFTRI computes the inverse of a triangular matrix A stored in RFP +* format. +* +* This is a Level 3 BLAS version of the algorithm. +* +* Arguments +* ========= +* +* TRANSR (input) CHARACTER +* = 'N': The Normal TRANSR of RFP A is stored; +* = 'T': The Transpose TRANSR of RFP A is stored. +* +* UPLO (input) CHARACTER +* = 'U': A is upper triangular; +* = 'L': A is lower triangular. +* +* DIAG (input) CHARACTER +* = 'N': A is non-unit triangular; +* = 'U': A is unit triangular. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (0:nt-1); +* nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian +* Positive Definite matrix A in RFP format. RFP format is +* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' +* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is +* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is +* the transpose of RFP A as defined when +* TRANSR = 'N'. The contents of RFP A are defined by UPLO as +* follows: If UPLO = 'U' the RFP A contains the nt elements of +* upper packed A; If UPLO = 'L' the RFP A contains the nt +* elements of lower packed A. The LDA of RFP A is (N+1)/2 when +* TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is +* even and N is odd. See the Note below for more details. +* +* On exit, the (triangular) inverse of the original matrix, in +* the same storage format. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, A(i,i) is exactly zero. The triangular +* matrix is singular and its inverse can not be computed. +* +* 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 +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LOWER, NISODD, NORMALTRANSR + INTEGER N1, N2, K +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, DTRMM, DTRTRI +* .. +* .. 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( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) ) + + THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DTFTRI', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + + RETURN +* +* If N is odd, set NISODD = .TRUE. +* If N is even, set K = N/2 and NISODD = .FALSE. +* + IF( MOD( N, 2 ).EQ.0 ) THEN + K = N / 2 + NISODD = .FALSE. + ELSE + NISODD = .TRUE. + END IF +* +* 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 +* +* +* 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) +* + CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ), + + N, A( N1 ), N ) + CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + N1 + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N, + + A( N1 ), N ) +* + 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) +* + CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ), + + N, A( 0 ), N ) + CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + N1 + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ), + + N, A( 0 ), N ) +* + END IF +* + ELSE +* +* N is odd and TRANSR = 'T' +* + IF( LOWER ) THEN +* +* SRPA for LOWER, TRANSPOSE and N is odd +* T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1) +* + CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ), + + N1, A( N1*N1 ), N1 ) + CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + N1 + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ), + + N1, A( N1*N1 ), N1 ) +* + ELSE +* +* SRPA for UPPER, TRANSPOSE and N is odd +* T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0) +* + CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE, + + A( N2*N2 ), N2, A( 0 ), N2 ) + CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + N1 + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE, + + A( N1*N2 ), N2, A( 0 ), N2 ) + 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) +* + CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ), + + N+1, A( K+1 ), N+1 ) + CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + K + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1, + + A( K+1 ), N+1 ) +* + 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) +* + CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ), + + N+1, A( 0 ), N+1 ) + CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + K + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1, + + A( 0 ), N+1 ) + END IF + ELSE +* +* N is even and TRANSR = 'T' +* + 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 +* + CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K, + + A( K*( K+1 ) ), K ) + CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + K + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K, + + A( K*( K+1 ) ), K ) + 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 +* + CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO ) + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE, + + A( K*( K+1 ) ), K, A( 0 ), K ) + CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO ) + IF( INFO.GT.0 ) + + INFO = INFO + K + IF( INFO.GT.0 ) + + RETURN + CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K, + + A( 0 ), K ) + END IF + END IF + END IF +* + RETURN +* +* End of DTFTRI +* + END |