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authorjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
committerjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
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+ 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