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author | jofret | 2009-04-28 07:17:00 +0000 |
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committer | jofret | 2009-04-28 07:17:00 +0000 |
commit | 8c8d2f518968ce7057eec6aa5cd5aec8faab861a (patch) | |
tree | 3dd1788b71d6a3ce2b73d2d475a3133580e17530 /src/lib/lapack/ztrevc.f | |
parent | 9f652ffc16a310ac6641a9766c5b9e2671e0e9cb (diff) | |
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Moving lapack to right place
Diffstat (limited to 'src/lib/lapack/ztrevc.f')
-rw-r--r-- | src/lib/lapack/ztrevc.f | 386 |
1 files changed, 0 insertions, 386 deletions
diff --git a/src/lib/lapack/ztrevc.f b/src/lib/lapack/ztrevc.f deleted file mode 100644 index 21142f42..00000000 --- a/src/lib/lapack/ztrevc.f +++ /dev/null @@ -1,386 +0,0 @@ - SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, - $ LDVR, MM, M, WORK, RWORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER HOWMNY, SIDE - INTEGER INFO, LDT, LDVL, LDVR, M, MM, N -* .. -* .. Array Arguments .. - LOGICAL SELECT( * ) - DOUBLE PRECISION RWORK( * ) - COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), - $ WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZTREVC computes some or all of the right and/or left eigenvectors of -* a complex upper triangular matrix T. -* Matrices of this type are produced by the Schur factorization of -* a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. -* -* The right eigenvector x and the left eigenvector y of T corresponding -* to an eigenvalue w are defined by: -* -* T*x = w*x, (y**H)*T = w*(y**H) -* -* where y**H denotes the conjugate transpose of the vector y. -* The eigenvalues are not input to this routine, but are read directly -* from the diagonal of T. -* -* This routine returns the matrices X and/or Y of right and left -* eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an -* input matrix. If Q is the unitary factor that reduces a matrix A to -* Schur form T, then Q*X and Q*Y are the matrices of right and left -* eigenvectors of A. -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* = 'R': compute right eigenvectors only; -* = 'L': compute left eigenvectors only; -* = 'B': compute both right and left eigenvectors. -* -* HOWMNY (input) CHARACTER*1 -* = 'A': compute all right and/or left eigenvectors; -* = 'B': compute all right and/or left eigenvectors, -* backtransformed using the matrices supplied in -* VR and/or VL; -* = 'S': compute selected right and/or left eigenvectors, -* as indicated by the logical array SELECT. -* -* SELECT (input) LOGICAL array, dimension (N) -* If HOWMNY = 'S', SELECT specifies the eigenvectors to be -* computed. -* The eigenvector corresponding to the j-th eigenvalue is -* computed if SELECT(j) = .TRUE.. -* Not referenced if HOWMNY = 'A' or 'B'. -* -* N (input) INTEGER -* The order of the matrix T. N >= 0. -* -* T (input/output) COMPLEX*16 array, dimension (LDT,N) -* The upper triangular matrix T. T is modified, but restored -* on exit. -* -* LDT (input) INTEGER -* The leading dimension of the array T. LDT >= max(1,N). -* -* VL (input/output) COMPLEX*16 array, dimension (LDVL,MM) -* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must -* contain an N-by-N matrix Q (usually the unitary matrix Q of -* Schur vectors returned by ZHSEQR). -* On exit, if SIDE = 'L' or 'B', VL contains: -* if HOWMNY = 'A', the matrix Y of left eigenvectors of T; -* if HOWMNY = 'B', the matrix Q*Y; -* if HOWMNY = 'S', the left eigenvectors of T specified by -* SELECT, stored consecutively in the columns -* of VL, in the same order as their -* eigenvalues. -* Not referenced if SIDE = 'R'. -* -* LDVL (input) INTEGER -* The leading dimension of the array VL. LDVL >= 1, and if -* SIDE = 'L' or 'B', LDVL >= N. -* -* VR (input/output) COMPLEX*16 array, dimension (LDVR,MM) -* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must -* contain an N-by-N matrix Q (usually the unitary matrix Q of -* Schur vectors returned by ZHSEQR). -* On exit, if SIDE = 'R' or 'B', VR contains: -* if HOWMNY = 'A', the matrix X of right eigenvectors of T; -* if HOWMNY = 'B', the matrix Q*X; -* if HOWMNY = 'S', the right eigenvectors of T specified by -* SELECT, stored consecutively in the columns -* of VR, in the same order as their -* eigenvalues. -* Not referenced if SIDE = 'L'. -* -* LDVR (input) INTEGER -* The leading dimension of the array VR. LDVR >= 1, and if -* SIDE = 'R' or 'B'; LDVR >= N. -* -* MM (input) INTEGER -* The number of columns in the arrays VL and/or VR. MM >= M. -* -* M (output) INTEGER -* The number of columns in the arrays VL and/or VR actually -* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M -* is set to N. Each selected eigenvector occupies one -* column. -* -* WORK (workspace) COMPLEX*16 array, dimension (2*N) -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* -* Further Details -* =============== -* -* The algorithm used in this program is basically backward (forward) -* substitution, with scaling to make the the code robust against -* possible overflow. -* -* Each eigenvector is normalized so that the element of largest -* magnitude has magnitude 1; here the magnitude of a complex number -* (x,y) is taken to be |x| + |y|. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) - COMPLEX*16 CMZERO, CMONE - PARAMETER ( CMZERO = ( 0.0D+0, 0.0D+0 ), - $ CMONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL ALLV, BOTHV, LEFTV, OVER, RIGHTV, SOMEV - INTEGER I, II, IS, J, K, KI - DOUBLE PRECISION OVFL, REMAX, SCALE, SMIN, SMLNUM, ULP, UNFL - COMPLEX*16 CDUM -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER IZAMAX - DOUBLE PRECISION DLAMCH, DZASUM - EXTERNAL LSAME, IZAMAX, DLAMCH, DZASUM -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZCOPY, ZDSCAL, ZGEMV, ZLATRS -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX -* .. -* .. Statement Functions .. - DOUBLE PRECISION CABS1 -* .. -* .. Statement Function definitions .. - CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) -* .. -* .. Executable Statements .. -* -* Decode and test the input parameters -* - BOTHV = LSAME( SIDE, 'B' ) - RIGHTV = LSAME( SIDE, 'R' ) .OR. BOTHV - LEFTV = LSAME( SIDE, 'L' ) .OR. BOTHV -* - ALLV = LSAME( HOWMNY, 'A' ) - OVER = LSAME( HOWMNY, 'B' ) - SOMEV = LSAME( HOWMNY, 'S' ) -* -* Set M to the number of columns required to store the selected -* eigenvectors. -* - IF( SOMEV ) THEN - M = 0 - DO 10 J = 1, N - IF( SELECT( J ) ) - $ M = M + 1 - 10 CONTINUE - ELSE - M = N - END IF -* - INFO = 0 - IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN - INFO = -1 - ELSE IF( .NOT.ALLV .AND. .NOT.OVER .AND. .NOT.SOMEV ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDT.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDVL.LT.1 .OR. ( LEFTV .AND. LDVL.LT.N ) ) THEN - INFO = -8 - ELSE IF( LDVR.LT.1 .OR. ( RIGHTV .AND. LDVR.LT.N ) ) THEN - INFO = -10 - ELSE IF( MM.LT.M ) THEN - INFO = -11 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZTREVC', -INFO ) - RETURN - END IF -* -* Quick return if possible. -* - IF( N.EQ.0 ) - $ RETURN -* -* Set the constants to control overflow. -* - UNFL = DLAMCH( 'Safe minimum' ) - OVFL = ONE / UNFL - CALL DLABAD( UNFL, OVFL ) - ULP = DLAMCH( 'Precision' ) - SMLNUM = UNFL*( N / ULP ) -* -* Store the diagonal elements of T in working array WORK. -* - DO 20 I = 1, N - WORK( I+N ) = T( I, I ) - 20 CONTINUE -* -* Compute 1-norm of each column of strictly upper triangular -* part of T to control overflow in triangular solver. -* - RWORK( 1 ) = ZERO - DO 30 J = 2, N - RWORK( J ) = DZASUM( J-1, T( 1, J ), 1 ) - 30 CONTINUE -* - IF( RIGHTV ) THEN -* -* Compute right eigenvectors. -* - IS = M - DO 80 KI = N, 1, -1 -* - IF( SOMEV ) THEN - IF( .NOT.SELECT( KI ) ) - $ GO TO 80 - END IF - SMIN = MAX( ULP*( CABS1( T( KI, KI ) ) ), SMLNUM ) -* - WORK( 1 ) = CMONE -* -* Form right-hand side. -* - DO 40 K = 1, KI - 1 - WORK( K ) = -T( K, KI ) - 40 CONTINUE -* -* Solve the triangular system: -* (T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK. -* - DO 50 K = 1, KI - 1 - T( K, K ) = T( K, K ) - T( KI, KI ) - IF( CABS1( T( K, K ) ).LT.SMIN ) - $ T( K, K ) = SMIN - 50 CONTINUE -* - IF( KI.GT.1 ) THEN - CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', 'Y', - $ KI-1, T, LDT, WORK( 1 ), SCALE, RWORK, - $ INFO ) - WORK( KI ) = SCALE - END IF -* -* Copy the vector x or Q*x to VR and normalize. -* - IF( .NOT.OVER ) THEN - CALL ZCOPY( KI, WORK( 1 ), 1, VR( 1, IS ), 1 ) -* - II = IZAMAX( KI, VR( 1, IS ), 1 ) - REMAX = ONE / CABS1( VR( II, IS ) ) - CALL ZDSCAL( KI, REMAX, VR( 1, IS ), 1 ) -* - DO 60 K = KI + 1, N - VR( K, IS ) = CMZERO - 60 CONTINUE - ELSE - IF( KI.GT.1 ) - $ CALL ZGEMV( 'N', N, KI-1, CMONE, VR, LDVR, WORK( 1 ), - $ 1, DCMPLX( SCALE ), VR( 1, KI ), 1 ) -* - II = IZAMAX( N, VR( 1, KI ), 1 ) - REMAX = ONE / CABS1( VR( II, KI ) ) - CALL ZDSCAL( N, REMAX, VR( 1, KI ), 1 ) - END IF -* -* Set back the original diagonal elements of T. -* - DO 70 K = 1, KI - 1 - T( K, K ) = WORK( K+N ) - 70 CONTINUE -* - IS = IS - 1 - 80 CONTINUE - END IF -* - IF( LEFTV ) THEN -* -* Compute left eigenvectors. -* - IS = 1 - DO 130 KI = 1, N -* - IF( SOMEV ) THEN - IF( .NOT.SELECT( KI ) ) - $ GO TO 130 - END IF - SMIN = MAX( ULP*( CABS1( T( KI, KI ) ) ), SMLNUM ) -* - WORK( N ) = CMONE -* -* Form right-hand side. -* - DO 90 K = KI + 1, N - WORK( K ) = -DCONJG( T( KI, K ) ) - 90 CONTINUE -* -* Solve the triangular system: -* (T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK. -* - DO 100 K = KI + 1, N - T( K, K ) = T( K, K ) - T( KI, KI ) - IF( CABS1( T( K, K ) ).LT.SMIN ) - $ T( K, K ) = SMIN - 100 CONTINUE -* - IF( KI.LT.N ) THEN - CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit', - $ 'Y', N-KI, T( KI+1, KI+1 ), LDT, - $ WORK( KI+1 ), SCALE, RWORK, INFO ) - WORK( KI ) = SCALE - END IF -* -* Copy the vector x or Q*x to VL and normalize. -* - IF( .NOT.OVER ) THEN - CALL ZCOPY( N-KI+1, WORK( KI ), 1, VL( KI, IS ), 1 ) -* - II = IZAMAX( N-KI+1, VL( KI, IS ), 1 ) + KI - 1 - REMAX = ONE / CABS1( VL( II, IS ) ) - CALL ZDSCAL( N-KI+1, REMAX, VL( KI, IS ), 1 ) -* - DO 110 K = 1, KI - 1 - VL( K, IS ) = CMZERO - 110 CONTINUE - ELSE - IF( KI.LT.N ) - $ CALL ZGEMV( 'N', N, N-KI, CMONE, VL( 1, KI+1 ), LDVL, - $ WORK( KI+1 ), 1, DCMPLX( SCALE ), - $ VL( 1, KI ), 1 ) -* - II = IZAMAX( N, VL( 1, KI ), 1 ) - REMAX = ONE / CABS1( VL( II, KI ) ) - CALL ZDSCAL( N, REMAX, VL( 1, KI ), 1 ) - END IF -* -* Set back the original diagonal elements of T. -* - DO 120 K = KI + 1, N - T( K, K ) = WORK( K+N ) - 120 CONTINUE -* - IS = IS + 1 - 130 CONTINUE - END IF -* - RETURN -* -* End of ZTREVC -* - END |