diff options
Diffstat (limited to 'src/lib/lapack/dtgsyl.f')
| -rw-r--r-- | src/lib/lapack/dtgsyl.f | 556 |
1 files changed, 0 insertions, 556 deletions
diff --git a/src/lib/lapack/dtgsyl.f b/src/lib/lapack/dtgsyl.f deleted file mode 100644 index 01866717..00000000 --- a/src/lib/lapack/dtgsyl.f +++ /dev/null @@ -1,556 +0,0 @@ - SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, - $ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, - $ IWORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER TRANS - INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, - $ LWORK, M, N - DOUBLE PRECISION DIF, SCALE -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), E( LDE, * ), F( LDF, * ), - $ WORK( * ) -* .. -* -* Purpose -* ======= -* -* DTGSYL solves the generalized Sylvester equation: -* -* A * R - L * B = scale * C (1) -* D * R - L * E = scale * F -* -* where R and L are unknown m-by-n matrices, (A, D), (B, E) and -* (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, -* respectively, with real entries. (A, D) and (B, E) must be in -* generalized (real) Schur canonical form, i.e. A, B are upper quasi -* triangular and D, E are upper triangular. -* -* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output -* scaling factor chosen to avoid overflow. -* -* In matrix notation (1) is equivalent to solve Zx = scale b, where -* Z is defined as -* -* Z = [ kron(In, A) -kron(B', Im) ] (2) -* [ kron(In, D) -kron(E', Im) ]. -* -* Here Ik is the identity matrix of size k and X' is the transpose of -* X. kron(X, Y) is the Kronecker product between the matrices X and Y. -* -* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b, -* which is equivalent to solve for R and L in -* -* A' * R + D' * L = scale * C (3) -* R * B' + L * E' = scale * (-F) -* -* This case (TRANS = 'T') is used to compute an one-norm-based estimate -* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) -* and (B,E), using DLACON. -* -* If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate -* of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the -* reciprocal of the smallest singular value of Z. See [1-2] for more -* information. -* -* This is a level 3 BLAS algorithm. -* -* Arguments -* ========= -* -* TRANS (input) CHARACTER*1 -* = 'N', solve the generalized Sylvester equation (1). -* = 'T', solve the 'transposed' system (3). -* -* IJOB (input) INTEGER -* Specifies what kind of functionality to be performed. -* =0: solve (1) only. -* =1: The functionality of 0 and 3. -* =2: The functionality of 0 and 4. -* =3: Only an estimate of Dif[(A,D), (B,E)] is computed. -* (look ahead strategy IJOB = 1 is used). -* =4: Only an estimate of Dif[(A,D), (B,E)] is computed. -* ( DGECON on sub-systems is used ). -* Not referenced if TRANS = 'T'. -* -* M (input) INTEGER -* The order of the matrices A and D, and the row dimension of -* the matrices C, F, R and L. -* -* N (input) INTEGER -* The order of the matrices B and E, and the column dimension -* of the matrices C, F, R and L. -* -* A (input) DOUBLE PRECISION array, dimension (LDA, M) -* The upper quasi triangular matrix A. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1, M). -* -* B (input) DOUBLE PRECISION array, dimension (LDB, N) -* The upper quasi triangular matrix B. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1, N). -* -* C (input/output) DOUBLE PRECISION array, dimension (LDC, N) -* On entry, C contains the right-hand-side of the first matrix -* equation in (1) or (3). -* On exit, if IJOB = 0, 1 or 2, C has been overwritten by -* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, -* the solution achieved during the computation of the -* Dif-estimate. -* -* LDC (input) INTEGER -* The leading dimension of the array C. LDC >= max(1, M). -* -* D (input) DOUBLE PRECISION array, dimension (LDD, M) -* The upper triangular matrix D. -* -* LDD (input) INTEGER -* The leading dimension of the array D. LDD >= max(1, M). -* -* E (input) DOUBLE PRECISION array, dimension (LDE, N) -* The upper triangular matrix E. -* -* LDE (input) INTEGER -* The leading dimension of the array E. LDE >= max(1, N). -* -* F (input/output) DOUBLE PRECISION array, dimension (LDF, N) -* On entry, F contains the right-hand-side of the second matrix -* equation in (1) or (3). -* On exit, if IJOB = 0, 1 or 2, F has been overwritten by -* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, -* the solution achieved during the computation of the -* Dif-estimate. -* -* LDF (input) INTEGER -* The leading dimension of the array F. LDF >= max(1, M). -* -* DIF (output) DOUBLE PRECISION -* On exit DIF is the reciprocal of a lower bound of the -* reciprocal of the Dif-function, i.e. DIF is an upper bound of -* Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2). -* IF IJOB = 0 or TRANS = 'T', DIF is not touched. -* -* SCALE (output) DOUBLE PRECISION -* On exit SCALE is the scaling factor in (1) or (3). -* If 0 < SCALE < 1, C and F hold the solutions R and L, resp., -* to a slightly perturbed system but the input matrices A, B, D -* and E have not been changed. If SCALE = 0, C and F hold the -* solutions R and L, respectively, to the homogeneous system -* with C = F = 0. Normally, SCALE = 1. -* -* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. LWORK > = 1. -* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* IWORK (workspace) INTEGER array, dimension (M+N+6) -* -* INFO (output) INTEGER -* =0: successful exit -* <0: If INFO = -i, the i-th argument had an illegal value. -* >0: (A, D) and (B, E) have common or close eigenvalues. -* -* Further Details -* =============== -* -* Based on contributions by -* Bo Kagstrom and Peter Poromaa, Department of Computing Science, -* Umea University, S-901 87 Umea, Sweden. -* -* [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software -* for Solving the Generalized Sylvester Equation and Estimating the -* Separation between Regular Matrix Pairs, Report UMINF - 93.23, -* Department of Computing Science, Umea University, S-901 87 Umea, -* Sweden, December 1993, Revised April 1994, Also as LAPACK Working -* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, -* No 1, 1996. -* -* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester -* Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. -* Appl., 15(4):1045-1060, 1994 -* -* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with -* Condition Estimators for Solving the Generalized Sylvester -* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, -* July 1989, pp 745-751. -* -* ===================================================================== -* Replaced various illegal calls to DCOPY by calls to DLASET. -* Sven Hammarling, 1/5/02. -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, NOTRAN - INTEGER I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K, - $ LINFO, LWMIN, MB, NB, P, PPQQ, PQ, Q - DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DLACPY, DLASET, DSCAL, DTGSY2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, MAX, SQRT -* .. -* .. Executable Statements .. -* -* Decode and test input parameters -* - INFO = 0 - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* - IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -1 - ELSE IF( NOTRAN ) THEN - IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN - INFO = -2 - END IF - END IF - IF( INFO.EQ.0 ) THEN - IF( M.LE.0 ) THEN - INFO = -3 - ELSE IF( N.LE.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -6 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LDD.LT.MAX( 1, M ) ) THEN - INFO = -12 - ELSE IF( LDE.LT.MAX( 1, N ) ) THEN - INFO = -14 - ELSE IF( LDF.LT.MAX( 1, M ) ) THEN - INFO = -16 - END IF - END IF -* - IF( INFO.EQ.0 ) THEN - IF( NOTRAN ) THEN - IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN - LWMIN = MAX( 1, 2*M*N ) - ELSE - LWMIN = 1 - END IF - ELSE - LWMIN = 1 - END IF - WORK( 1 ) = LWMIN -* - IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN - INFO = -20 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DTGSYL', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - SCALE = 1 - IF( NOTRAN ) THEN - IF( IJOB.NE.0 ) THEN - DIF = 0 - END IF - END IF - RETURN - END IF -* -* Determine optimal block sizes MB and NB -* - MB = ILAENV( 2, 'DTGSYL', TRANS, M, N, -1, -1 ) - NB = ILAENV( 5, 'DTGSYL', TRANS, M, N, -1, -1 ) -* - ISOLVE = 1 - IFUNC = 0 - IF( NOTRAN ) THEN - IF( IJOB.GE.3 ) THEN - IFUNC = IJOB - 2 - CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC ) - CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF ) - ELSE IF( IJOB.GE.1 ) THEN - ISOLVE = 2 - END IF - END IF -* - IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) ) - $ THEN -* - DO 30 IROUND = 1, ISOLVE -* -* Use unblocked Level 2 solver -* - DSCALE = ZERO - DSUM = ONE - PQ = 0 - CALL DTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D, - $ LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE, - $ IWORK, PQ, INFO ) - IF( DSCALE.NE.ZERO ) THEN - IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN - DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) ) - ELSE - DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) ) - END IF - END IF -* - IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN - IF( NOTRAN ) THEN - IFUNC = IJOB - END IF - SCALE2 = SCALE - CALL DLACPY( 'F', M, N, C, LDC, WORK, M ) - CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M ) - CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC ) - CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF ) - ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN - CALL DLACPY( 'F', M, N, WORK, M, C, LDC ) - CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF ) - SCALE = SCALE2 - END IF - 30 CONTINUE -* - RETURN - END IF -* -* Determine block structure of A -* - P = 0 - I = 1 - 40 CONTINUE - IF( I.GT.M ) - $ GO TO 50 - P = P + 1 - IWORK( P ) = I - I = I + MB - IF( I.GE.M ) - $ GO TO 50 - IF( A( I, I-1 ).NE.ZERO ) - $ I = I + 1 - GO TO 40 - 50 CONTINUE -* - IWORK( P+1 ) = M + 1 - IF( IWORK( P ).EQ.IWORK( P+1 ) ) - $ P = P - 1 -* -* Determine block structure of B -* - Q = P + 1 - J = 1 - 60 CONTINUE - IF( J.GT.N ) - $ GO TO 70 - Q = Q + 1 - IWORK( Q ) = J - J = J + NB - IF( J.GE.N ) - $ GO TO 70 - IF( B( J, J-1 ).NE.ZERO ) - $ J = J + 1 - GO TO 60 - 70 CONTINUE -* - IWORK( Q+1 ) = N + 1 - IF( IWORK( Q ).EQ.IWORK( Q+1 ) ) - $ Q = Q - 1 -* - IF( NOTRAN ) THEN -* - DO 150 IROUND = 1, ISOLVE -* -* Solve (I, J)-subsystem -* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) -* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) -* for I = P, P - 1,..., 1; J = 1, 2,..., Q -* - DSCALE = ZERO - DSUM = ONE - PQ = 0 - SCALE = ONE - DO 130 J = P + 2, Q - JS = IWORK( J ) - JE = IWORK( J+1 ) - 1 - NB = JE - JS + 1 - DO 120 I = P, 1, -1 - IS = IWORK( I ) - IE = IWORK( I+1 ) - 1 - MB = IE - IS + 1 - PPQQ = 0 - CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA, - $ B( JS, JS ), LDB, C( IS, JS ), LDC, - $ D( IS, IS ), LDD, E( JS, JS ), LDE, - $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE, - $ IWORK( Q+2 ), PPQQ, LINFO ) - IF( LINFO.GT.0 ) - $ INFO = LINFO -* - PQ = PQ + PPQQ - IF( SCALOC.NE.ONE ) THEN - DO 80 K = 1, JS - 1 - CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) - 80 CONTINUE - DO 90 K = JS, JE - CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 ) - 90 CONTINUE - DO 100 K = JS, JE - CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 ) - CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 ) - 100 CONTINUE - DO 110 K = JE + 1, N - CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) - 110 CONTINUE - SCALE = SCALE*SCALOC - END IF -* -* Substitute R(I, J) and L(I, J) into remaining -* equation. -* - IF( I.GT.1 ) THEN - CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE, - $ A( 1, IS ), LDA, C( IS, JS ), LDC, ONE, - $ C( 1, JS ), LDC ) - CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE, - $ D( 1, IS ), LDD, C( IS, JS ), LDC, ONE, - $ F( 1, JS ), LDF ) - END IF - IF( J.LT.Q ) THEN - CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE, - $ F( IS, JS ), LDF, B( JS, JE+1 ), LDB, - $ ONE, C( IS, JE+1 ), LDC ) - CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE, - $ F( IS, JS ), LDF, E( JS, JE+1 ), LDE, - $ ONE, F( IS, JE+1 ), LDF ) - END IF - 120 CONTINUE - 130 CONTINUE - IF( DSCALE.NE.ZERO ) THEN - IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN - DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) ) - ELSE - DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) ) - END IF - END IF - IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN - IF( NOTRAN ) THEN - IFUNC = IJOB - END IF - SCALE2 = SCALE - CALL DLACPY( 'F', M, N, C, LDC, WORK, M ) - CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M ) - CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC ) - CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF ) - ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN - CALL DLACPY( 'F', M, N, WORK, M, C, LDC ) - CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF ) - SCALE = SCALE2 - END IF - 150 CONTINUE -* - ELSE -* -* Solve transposed (I, J)-subsystem -* A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J) -* R(I, J) * B(J, J)' + L(I, J) * E(J, J)' = -F(I, J) -* for I = 1,2,..., P; J = Q, Q-1,..., 1 -* - SCALE = ONE - DO 210 I = 1, P - IS = IWORK( I ) - IE = IWORK( I+1 ) - 1 - MB = IE - IS + 1 - DO 200 J = Q, P + 2, -1 - JS = IWORK( J ) - JE = IWORK( J+1 ) - 1 - NB = JE - JS + 1 - CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA, - $ B( JS, JS ), LDB, C( IS, JS ), LDC, - $ D( IS, IS ), LDD, E( JS, JS ), LDE, - $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE, - $ IWORK( Q+2 ), PPQQ, LINFO ) - IF( LINFO.GT.0 ) - $ INFO = LINFO - IF( SCALOC.NE.ONE ) THEN - DO 160 K = 1, JS - 1 - CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) - 160 CONTINUE - DO 170 K = JS, JE - CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 ) - 170 CONTINUE - DO 180 K = JS, JE - CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 ) - CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 ) - 180 CONTINUE - DO 190 K = JE + 1, N - CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) - CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) - 190 CONTINUE - SCALE = SCALE*SCALOC - END IF -* -* Substitute R(I, J) and L(I, J) into remaining equation. -* - IF( J.GT.P+2 ) THEN - CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, C( IS, JS ), - $ LDC, B( 1, JS ), LDB, ONE, F( IS, 1 ), - $ LDF ) - CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, F( IS, JS ), - $ LDF, E( 1, JS ), LDE, ONE, F( IS, 1 ), - $ LDF ) - END IF - IF( I.LT.P ) THEN - CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE, - $ A( IS, IE+1 ), LDA, C( IS, JS ), LDC, ONE, - $ C( IE+1, JS ), LDC ) - CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE, - $ D( IS, IE+1 ), LDD, F( IS, JS ), LDF, ONE, - $ C( IE+1, JS ), LDC ) - END IF - 200 CONTINUE - 210 CONTINUE -* - END IF -* - WORK( 1 ) = LWMIN -* - RETURN -* -* End of DTGSYL -* - END |