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Diffstat (limited to '2.3-1/src/fortran/lapack/dtgsy2.f')
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diff --git a/2.3-1/src/fortran/lapack/dtgsy2.f b/2.3-1/src/fortran/lapack/dtgsy2.f new file mode 100644 index 00000000..3ebc912f --- /dev/null +++ b/2.3-1/src/fortran/lapack/dtgsy2.f @@ -0,0 +1,956 @@ + SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, + $ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, + $ IWORK, PQ, INFO ) +* +* -- LAPACK auxiliary 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, M, N, + $ PQ + DOUBLE PRECISION RDSCAL, RDSUM, SCALE +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), + $ D( LDD, * ), E( LDE, * ), F( LDF, * ) +* .. +* +* Purpose +* ======= +* +* DTGSY2 solves the generalized Sylvester equation: +* +* A * R - L * B = scale * C (1) +* D * R - L * E = scale * F, +* +* using Level 1 and 2 BLAS. 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 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 solving equation (1) corresponds to solve +* Z*x = scale*b, where Z is defined as +* +* Z = [ kron(In, A) -kron(B', Im) ] (2) +* [ kron(In, D) -kron(E', Im) ], +* +* 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. +* In the process of solving (1), we solve a number of such systems +* where Dim(In), Dim(In) = 1 or 2. +* +* If TRANS = 'T', solve the transposed system Z'*y = scale*b for y, +* 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 is used to compute an estimate of Dif[(A, D), (B, E)] = +* sigma_min(Z) using reverse communicaton with DLACON. +* +* DTGSY2 also (IJOB >= 1) contributes to the computation in STGSYL +* of an upper bound on the separation between to matrix pairs. Then +* the input (A, D), (B, E) are sub-pencils of the matrix pair in +* DTGSYL. See STGSYL for details. +* +* 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: A contribution from this subsystem to a Frobenius +* norm-based estimate of the separation between two matrix +* pairs is computed. (look ahead strategy is used). +* = 2: A contribution from this subsystem to a Frobenius +* norm-based estimate of the separation between two matrix +* pairs is computed. (DGECON on sub-systems is used.) +* Not referenced if TRANS = 'T'. +* +* M (input) INTEGER +* On entry, M specifies the order of A and D, and the row +* dimension of C, F, R and L. +* +* N (input) INTEGER +* On entry, N specifies the order of B and E, and the column +* dimension of C, F, R and L. +* +* A (input) DOUBLE PRECISION array, dimension (LDA, M) +* On entry, A contains an upper quasi triangular matrix. +* +* LDA (input) INTEGER +* The leading dimension of the matrix A. LDA >= max(1, M). +* +* B (input) DOUBLE PRECISION array, dimension (LDB, N) +* On entry, B contains an upper quasi triangular matrix. +* +* LDB (input) INTEGER +* The leading dimension of the matrix 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). +* On exit, if IJOB = 0, C has been overwritten by the +* solution R. +* +* LDC (input) INTEGER +* The leading dimension of the matrix C. LDC >= max(1, M). +* +* D (input) DOUBLE PRECISION array, dimension (LDD, M) +* On entry, D contains an upper triangular matrix. +* +* LDD (input) INTEGER +* The leading dimension of the matrix D. LDD >= max(1, M). +* +* E (input) DOUBLE PRECISION array, dimension (LDE, N) +* On entry, E contains an upper triangular matrix. +* +* LDE (input) INTEGER +* The leading dimension of the matrix 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). +* On exit, if IJOB = 0, F has been overwritten by the +* solution L. +* +* LDF (input) INTEGER +* The leading dimension of the matrix F. LDF >= max(1, M). +* +* SCALE (output) DOUBLE PRECISION +* On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions +* R and L (C and F on entry) will hold the solutions to a +* slightly perturbed system but the input matrices A, B, D and +* E have not been changed. If SCALE = 0, R and L will hold the +* solutions to the homogeneous system with C = F = 0. Normally, +* SCALE = 1. +* +* RDSUM (input/output) DOUBLE PRECISION +* On entry, the sum of squares of computed contributions to +* the Dif-estimate under computation by DTGSYL, where the +* scaling factor RDSCAL (see below) has been factored out. +* On exit, the corresponding sum of squares updated with the +* contributions from the current sub-system. +* If TRANS = 'T' RDSUM is not touched. +* NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL. +* +* RDSCAL (input/output) DOUBLE PRECISION +* On entry, scaling factor used to prevent overflow in RDSUM. +* On exit, RDSCAL is updated w.r.t. the current contributions +* in RDSUM. +* If TRANS = 'T', RDSCAL is not touched. +* NOTE: RDSCAL only makes sense when DTGSY2 is called by +* DTGSYL. +* +* IWORK (workspace) INTEGER array, dimension (M+N+2) +* +* PQ (output) INTEGER +* On exit, the number of subsystems (of size 2-by-2, 4-by-4 and +* 8-by-8) solved by this routine. +* +* INFO (output) INTEGER +* On exit, if INFO is set to +* =0: Successful exit +* <0: If INFO = -i, the i-th argument had an illegal value. +* >0: The matrix pairs (A, D) and (B, E) have common or very +* close eigenvalues. +* +* Further Details +* =============== +* +* Based on contributions by +* Bo Kagstrom and Peter Poromaa, Department of Computing Science, +* Umea University, S-901 87 Umea, Sweden. +* +* ===================================================================== +* Replaced various illegal calls to DCOPY by calls to DLASET. +* Sven Hammarling, 27/5/02. +* +* .. Parameters .. + INTEGER LDZ + PARAMETER ( LDZ = 8 ) + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL NOTRAN + INTEGER I, IE, IERR, II, IS, ISP1, J, JE, JJ, JS, JSP1, + $ K, MB, NB, P, Q, ZDIM + DOUBLE PRECISION ALPHA, SCALOC +* .. +* .. Local Arrays .. + INTEGER IPIV( LDZ ), JPIV( LDZ ) + DOUBLE PRECISION RHS( LDZ ), Z( LDZ, LDZ ) +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DCOPY, DGEMM, DGEMV, DGER, DGESC2, + $ DGETC2, DLASET, DLATDF, DSCAL, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Decode and test input parameters +* + INFO = 0 + IERR = 0 + NOTRAN = LSAME( TRANS, 'N' ) + IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN + INFO = -1 + ELSE IF( NOTRAN ) THEN + IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.2 ) ) 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 = -5 + 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.NE.0 ) THEN + CALL XERBLA( 'DTGSY2', -INFO ) + RETURN + END IF +* +* Determine block structure of A +* + PQ = 0 + P = 0 + I = 1 + 10 CONTINUE + IF( I.GT.M ) + $ GO TO 20 + P = P + 1 + IWORK( P ) = I + IF( I.EQ.M ) + $ GO TO 20 + IF( A( I+1, I ).NE.ZERO ) THEN + I = I + 2 + ELSE + I = I + 1 + END IF + GO TO 10 + 20 CONTINUE + IWORK( P+1 ) = M + 1 +* +* Determine block structure of B +* + Q = P + 1 + J = 1 + 30 CONTINUE + IF( J.GT.N ) + $ GO TO 40 + Q = Q + 1 + IWORK( Q ) = J + IF( J.EQ.N ) + $ GO TO 40 + IF( B( J+1, J ).NE.ZERO ) THEN + J = J + 2 + ELSE + J = J + 1 + END IF + GO TO 30 + 40 CONTINUE + IWORK( Q+1 ) = N + 1 + PQ = P*( Q-P-1 ) +* + IF( NOTRAN ) THEN +* +* 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 +* + SCALE = ONE + SCALOC = ONE + DO 120 J = P + 2, Q + JS = IWORK( J ) + JSP1 = JS + 1 + JE = IWORK( J+1 ) - 1 + NB = JE - JS + 1 + DO 110 I = P, 1, -1 +* + IS = IWORK( I ) + ISP1 = IS + 1 + IE = IWORK( I+1 ) - 1 + MB = IE - IS + 1 + ZDIM = MB*NB*2 +* + IF( ( MB.EQ.1 ) .AND. ( NB.EQ.1 ) ) THEN +* +* Build a 2-by-2 system Z * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = D( IS, IS ) + Z( 1, 2 ) = -B( JS, JS ) + Z( 2, 2 ) = -E( JS, JS ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = F( IS, JS ) +* +* Solve Z * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR +* + IF( IJOB.EQ.0 ) THEN + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, + $ SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 50 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 50 CONTINUE + SCALE = SCALE*SCALOC + END IF + ELSE + CALL DLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM, + $ RDSCAL, IPIV, JPIV ) + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + F( IS, JS ) = RHS( 2 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( I.GT.1 ) THEN + ALPHA = -RHS( 1 ) + CALL DAXPY( IS-1, ALPHA, A( 1, IS ), 1, C( 1, JS ), + $ 1 ) + CALL DAXPY( IS-1, ALPHA, D( 1, IS ), 1, F( 1, JS ), + $ 1 ) + END IF + IF( J.LT.Q ) THEN + CALL DAXPY( N-JE, RHS( 2 ), B( JS, JE+1 ), LDB, + $ C( IS, JE+1 ), LDC ) + CALL DAXPY( N-JE, RHS( 2 ), E( JS, JE+1 ), LDE, + $ F( IS, JE+1 ), LDF ) + END IF +* + ELSE IF( ( MB.EQ.1 ) .AND. ( NB.EQ.2 ) ) THEN +* +* Build a 4-by-4 system Z * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = ZERO + Z( 3, 1 ) = D( IS, IS ) + Z( 4, 1 ) = ZERO +* + Z( 1, 2 ) = ZERO + Z( 2, 2 ) = A( IS, IS ) + Z( 3, 2 ) = ZERO + Z( 4, 2 ) = D( IS, IS ) +* + Z( 1, 3 ) = -B( JS, JS ) + Z( 2, 3 ) = -B( JS, JSP1 ) + Z( 3, 3 ) = -E( JS, JS ) + Z( 4, 3 ) = -E( JS, JSP1 ) +* + Z( 1, 4 ) = -B( JSP1, JS ) + Z( 2, 4 ) = -B( JSP1, JSP1 ) + Z( 3, 4 ) = ZERO + Z( 4, 4 ) = -E( JSP1, JSP1 ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = C( IS, JSP1 ) + RHS( 3 ) = F( IS, JS ) + RHS( 4 ) = F( IS, JSP1 ) +* +* Solve Z * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR +* + IF( IJOB.EQ.0 ) THEN + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, + $ SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 60 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 60 CONTINUE + SCALE = SCALE*SCALOC + END IF + ELSE + CALL DLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM, + $ RDSCAL, IPIV, JPIV ) + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + C( IS, JSP1 ) = RHS( 2 ) + F( IS, JS ) = RHS( 3 ) + F( IS, JSP1 ) = RHS( 4 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( I.GT.1 ) THEN + CALL DGER( IS-1, NB, -ONE, A( 1, IS ), 1, RHS( 1 ), + $ 1, C( 1, JS ), LDC ) + CALL DGER( IS-1, NB, -ONE, D( 1, IS ), 1, RHS( 1 ), + $ 1, F( 1, JS ), LDF ) + END IF + IF( J.LT.Q ) THEN + CALL DAXPY( N-JE, RHS( 3 ), B( JS, JE+1 ), LDB, + $ C( IS, JE+1 ), LDC ) + CALL DAXPY( N-JE, RHS( 3 ), E( JS, JE+1 ), LDE, + $ F( IS, JE+1 ), LDF ) + CALL DAXPY( N-JE, RHS( 4 ), B( JSP1, JE+1 ), LDB, + $ C( IS, JE+1 ), LDC ) + CALL DAXPY( N-JE, RHS( 4 ), E( JSP1, JE+1 ), LDE, + $ F( IS, JE+1 ), LDF ) + END IF +* + ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.1 ) ) THEN +* +* Build a 4-by-4 system Z * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = A( ISP1, IS ) + Z( 3, 1 ) = D( IS, IS ) + Z( 4, 1 ) = ZERO +* + Z( 1, 2 ) = A( IS, ISP1 ) + Z( 2, 2 ) = A( ISP1, ISP1 ) + Z( 3, 2 ) = D( IS, ISP1 ) + Z( 4, 2 ) = D( ISP1, ISP1 ) +* + Z( 1, 3 ) = -B( JS, JS ) + Z( 2, 3 ) = ZERO + Z( 3, 3 ) = -E( JS, JS ) + Z( 4, 3 ) = ZERO +* + Z( 1, 4 ) = ZERO + Z( 2, 4 ) = -B( JS, JS ) + Z( 3, 4 ) = ZERO + Z( 4, 4 ) = -E( JS, JS ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = C( ISP1, JS ) + RHS( 3 ) = F( IS, JS ) + RHS( 4 ) = F( ISP1, JS ) +* +* Solve Z * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR + IF( IJOB.EQ.0 ) THEN + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, + $ SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 70 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 70 CONTINUE + SCALE = SCALE*SCALOC + END IF + ELSE + CALL DLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM, + $ RDSCAL, IPIV, JPIV ) + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + C( ISP1, JS ) = RHS( 2 ) + F( IS, JS ) = RHS( 3 ) + F( ISP1, JS ) = RHS( 4 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( I.GT.1 ) THEN + CALL DGEMV( 'N', IS-1, MB, -ONE, A( 1, IS ), LDA, + $ RHS( 1 ), 1, ONE, C( 1, JS ), 1 ) + CALL DGEMV( 'N', IS-1, MB, -ONE, D( 1, IS ), LDD, + $ RHS( 1 ), 1, ONE, F( 1, JS ), 1 ) + END IF + IF( J.LT.Q ) THEN + CALL DGER( MB, N-JE, ONE, RHS( 3 ), 1, + $ B( JS, JE+1 ), LDB, C( IS, JE+1 ), LDC ) + CALL DGER( MB, N-JE, ONE, RHS( 3 ), 1, + $ E( JS, JE+1 ), LDB, F( IS, JE+1 ), LDC ) + END IF +* + ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.2 ) ) THEN +* +* Build an 8-by-8 system Z * x = RHS +* + CALL DLASET( 'F', LDZ, LDZ, ZERO, ZERO, Z, LDZ ) +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = A( ISP1, IS ) + Z( 5, 1 ) = D( IS, IS ) +* + Z( 1, 2 ) = A( IS, ISP1 ) + Z( 2, 2 ) = A( ISP1, ISP1 ) + Z( 5, 2 ) = D( IS, ISP1 ) + Z( 6, 2 ) = D( ISP1, ISP1 ) +* + Z( 3, 3 ) = A( IS, IS ) + Z( 4, 3 ) = A( ISP1, IS ) + Z( 7, 3 ) = D( IS, IS ) +* + Z( 3, 4 ) = A( IS, ISP1 ) + Z( 4, 4 ) = A( ISP1, ISP1 ) + Z( 7, 4 ) = D( IS, ISP1 ) + Z( 8, 4 ) = D( ISP1, ISP1 ) +* + Z( 1, 5 ) = -B( JS, JS ) + Z( 3, 5 ) = -B( JS, JSP1 ) + Z( 5, 5 ) = -E( JS, JS ) + Z( 7, 5 ) = -E( JS, JSP1 ) +* + Z( 2, 6 ) = -B( JS, JS ) + Z( 4, 6 ) = -B( JS, JSP1 ) + Z( 6, 6 ) = -E( JS, JS ) + Z( 8, 6 ) = -E( JS, JSP1 ) +* + Z( 1, 7 ) = -B( JSP1, JS ) + Z( 3, 7 ) = -B( JSP1, JSP1 ) + Z( 7, 7 ) = -E( JSP1, JSP1 ) +* + Z( 2, 8 ) = -B( JSP1, JS ) + Z( 4, 8 ) = -B( JSP1, JSP1 ) + Z( 8, 8 ) = -E( JSP1, JSP1 ) +* +* Set up right hand side(s) +* + K = 1 + II = MB*NB + 1 + DO 80 JJ = 0, NB - 1 + CALL DCOPY( MB, C( IS, JS+JJ ), 1, RHS( K ), 1 ) + CALL DCOPY( MB, F( IS, JS+JJ ), 1, RHS( II ), 1 ) + K = K + MB + II = II + MB + 80 CONTINUE +* +* Solve Z * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR + IF( IJOB.EQ.0 ) THEN + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, + $ SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 90 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 90 CONTINUE + SCALE = SCALE*SCALOC + END IF + ELSE + CALL DLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM, + $ RDSCAL, IPIV, JPIV ) + END IF +* +* Unpack solution vector(s) +* + K = 1 + II = MB*NB + 1 + DO 100 JJ = 0, NB - 1 + CALL DCOPY( MB, RHS( K ), 1, C( IS, JS+JJ ), 1 ) + CALL DCOPY( MB, RHS( II ), 1, F( IS, JS+JJ ), 1 ) + K = K + MB + II = II + MB + 100 CONTINUE +* +* 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, RHS( 1 ), MB, ONE, + $ C( 1, JS ), LDC ) + CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE, + $ D( 1, IS ), LDD, RHS( 1 ), MB, ONE, + $ F( 1, JS ), LDF ) + END IF + IF( J.LT.Q ) THEN + K = MB*NB + 1 + CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE, RHS( K ), + $ MB, B( JS, JE+1 ), LDB, ONE, + $ C( IS, JE+1 ), LDC ) + CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE, RHS( K ), + $ MB, E( JS, JE+1 ), LDE, ONE, + $ F( IS, JE+1 ), LDF ) + END IF +* + END IF +* + 110 CONTINUE + 120 CONTINUE + ELSE +* +* Solve (I, J) - subsystem +* A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J) +* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) +* for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1 +* + SCALE = ONE + SCALOC = ONE + DO 200 I = 1, P +* + IS = IWORK( I ) + ISP1 = IS + 1 + IE = ( I+1 ) - 1 + MB = IE - IS + 1 + DO 190 J = Q, P + 2, -1 +* + JS = IWORK( J ) + JSP1 = JS + 1 + JE = IWORK( J+1 ) - 1 + NB = JE - JS + 1 + ZDIM = MB*NB*2 + IF( ( MB.EQ.1 ) .AND. ( NB.EQ.1 ) ) THEN +* +* Build a 2-by-2 system Z' * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = -B( JS, JS ) + Z( 1, 2 ) = D( IS, IS ) + Z( 2, 2 ) = -E( JS, JS ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = F( IS, JS ) +* +* Solve Z' * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR +* + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 130 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 130 CONTINUE + SCALE = SCALE*SCALOC + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + F( IS, JS ) = RHS( 2 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( J.GT.P+2 ) THEN + ALPHA = RHS( 1 ) + CALL DAXPY( JS-1, ALPHA, B( 1, JS ), 1, F( IS, 1 ), + $ LDF ) + ALPHA = RHS( 2 ) + CALL DAXPY( JS-1, ALPHA, E( 1, JS ), 1, F( IS, 1 ), + $ LDF ) + END IF + IF( I.LT.P ) THEN + ALPHA = -RHS( 1 ) + CALL DAXPY( M-IE, ALPHA, A( IS, IE+1 ), LDA, + $ C( IE+1, JS ), 1 ) + ALPHA = -RHS( 2 ) + CALL DAXPY( M-IE, ALPHA, D( IS, IE+1 ), LDD, + $ C( IE+1, JS ), 1 ) + END IF +* + ELSE IF( ( MB.EQ.1 ) .AND. ( NB.EQ.2 ) ) THEN +* +* Build a 4-by-4 system Z' * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = ZERO + Z( 3, 1 ) = -B( JS, JS ) + Z( 4, 1 ) = -B( JSP1, JS ) +* + Z( 1, 2 ) = ZERO + Z( 2, 2 ) = A( IS, IS ) + Z( 3, 2 ) = -B( JS, JSP1 ) + Z( 4, 2 ) = -B( JSP1, JSP1 ) +* + Z( 1, 3 ) = D( IS, IS ) + Z( 2, 3 ) = ZERO + Z( 3, 3 ) = -E( JS, JS ) + Z( 4, 3 ) = ZERO +* + Z( 1, 4 ) = ZERO + Z( 2, 4 ) = D( IS, IS ) + Z( 3, 4 ) = -E( JS, JSP1 ) + Z( 4, 4 ) = -E( JSP1, JSP1 ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = C( IS, JSP1 ) + RHS( 3 ) = F( IS, JS ) + RHS( 4 ) = F( IS, JSP1 ) +* +* Solve Z' * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 140 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 140 CONTINUE + SCALE = SCALE*SCALOC + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + C( IS, JSP1 ) = RHS( 2 ) + F( IS, JS ) = RHS( 3 ) + F( IS, JSP1 ) = RHS( 4 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( J.GT.P+2 ) THEN + CALL DAXPY( JS-1, RHS( 1 ), B( 1, JS ), 1, + $ F( IS, 1 ), LDF ) + CALL DAXPY( JS-1, RHS( 2 ), B( 1, JSP1 ), 1, + $ F( IS, 1 ), LDF ) + CALL DAXPY( JS-1, RHS( 3 ), E( 1, JS ), 1, + $ F( IS, 1 ), LDF ) + CALL DAXPY( JS-1, RHS( 4 ), E( 1, JSP1 ), 1, + $ F( IS, 1 ), LDF ) + END IF + IF( I.LT.P ) THEN + CALL DGER( M-IE, NB, -ONE, A( IS, IE+1 ), LDA, + $ RHS( 1 ), 1, C( IE+1, JS ), LDC ) + CALL DGER( M-IE, NB, -ONE, D( IS, IE+1 ), LDD, + $ RHS( 3 ), 1, C( IE+1, JS ), LDC ) + END IF +* + ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.1 ) ) THEN +* +* Build a 4-by-4 system Z' * x = RHS +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = A( IS, ISP1 ) + Z( 3, 1 ) = -B( JS, JS ) + Z( 4, 1 ) = ZERO +* + Z( 1, 2 ) = A( ISP1, IS ) + Z( 2, 2 ) = A( ISP1, ISP1 ) + Z( 3, 2 ) = ZERO + Z( 4, 2 ) = -B( JS, JS ) +* + Z( 1, 3 ) = D( IS, IS ) + Z( 2, 3 ) = D( IS, ISP1 ) + Z( 3, 3 ) = -E( JS, JS ) + Z( 4, 3 ) = ZERO +* + Z( 1, 4 ) = ZERO + Z( 2, 4 ) = D( ISP1, ISP1 ) + Z( 3, 4 ) = ZERO + Z( 4, 4 ) = -E( JS, JS ) +* +* Set up right hand side(s) +* + RHS( 1 ) = C( IS, JS ) + RHS( 2 ) = C( ISP1, JS ) + RHS( 3 ) = F( IS, JS ) + RHS( 4 ) = F( ISP1, JS ) +* +* Solve Z' * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR +* + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 150 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 150 CONTINUE + SCALE = SCALE*SCALOC + END IF +* +* Unpack solution vector(s) +* + C( IS, JS ) = RHS( 1 ) + C( ISP1, JS ) = RHS( 2 ) + F( IS, JS ) = RHS( 3 ) + F( ISP1, JS ) = RHS( 4 ) +* +* Substitute R(I, J) and L(I, J) into remaining +* equation. +* + IF( J.GT.P+2 ) THEN + CALL DGER( MB, JS-1, ONE, RHS( 1 ), 1, B( 1, JS ), + $ 1, F( IS, 1 ), LDF ) + CALL DGER( MB, JS-1, ONE, RHS( 3 ), 1, E( 1, JS ), + $ 1, F( IS, 1 ), LDF ) + END IF + IF( I.LT.P ) THEN + CALL DGEMV( 'T', MB, M-IE, -ONE, A( IS, IE+1 ), + $ LDA, RHS( 1 ), 1, ONE, C( IE+1, JS ), + $ 1 ) + CALL DGEMV( 'T', MB, M-IE, -ONE, D( IS, IE+1 ), + $ LDD, RHS( 3 ), 1, ONE, C( IE+1, JS ), + $ 1 ) + END IF +* + ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.2 ) ) THEN +* +* Build an 8-by-8 system Z' * x = RHS +* + CALL DLASET( 'F', LDZ, LDZ, ZERO, ZERO, Z, LDZ ) +* + Z( 1, 1 ) = A( IS, IS ) + Z( 2, 1 ) = A( IS, ISP1 ) + Z( 5, 1 ) = -B( JS, JS ) + Z( 7, 1 ) = -B( JSP1, JS ) +* + Z( 1, 2 ) = A( ISP1, IS ) + Z( 2, 2 ) = A( ISP1, ISP1 ) + Z( 6, 2 ) = -B( JS, JS ) + Z( 8, 2 ) = -B( JSP1, JS ) +* + Z( 3, 3 ) = A( IS, IS ) + Z( 4, 3 ) = A( IS, ISP1 ) + Z( 5, 3 ) = -B( JS, JSP1 ) + Z( 7, 3 ) = -B( JSP1, JSP1 ) +* + Z( 3, 4 ) = A( ISP1, IS ) + Z( 4, 4 ) = A( ISP1, ISP1 ) + Z( 6, 4 ) = -B( JS, JSP1 ) + Z( 8, 4 ) = -B( JSP1, JSP1 ) +* + Z( 1, 5 ) = D( IS, IS ) + Z( 2, 5 ) = D( IS, ISP1 ) + Z( 5, 5 ) = -E( JS, JS ) +* + Z( 2, 6 ) = D( ISP1, ISP1 ) + Z( 6, 6 ) = -E( JS, JS ) +* + Z( 3, 7 ) = D( IS, IS ) + Z( 4, 7 ) = D( IS, ISP1 ) + Z( 5, 7 ) = -E( JS, JSP1 ) + Z( 7, 7 ) = -E( JSP1, JSP1 ) +* + Z( 4, 8 ) = D( ISP1, ISP1 ) + Z( 6, 8 ) = -E( JS, JSP1 ) + Z( 8, 8 ) = -E( JSP1, JSP1 ) +* +* Set up right hand side(s) +* + K = 1 + II = MB*NB + 1 + DO 160 JJ = 0, NB - 1 + CALL DCOPY( MB, C( IS, JS+JJ ), 1, RHS( K ), 1 ) + CALL DCOPY( MB, F( IS, JS+JJ ), 1, RHS( II ), 1 ) + K = K + MB + II = II + MB + 160 CONTINUE +* +* +* Solve Z' * x = RHS +* + CALL DGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR ) + IF( IERR.GT.0 ) + $ INFO = IERR +* + CALL DGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC ) + IF( SCALOC.NE.ONE ) THEN + DO 170 K = 1, N + CALL DSCAL( M, SCALOC, C( 1, K ), 1 ) + CALL DSCAL( M, SCALOC, F( 1, K ), 1 ) + 170 CONTINUE + SCALE = SCALE*SCALOC + END IF +* +* Unpack solution vector(s) +* + K = 1 + II = MB*NB + 1 + DO 180 JJ = 0, NB - 1 + CALL DCOPY( MB, RHS( K ), 1, C( IS, JS+JJ ), 1 ) + CALL DCOPY( MB, RHS( II ), 1, F( IS, JS+JJ ), 1 ) + K = K + MB + II = II + MB + 180 CONTINUE +* +* 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 +* + END IF +* + 190 CONTINUE + 200 CONTINUE +* + END IF + RETURN +* +* End of DTGSY2 +* + END |