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|
*> \brief \b DLATM5
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
* QBLCKB )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
* $ PRTYPE, QBLCKA, QBLCKB
* DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
* $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
* $ L( LDL, * ), R( LDR, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLATM5 generates matrices involved in the Generalized Sylvester
*> equation:
*>
*> A * R - L * B = C
*> D * R - L * E = F
*>
*> They also satisfy (the diagonalization condition)
*>
*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] PRTYPE
*> \verbatim
*> PRTYPE is INTEGER
*> "Points" to a certain type of the matrices to generate
*> (see further details).
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> Specifies the order of A and D and the number of rows in
*> C, F, R and L.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> Specifies the order of B and E and the number of columns in
*> C, F, R and L.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA, M).
*> On exit A M-by-M is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A.
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB, N).
*> On exit B N-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of B.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (LDC, N).
*> On exit C M-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of C.
*> \endverbatim
*>
*> \param[out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (LDD, M).
*> On exit D M-by-M is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDD
*> \verbatim
*> LDD is INTEGER
*> The leading dimension of D.
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (LDE, N).
*> On exit E N-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDE
*> \verbatim
*> LDE is INTEGER
*> The leading dimension of E.
*> \endverbatim
*>
*> \param[out] F
*> \verbatim
*> F is DOUBLE PRECISION array, dimension (LDF, N).
*> On exit F M-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDF
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of F.
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*> R is DOUBLE PRECISION array, dimension (LDR, N).
*> On exit R M-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDR
*> \verbatim
*> LDR is INTEGER
*> The leading dimension of R.
*> \endverbatim
*>
*> \param[out] L
*> \verbatim
*> L is DOUBLE PRECISION array, dimension (LDL, N).
*> On exit L M-by-N is initialized according to PRTYPE.
*> \endverbatim
*>
*> \param[in] LDL
*> \verbatim
*> LDL is INTEGER
*> The leading dimension of L.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION
*> Parameter used in generating PRTYPE = 1 and 5 matrices.
*> \endverbatim
*>
*> \param[in] QBLCKA
*> \verbatim
*> QBLCKA is INTEGER
*> When PRTYPE = 3, specifies the distance between 2-by-2
*> blocks on the diagonal in A. Otherwise, QBLCKA is not
*> referenced. QBLCKA > 1.
*> \endverbatim
*>
*> \param[in] QBLCKB
*> \verbatim
*> QBLCKB is INTEGER
*> When PRTYPE = 3, specifies the distance between 2-by-2
*> blocks on the diagonal in B. Otherwise, QBLCKB is not
*> referenced. QBLCKB > 1.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2016
*
*> \ingroup double_matgen
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
*>
*> A : if (i == j) then A(i, j) = 1.0
*> if (j == i + 1) then A(i, j) = -1.0
*> else A(i, j) = 0.0, i, j = 1...M
*>
*> B : if (i == j) then B(i, j) = 1.0 - ALPHA
*> if (j == i + 1) then B(i, j) = 1.0
*> else B(i, j) = 0.0, i, j = 1...N
*>
*> D : if (i == j) then D(i, j) = 1.0
*> else D(i, j) = 0.0, i, j = 1...M
*>
*> E : if (i == j) then E(i, j) = 1.0
*> else E(i, j) = 0.0, i, j = 1...N
*>
*> L = R are chosen from [-10...10],
*> which specifies the right hand sides (C, F).
*>
*> PRTYPE = 2 or 3: Triangular and/or quasi- triangular.
*>
*> A : if (i <= j) then A(i, j) = [-1...1]
*> else A(i, j) = 0.0, i, j = 1...M
*>
*> if (PRTYPE = 3) then
*> A(k + 1, k + 1) = A(k, k)
*> A(k + 1, k) = [-1...1]
*> sign(A(k, k + 1) = -(sin(A(k + 1, k))
*> k = 1, M - 1, QBLCKA
*>
*> B : if (i <= j) then B(i, j) = [-1...1]
*> else B(i, j) = 0.0, i, j = 1...N
*>
*> if (PRTYPE = 3) then
*> B(k + 1, k + 1) = B(k, k)
*> B(k + 1, k) = [-1...1]
*> sign(B(k, k + 1) = -(sign(B(k + 1, k))
*> k = 1, N - 1, QBLCKB
*>
*> D : if (i <= j) then D(i, j) = [-1...1].
*> else D(i, j) = 0.0, i, j = 1...M
*>
*>
*> E : if (i <= j) then D(i, j) = [-1...1]
*> else E(i, j) = 0.0, i, j = 1...N
*>
*> L, R are chosen from [-10...10],
*> which specifies the right hand sides (C, F).
*>
*> PRTYPE = 4 Full
*> A(i, j) = [-10...10]
*> D(i, j) = [-1...1] i,j = 1...M
*> B(i, j) = [-10...10]
*> E(i, j) = [-1...1] i,j = 1...N
*> R(i, j) = [-10...10]
*> L(i, j) = [-1...1] i = 1..M ,j = 1...N
*>
*> L, R specifies the right hand sides (C, F).
*>
*> PRTYPE = 5 special case common and/or close eigs.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
$ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
$ QBLCKB )
*
* -- LAPACK computational routine (version 3.6.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2016
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
$ PRTYPE, QBLCKA, QBLCKB
DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
$ L( LDL, * ), R( LDR, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO, TWENTY, HALF, TWO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0, TWENTY = 2.0D+1,
$ HALF = 0.5D+0, TWO = 2.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K
DOUBLE PRECISION IMEPS, REEPS
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MOD, SIN
* ..
* .. External Subroutines ..
EXTERNAL DGEMM
* ..
* .. Executable Statements ..
*
IF( PRTYPE.EQ.1 ) THEN
DO 20 I = 1, M
DO 10 J = 1, M
IF( I.EQ.J ) THEN
A( I, J ) = ONE
D( I, J ) = ONE
ELSE IF( I.EQ.J-1 ) THEN
A( I, J ) = -ONE
D( I, J ) = ZERO
ELSE
A( I, J ) = ZERO
D( I, J ) = ZERO
END IF
10 CONTINUE
20 CONTINUE
*
DO 40 I = 1, N
DO 30 J = 1, N
IF( I.EQ.J ) THEN
B( I, J ) = ONE - ALPHA
E( I, J ) = ONE
ELSE IF( I.EQ.J-1 ) THEN
B( I, J ) = ONE
E( I, J ) = ZERO
ELSE
B( I, J ) = ZERO
E( I, J ) = ZERO
END IF
30 CONTINUE
40 CONTINUE
*
DO 60 I = 1, M
DO 50 J = 1, N
R( I, J ) = ( HALF-SIN( DBLE( I / J ) ) )*TWENTY
L( I, J ) = R( I, J )
50 CONTINUE
60 CONTINUE
*
ELSE IF( PRTYPE.EQ.2 .OR. PRTYPE.EQ.3 ) THEN
DO 80 I = 1, M
DO 70 J = 1, M
IF( I.LE.J ) THEN
A( I, J ) = ( HALF-SIN( DBLE( I ) ) )*TWO
D( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*TWO
ELSE
A( I, J ) = ZERO
D( I, J ) = ZERO
END IF
70 CONTINUE
80 CONTINUE
*
DO 100 I = 1, N
DO 90 J = 1, N
IF( I.LE.J ) THEN
B( I, J ) = ( HALF-SIN( DBLE( I+J ) ) )*TWO
E( I, J ) = ( HALF-SIN( DBLE( J ) ) )*TWO
ELSE
B( I, J ) = ZERO
E( I, J ) = ZERO
END IF
90 CONTINUE
100 CONTINUE
*
DO 120 I = 1, M
DO 110 J = 1, N
R( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*TWENTY
L( I, J ) = ( HALF-SIN( DBLE( I+J ) ) )*TWENTY
110 CONTINUE
120 CONTINUE
*
IF( PRTYPE.EQ.3 ) THEN
IF( QBLCKA.LE.1 )
$ QBLCKA = 2
DO 130 K = 1, M - 1, QBLCKA
A( K+1, K+1 ) = A( K, K )
A( K+1, K ) = -SIN( A( K, K+1 ) )
130 CONTINUE
*
IF( QBLCKB.LE.1 )
$ QBLCKB = 2
DO 140 K = 1, N - 1, QBLCKB
B( K+1, K+1 ) = B( K, K )
B( K+1, K ) = -SIN( B( K, K+1 ) )
140 CONTINUE
END IF
*
ELSE IF( PRTYPE.EQ.4 ) THEN
DO 160 I = 1, M
DO 150 J = 1, M
A( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*TWENTY
D( I, J ) = ( HALF-SIN( DBLE( I+J ) ) )*TWO
150 CONTINUE
160 CONTINUE
*
DO 180 I = 1, N
DO 170 J = 1, N
B( I, J ) = ( HALF-SIN( DBLE( I+J ) ) )*TWENTY
E( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*TWO
170 CONTINUE
180 CONTINUE
*
DO 200 I = 1, M
DO 190 J = 1, N
R( I, J ) = ( HALF-SIN( DBLE( J / I ) ) )*TWENTY
L( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*TWO
190 CONTINUE
200 CONTINUE
*
ELSE IF( PRTYPE.GE.5 ) THEN
REEPS = HALF*TWO*TWENTY / ALPHA
IMEPS = ( HALF-TWO ) / ALPHA
DO 220 I = 1, M
DO 210 J = 1, N
R( I, J ) = ( HALF-SIN( DBLE( I*J ) ) )*ALPHA / TWENTY
L( I, J ) = ( HALF-SIN( DBLE( I+J ) ) )*ALPHA / TWENTY
210 CONTINUE
220 CONTINUE
*
DO 230 I = 1, M
D( I, I ) = ONE
230 CONTINUE
*
DO 240 I = 1, M
IF( I.LE.4 ) THEN
A( I, I ) = ONE
IF( I.GT.2 )
$ A( I, I ) = ONE + REEPS
IF( MOD( I, 2 ).NE.0 .AND. I.LT.M ) THEN
A( I, I+1 ) = IMEPS
ELSE IF( I.GT.1 ) THEN
A( I, I-1 ) = -IMEPS
END IF
ELSE IF( I.LE.8 ) THEN
IF( I.LE.6 ) THEN
A( I, I ) = REEPS
ELSE
A( I, I ) = -REEPS
END IF
IF( MOD( I, 2 ).NE.0 .AND. I.LT.M ) THEN
A( I, I+1 ) = ONE
ELSE IF( I.GT.1 ) THEN
A( I, I-1 ) = -ONE
END IF
ELSE
A( I, I ) = ONE
IF( MOD( I, 2 ).NE.0 .AND. I.LT.M ) THEN
A( I, I+1 ) = IMEPS*2
ELSE IF( I.GT.1 ) THEN
A( I, I-1 ) = -IMEPS*2
END IF
END IF
240 CONTINUE
*
DO 250 I = 1, N
E( I, I ) = ONE
IF( I.LE.4 ) THEN
B( I, I ) = -ONE
IF( I.GT.2 )
$ B( I, I ) = ONE - REEPS
IF( MOD( I, 2 ).NE.0 .AND. I.LT.N ) THEN
B( I, I+1 ) = IMEPS
ELSE IF( I.GT.1 ) THEN
B( I, I-1 ) = -IMEPS
END IF
ELSE IF( I.LE.8 ) THEN
IF( I.LE.6 ) THEN
B( I, I ) = REEPS
ELSE
B( I, I ) = -REEPS
END IF
IF( MOD( I, 2 ).NE.0 .AND. I.LT.N ) THEN
B( I, I+1 ) = ONE + IMEPS
ELSE IF( I.GT.1 ) THEN
B( I, I-1 ) = -ONE - IMEPS
END IF
ELSE
B( I, I ) = ONE - REEPS
IF( MOD( I, 2 ).NE.0 .AND. I.LT.N ) THEN
B( I, I+1 ) = IMEPS*2
ELSE IF( I.GT.1 ) THEN
B( I, I-1 ) = -IMEPS*2
END IF
END IF
250 CONTINUE
END IF
*
* Compute rhs (C, F)
*
CALL DGEMM( 'N', 'N', M, N, M, ONE, A, LDA, R, LDR, ZERO, C, LDC )
CALL DGEMM( 'N', 'N', M, N, N, -ONE, L, LDL, B, LDB, ONE, C, LDC )
CALL DGEMM( 'N', 'N', M, N, M, ONE, D, LDD, R, LDR, ZERO, F, LDF )
CALL DGEMM( 'N', 'N', M, N, N, -ONE, L, LDL, E, LDE, ONE, F, LDF )
*
* End of DLATM5
*
END
|
