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SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
$ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
$ QBLCKB )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
$ PRTYPE, QBLCKA, QBLCKB
REAL ALPHA
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), C( LDC, * ),
$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
$ L( LDL, * ), R( LDR, * )
* ..
*
* Purpose
* =======
*
* SLATM5 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 ] )
*
*
* Arguments
* =========
*
* PRTYPE (input) INTEGER
* "Points" to a certian type of the matrices to generate
* (see futher details).
*
* M (input) INTEGER
* Specifies the order of A and D and the number of rows in
* C, F, R and L.
*
* N (input) INTEGER
* Specifies the order of B and E and the number of columns in
* C, F, R and L.
*
* A (output) REAL array, dimension (LDA, M).
* On exit A M-by-M is initialized according to PRTYPE.
*
* LDA (input) INTEGER
* The leading dimension of A.
*
* B (output) REAL array, dimension (LDB, N).
* On exit B N-by-N is initialized according to PRTYPE.
*
* LDB (input) INTEGER
* The leading dimension of B.
*
* C (output) REAL array, dimension (LDC, N).
* On exit C M-by-N is initialized according to PRTYPE.
*
* LDC (input) INTEGER
* The leading dimension of C.
*
* D (output) REAL array, dimension (LDD, M).
* On exit D M-by-M is initialized according to PRTYPE.
*
* LDD (input) INTEGER
* The leading dimension of D.
*
* E (output) REAL array, dimension (LDE, N).
* On exit E N-by-N is initialized according to PRTYPE.
*
* LDE (input) INTEGER
* The leading dimension of E.
*
* F (output) REAL array, dimension (LDF, N).
* On exit F M-by-N is initialized according to PRTYPE.
*
* LDF (input) INTEGER
* The leading dimension of F.
*
* R (output) REAL array, dimension (LDR, N).
* On exit R M-by-N is initialized according to PRTYPE.
*
* LDR (input) INTEGER
* The leading dimension of R.
*
* L (output) REAL array, dimension (LDL, N).
* On exit L M-by-N is initialized according to PRTYPE.
*
* LDL (input) INTEGER
* The leading dimension of L.
*
* ALPHA (input) REAL
* Parameter used in generating PRTYPE = 1 and 5 matrices.
*
* QBLCKA (input) INTEGER
* When PRTYPE = 3, specifies the distance between 2-by-2
* blocks on the diagonal in A. Otherwise, QBLCKA is not
* referenced. QBLCKA > 1.
*
* QBLCKB (input) INTEGER
* When PRTYPE = 3, specifies the distance between 2-by-2
* blocks on the diagonal in B. Otherwise, QBLCKB is not
* referenced. QBLCKB > 1.
*
*
* Further Details
* ===============
*
* 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.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO, TWENTY, HALF, TWO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0, TWENTY = 2.0E+1,
$ HALF = 0.5E+0, TWO = 2.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K
REAL IMEPS, REEPS
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD, REAL, SIN
* ..
* .. External Subroutines ..
EXTERNAL SGEMM
* ..
* .. 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( REAL( 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( REAL( I ) ) )*TWO
D( I, J ) = ( HALF-SIN( REAL( 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( REAL( I+J ) ) )*TWO
E( I, J ) = ( HALF-SIN( REAL( 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( REAL( I*J ) ) )*TWENTY
L( I, J ) = ( HALF-SIN( REAL( 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( REAL( I*J ) ) )*TWENTY
D( I, J ) = ( HALF-SIN( REAL( I+J ) ) )*TWO
150 CONTINUE
160 CONTINUE
*
DO 180 I = 1, N
DO 170 J = 1, N
B( I, J ) = ( HALF-SIN( REAL( I+J ) ) )*TWENTY
E( I, J ) = ( HALF-SIN( REAL( I*J ) ) )*TWO
170 CONTINUE
180 CONTINUE
*
DO 200 I = 1, M
DO 190 J = 1, N
R( I, J ) = ( HALF-SIN( REAL( J / I ) ) )*TWENTY
L( I, J ) = ( HALF-SIN( REAL( 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( REAL( I*J ) ) )*ALPHA / TWENTY
L( I, J ) = ( HALF-SIN( REAL( 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 SGEMM( 'N', 'N', M, N, M, ONE, A, LDA, R, LDR, ZERO, C, LDC )
CALL SGEMM( 'N', 'N', M, N, N, -ONE, L, LDL, B, LDB, ONE, C, LDC )
CALL SGEMM( 'N', 'N', M, N, M, ONE, D, LDD, R, LDR, ZERO, F, LDF )
CALL SGEMM( 'N', 'N', M, N, N, -ONE, L, LDL, E, LDE, ONE, F, LDF )
*
* End of SLATM5
*
END
|
