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SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
$ BETA, WX, WY, S, DIF ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * June 2010 * * .. Scalar Arguments .. INTEGER LDA, LDX, LDY, N, TYPE COMPLEX ALPHA, BETA, WX, WY * .. * .. Array Arguments .. REAL DIF( * ), S( * ) COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ), $ Y( LDY, * ) * .. * * Purpose * ======= * * CLATM6 generates test matrices for the generalized eigenvalue * problem, their corresponding right and left eigenvector matrices, * and also reciprocal condition numbers for all eigenvalues and * the reciprocal condition numbers of eigenvectors corresponding to * the 1th and 5th eigenvalues. * * Test Matrices * ============= * * Two kinds of test matrix pairs * (A, B) = inverse(YH) * (Da, Db) * inverse(X) * are used in the tests: * * Type 1: * Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 * 0 2+a 0 0 0 0 1 0 0 0 * 0 0 3+a 0 0 0 0 1 0 0 * 0 0 0 4+a 0 0 0 0 1 0 * 0 0 0 0 5+a , 0 0 0 0 1 * and Type 2: * Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 * 0 1-i 0 0 0 0 1 0 0 0 * 0 0 1 0 0 0 0 1 0 0 * 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 * 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . * * In both cases the same inverse(YH) and inverse(X) are used to compute * (A, B), giving the exact eigenvectors to (A,B) as (YH, X): * * YH: = 1 0 -y y -y X = 1 0 -x -x x * 0 1 -y y -y 0 1 x -x -x * 0 0 1 0 0 0 0 1 0 0 * 0 0 0 1 0 0 0 0 1 0 * 0 0 0 0 1, 0 0 0 0 1 , where * * a, b, x and y will have all values independently of each other. * * Arguments * ========= * * TYPE (input) INTEGER * Specifies the problem type (see futher details). * * N (input) INTEGER * Size of the matrices A and B. * * A (output) COMPLEX array, dimension (LDA, N). * On exit A N-by-N is initialized according to TYPE. * * LDA (input) INTEGER * The leading dimension of A and of B. * * B (output) COMPLEX array, dimension (LDA, N). * On exit B N-by-N is initialized according to TYPE. * * X (output) COMPLEX array, dimension (LDX, N). * On exit X is the N-by-N matrix of right eigenvectors. * * LDX (input) INTEGER * The leading dimension of X. * * Y (output) COMPLEX array, dimension (LDY, N). * On exit Y is the N-by-N matrix of left eigenvectors. * * LDY (input) INTEGER * The leading dimension of Y. * * ALPHA (input) COMPLEX * * BETA (input) COMPLEX * Weighting constants for matrix A. * * WX (input) COMPLEX * Constant for right eigenvector matrix. * * WY (input) COMPLEX * Constant for left eigenvector matrix. * * S (output) REAL array, dimension (N) * S(i) is the reciprocal condition number for eigenvalue i. * * DIF (output) REAL array, dimension (N) * DIF(i) is the reciprocal condition number for eigenvector i. * * ===================================================================== * * .. Parameters .. REAL RONE, TWO, THREE PARAMETER ( RONE = 1.0E+0, TWO = 2.0E+0, THREE = 3.0E+0 ) COMPLEX ZERO, ONE PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ), $ ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, J * .. * .. Local Arrays .. REAL RWORK( 50 ) COMPLEX WORK( 26 ), Z( 8, 8 ) * .. * .. Intrinsic Functions .. INTRINSIC CABS, CMPLX, CONJG, REAL, SQRT * .. * .. External Subroutines .. EXTERNAL CGESVD, CLACPY, CLAKF2 * .. * .. Executable Statements .. * * Generate test problem ... * (Da, Db) ... * DO 20 I = 1, N DO 10 J = 1, N * IF( I.EQ.J ) THEN A( I, I ) = CMPLX( I ) + ALPHA B( I, I ) = ONE ELSE A( I, J ) = ZERO B( I, J ) = ZERO END IF * 10 CONTINUE 20 CONTINUE IF( TYPE.EQ.2 ) THEN A( 1, 1 ) = CMPLX( RONE, RONE ) A( 2, 2 ) = CONJG( A( 1, 1 ) ) A( 3, 3 ) = ONE A( 4, 4 ) = CMPLX( REAL( ONE+ALPHA ), REAL( ONE+BETA ) ) A( 5, 5 ) = CONJG( A( 4, 4 ) ) END IF * * Form X and Y * CALL CLACPY( 'F', N, N, B, LDA, Y, LDY ) Y( 3, 1 ) = -CONJG( WY ) Y( 4, 1 ) = CONJG( WY ) Y( 5, 1 ) = -CONJG( WY ) Y( 3, 2 ) = -CONJG( WY ) Y( 4, 2 ) = CONJG( WY ) Y( 5, 2 ) = -CONJG( WY ) * CALL CLACPY( 'F', N, N, B, LDA, X, LDX ) X( 1, 3 ) = -WX X( 1, 4 ) = -WX X( 1, 5 ) = WX X( 2, 3 ) = WX X( 2, 4 ) = -WX X( 2, 5 ) = -WX * * Form (A, B) * B( 1, 3 ) = WX + WY B( 2, 3 ) = -WX + WY B( 1, 4 ) = WX - WY B( 2, 4 ) = WX - WY B( 1, 5 ) = -WX + WY B( 2, 5 ) = WX + WY A( 1, 3 ) = WX*A( 1, 1 ) + WY*A( 3, 3 ) A( 2, 3 ) = -WX*A( 2, 2 ) + WY*A( 3, 3 ) A( 1, 4 ) = WX*A( 1, 1 ) - WY*A( 4, 4 ) A( 2, 4 ) = WX*A( 2, 2 ) - WY*A( 4, 4 ) A( 1, 5 ) = -WX*A( 1, 1 ) + WY*A( 5, 5 ) A( 2, 5 ) = WX*A( 2, 2 ) + WY*A( 5, 5 ) * * Compute condition numbers * S( 1 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) / $ ( RONE+CABS( A( 1, 1 ) )*CABS( A( 1, 1 ) ) ) ) S( 2 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) / $ ( RONE+CABS( A( 2, 2 ) )*CABS( A( 2, 2 ) ) ) ) S( 3 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) / $ ( RONE+CABS( A( 3, 3 ) )*CABS( A( 3, 3 ) ) ) ) S( 4 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) / $ ( RONE+CABS( A( 4, 4 ) )*CABS( A( 4, 4 ) ) ) ) S( 5 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) / $ ( RONE+CABS( A( 5, 5 ) )*CABS( A( 5, 5 ) ) ) ) * CALL CLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 8 ) CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1, $ WORK( 3 ), 24, RWORK( 9 ), INFO ) DIF( 1 ) = RWORK( 8 ) * CALL CLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 8 ) CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1, $ WORK( 3 ), 24, RWORK( 9 ), INFO ) DIF( 5 ) = RWORK( 8 ) * RETURN * * End of CLATM6 * END |