SUBROUTINE SLATM6( 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.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LDX, LDY, N, TYPE REAL ALPHA, BETA, WX, WY * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), \$ X( LDX, * ), Y( LDY, * ) * .. * * Purpose * ======= * * SLATM6 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 -1 0 0 0 Db = 1 0 0 0 0 * 1 1 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 0 0 0 1 0 * 0 0 0 -1-b 1+a , 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) REAL 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) REAL array, dimension (LDA, N). * On exit B N-by-N is initialized according to TYPE. * * X (output) REAL 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) REAL 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) REAL * BETA (input) REAL * Weighting constants for matrix A. * * WX (input) REAL * Constant for right eigenvector matrix. * * WY (input) REAL * 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 ZERO, ONE, TWO, THREE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0, \$ THREE = 3.0E+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J * .. * .. Local Arrays .. REAL WORK( 100 ), Z( 12, 12 ) * .. * .. Intrinsic Functions .. INTRINSIC REAL, SQRT * .. * .. External Subroutines .. EXTERNAL SGESVD, SLACPY, SLAKF2 * .. * .. 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 ) = REAL( I ) + ALPHA B( I, I ) = ONE ELSE A( I, J ) = ZERO B( I, J ) = ZERO END IF * 10 CONTINUE 20 CONTINUE * * Form X and Y * CALL SLACPY( 'F', N, N, B, LDA, Y, LDY ) Y( 3, 1 ) = -WY Y( 4, 1 ) = WY Y( 5, 1 ) = -WY Y( 3, 2 ) = -WY Y( 4, 2 ) = WY Y( 5, 2 ) = -WY * CALL SLACPY( '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 IF( TYPE.EQ.1 ) THEN 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 ) ELSE IF( TYPE.EQ.2 ) THEN A( 1, 3 ) = TWO*WX + WY A( 2, 3 ) = WY A( 1, 4 ) = -WY*( TWO+ALPHA+BETA ) A( 2, 4 ) = TWO*WX - WY*( TWO+ALPHA+BETA ) A( 1, 5 ) = -TWO*WX + WY*( ALPHA-BETA ) A( 2, 5 ) = WY*( ALPHA-BETA ) A( 1, 1 ) = ONE A( 1, 2 ) = -ONE A( 2, 1 ) = ONE A( 2, 2 ) = A( 1, 1 ) A( 3, 3 ) = ONE A( 4, 4 ) = ONE + ALPHA A( 4, 5 ) = ONE + BETA A( 5, 4 ) = -A( 4, 5 ) A( 5, 5 ) = A( 4, 4 ) END IF * * Compute condition numbers * IF( TYPE.EQ.1 ) THEN * S( 1 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) / \$ ( ONE+A( 1, 1 )*A( 1, 1 ) ) ) S( 2 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) / \$ ( ONE+A( 2, 2 )*A( 2, 2 ) ) ) S( 3 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) / \$ ( ONE+A( 3, 3 )*A( 3, 3 ) ) ) S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) / \$ ( ONE+A( 4, 4 )*A( 4, 4 ) ) ) S( 5 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) / \$ ( ONE+A( 5, 5 )*A( 5, 5 ) ) ) * CALL SLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 12 ) CALL SGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1, \$ WORK( 10 ), 1, WORK( 11 ), 40, INFO ) DIF( 1 ) = WORK( 8 ) * CALL SLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 12 ) CALL SGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1, \$ WORK( 10 ), 1, WORK( 11 ), 40, INFO ) DIF( 5 ) = WORK( 8 ) * ELSE IF( TYPE.EQ.2 ) THEN * S( 1 ) = ONE / SQRT( ONE / THREE+WY*WY ) S( 2 ) = S( 1 ) S( 3 ) = ONE / SQRT( ONE / TWO+WX*WX ) S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) / \$ ( ONE+( ONE+ALPHA )*( ONE+ALPHA )+( ONE+BETA )*( ONE+ \$ BETA ) ) ) S( 5 ) = S( 4 ) * CALL SLAKF2( 2, 3, A, LDA, A( 3, 3 ), B, B( 3, 3 ), Z, 12 ) CALL SGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1, \$ WORK( 14 ), 1, WORK( 15 ), 60, INFO ) DIF( 1 ) = WORK( 12 ) * CALL SLAKF2( 3, 2, A, LDA, A( 4, 4 ), B, B( 4, 4 ), Z, 12 ) CALL SGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1, \$ WORK( 14 ), 1, WORK( 15 ), 60, INFO ) DIF( 5 ) = WORK( 12 ) * END IF * RETURN * * End of SLATM6 * END