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SUBROUTINE SSYT22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
$ V, LDV, TAU, WORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), D( * ), E( * ), RESULT( 2 ), $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * ) * .. * * Purpose * ======= * * SSYT22 generally checks a decomposition of the form * * A U = U S * * where A is symmetric, the columns of U are orthonormal, and S * is diagonal (if KBAND=0) or symmetric tridiagonal (if * KBAND=1). If ITYPE=1, then U is represented as a dense matrix, * otherwise the U is expressed as a product of Householder * transformations, whose vectors are stored in the array "V" and * whose scaling constants are in "TAU"; we shall use the letter * "V" to refer to the product of Householder transformations * (which should be equal to U). * * Specifically, if ITYPE=1, then: * * RESULT(1) = | U' A U - S | / ( |A| m ulp ) *and* * RESULT(2) = | I - U'U | / ( m ulp ) * * Arguments * ========= * * ITYPE INTEGER * Specifies the type of tests to be performed. * 1: U expressed as a dense orthogonal matrix: * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* * RESULT(2) = | I - UU' | / ( n ulp ) * * UPLO CHARACTER * If UPLO='U', the upper triangle of A will be used and the * (strictly) lower triangle will not be referenced. If * UPLO='L', the lower triangle of A will be used and the * (strictly) upper triangle will not be referenced. * Not modified. * * N INTEGER * The size of the matrix. If it is zero, SSYT22 does nothing. * It must be at least zero. * Not modified. * * M INTEGER * The number of columns of U. If it is zero, SSYT22 does * nothing. It must be at least zero. * Not modified. * * KBAND INTEGER * The bandwidth of the matrix. It may only be zero or one. * If zero, then S is diagonal, and E is not referenced. If * one, then S is symmetric tri-diagonal. * Not modified. * * A REAL array, dimension (LDA , N) * The original (unfactored) matrix. It is assumed to be * symmetric, and only the upper (UPLO='U') or only the lower * (UPLO='L') will be referenced. * Not modified. * * LDA INTEGER * The leading dimension of A. It must be at least 1 * and at least N. * Not modified. * * D REAL array, dimension (N) * The diagonal of the (symmetric tri-) diagonal matrix. * Not modified. * * E REAL array, dimension (N) * The off-diagonal of the (symmetric tri-) diagonal matrix. * E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. * Not referenced if KBAND=0. * Not modified. * * U REAL array, dimension (LDU, N) * If ITYPE=1 or 3, this contains the orthogonal matrix in * the decomposition, expressed as a dense matrix. If ITYPE=2, * then it is not referenced. * Not modified. * * LDU INTEGER * The leading dimension of U. LDU must be at least N and * at least 1. * Not modified. * * V REAL array, dimension (LDV, N) * If ITYPE=2 or 3, the lower triangle of this array contains * the Householder vectors used to describe the orthogonal * matrix in the decomposition. If ITYPE=1, then it is not * referenced. * Not modified. * * LDV INTEGER * The leading dimension of V. LDV must be at least N and * at least 1. * Not modified. * * TAU REAL array, dimension (N) * If ITYPE >= 2, then TAU(j) is the scalar factor of * v(j) v(j)' in the Householder transformation H(j) of * the product U = H(1)...H(n-2) * If ITYPE < 2, then TAU is not referenced. * Not modified. * * WORK REAL array, dimension (2*N**2) * Workspace. * Modified. * * RESULT REAL array, dimension (2) * The values computed by the two tests described above. The * values are currently limited to 1/ulp, to avoid overflow. * RESULT(1) is always modified. RESULT(2) is modified only * if LDU is at least N. * Modified. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER J, JJ, JJ1, JJ2, NN, NNP1 REAL ANORM, ULP, UNFL, WNORM * .. * .. External Functions .. REAL SLAMCH, SLANSY EXTERNAL SLAMCH, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM, SSYMM * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Executable Statements .. * RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO IF( N.LE.0 .OR. M.LE.0 ) $ RETURN * UNFL = SLAMCH( 'Safe minimum' ) ULP = SLAMCH( 'Precision' ) * * Do Test 1 * * Norm of A: * ANORM = MAX( SLANSY( '1', UPLO, N, A, LDA, WORK ), UNFL ) * * Compute error matrix: * * ITYPE=1: error = U' A U - S * CALL SSYMM( 'L', UPLO, N, M, ONE, A, LDA, U, LDU, ZERO, WORK, N ) NN = N*N NNP1 = NN + 1 CALL SGEMM( 'T', 'N', M, M, N, ONE, U, LDU, WORK, N, ZERO, $ WORK( NNP1 ), N ) DO 10 J = 1, M JJ = NN + ( J-1 )*N + J WORK( JJ ) = WORK( JJ ) - D( J ) 10 CONTINUE IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN DO 20 J = 2, M JJ1 = NN + ( J-1 )*N + J - 1 JJ2 = NN + ( J-2 )*N + J WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 ) WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 ) 20 CONTINUE END IF WNORM = SLANSY( '1', UPLO, M, WORK( NNP1 ), N, WORK( 1 ) ) * IF( ANORM.GT.WNORM ) THEN RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP ) ELSE IF( ANORM.LT.ONE ) THEN RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP ) ELSE RESULT( 1 ) = MIN( WNORM / ANORM, REAL( M ) ) / ( M*ULP ) END IF END IF * * Do Test 2 * * Compute U'U - I * IF( ITYPE.EQ.1 ) $ CALL SORT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, $ RESULT( 2 ) ) * RETURN * * End of SSYT22 * END |