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DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
$ CMODE, C, INFO, WORK, $ IWORK ) * * -- LAPACK routine (version 3.2.2) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- June 2010 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. CHARACTER UPLO INTEGER N, LDA, LDAF, INFO, CMODE DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), $ C( * ) * .. * .. Array Arguments .. INTEGER IWORK( * ) * .. * * Purpose * ======= * * DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * The Skeel condition number cond(A) = norminf( |inv(A)||A| ) * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the N-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) * The triangular factor U or L from the Cholesky factorization * A = U**T*U or A = L*L**T, as computed by DPOTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * CMODE (input) INTEGER * Determines op2(C) in the formula op(A) * op2(C) as follows: * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * * C (input) DOUBLE PRECISION array, dimension (N) * The vector C in the formula op(A) * op2(C). * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) DOUBLE PRECISION array, dimension (3*N). * Workspace. * * IWORK (input) INTEGER array, dimension (N). * Workspace. * * ===================================================================== * * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, TMP LOGICAL UP * .. * .. Array Arguments .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX EXTERNAL LSAME, IDAMAX * .. * .. External Subroutines .. EXTERNAL DLACN2, DPOTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * DLA_PORCOND = 0.0D+0 * INFO = 0 IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLA_PORCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN DLA_PORCOND = 1.0D+0 RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * IF ( UP ) THEN DO I = 1, N TMP = 0.0D+0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( J ,I ) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ELSE DO I = 1, N TMP = 0.0D+0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ENDIF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0D+0 KASE = 0 10 CONTINUE CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.2 ) THEN * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO IF (UP) THEN CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) ELSE CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) ENDIF * * Multiply by inv(C). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF ELSE * * Multiply by inv(C**T). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF IF ( UP ) THEN CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) ELSE CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) ENDIF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM .NE. 0.0D+0 ) $ DLA_PORCOND = ( 1.0D+0 / AINVNM ) * RETURN * END |