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REAL FUNCTION SLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB,
$ IPIV, 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 TRANS INTEGER N, LDAB, LDAFB, INFO, KL, KU, CMODE * .. * .. Array Arguments .. INTEGER IWORK( * ), IPIV( * ) REAL AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ C( * ) * .. * * Purpose * ======= * * SLA_GBRCOND 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 * ========== * * TRANS (input) CHARACTER*1 * Specifies the form of the system of equations: * = 'N': A * X = B (No transpose) * = 'T': A**T * X = B (Transpose) * = 'C': A**H * X = B (Conjugate Transpose = Transpose) * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * AB (input) REAL array, dimension (LDAB,N) * On entry, the matrix A in band storage, in rows 1 to KL+KU+1. * The j-th column of A is stored in the j-th column of the * array AB as follows: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KL+KU+1. * * AFB (input) REAL array, dimension (LDAFB,N) * Details of the LU factorization of the band matrix A, as * computed by SGBTRF. U is stored as an upper triangular * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, * and the multipliers used during the factorization are stored * in rows KL+KU+2 to 2*KL+KU+1. * * LDAFB (input) INTEGER * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from the factorization A = P*L*U * as computed by SGBTRF; row i of the matrix was interchanged * with row IPIV(i). * * 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) REAL 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) REAL array, dimension (5*N). * Workspace. * * IWORK (input) INTEGER array, dimension (N). * Workspace. * * ===================================================================== * * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J, KD, KE REAL AINVNM, TMP * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SLACN2, SGBTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * SLA_GBRCOND = 0.0 * INFO = 0 NOTRANS = LSAME( TRANS, 'N' ) IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') $ .AND. .NOT. LSAME(TRANS, 'C') ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN INFO = -3 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN INFO = -4 ELSE IF( LDAB.LT.KL+KU+1 ) THEN INFO = -6 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLA_GBRCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN SLA_GBRCOND = 1.0 RETURN END IF * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * KD = KU + 1 KE = KL + 1 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KD+I-J, J ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KD+I-J, J ) ) END DO ELSE DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KD+I-J, J ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ELSE DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KE-I+J, I ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KE-I+J, I ) ) END DO ELSE DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + ABS( AB( KE-I+J, I ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO END IF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0 KASE = 0 10 CONTINUE CALL SLACN2( 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 ( NOTRANS ) THEN CALL SGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, $ IPIV, WORK, N, INFO ) ELSE CALL SGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV, $ WORK, N, INFO ) END IF * * 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 ( NOTRANS ) THEN CALL SGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV, $ WORK, N, INFO ) ELSE CALL SGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, $ IPIV, WORK, N, INFO ) END IF * * 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. 0.0 ) $ SLA_GBRCOND = ( 1.0 / AINVNM ) * RETURN * END |