Mercurial > octave-nkf
diff libcruft/lapack/dgbcon.f @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
author | jwe |
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date | Fri, 25 Feb 2005 19:55:28 +0000 |
parents | |
children | 68db500cb558 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/dgbcon.f Fri Feb 25 19:55:28 2005 +0000 @@ -0,0 +1,222 @@ + SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, + $ WORK, IWORK, INFO ) +* +* -- LAPACK routine (version 3.0) -- +* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., +* Courant Institute, Argonne National Lab, and Rice University +* September 30, 1994 +* +* .. Scalar Arguments .. + CHARACTER NORM + INTEGER INFO, KL, KU, LDAB, N + DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. + INTEGER IPIV( * ), IWORK( * ) + DOUBLE PRECISION AB( LDAB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* DGBCON estimates the reciprocal of the condition number of a real +* general band matrix A, in either the 1-norm or the infinity-norm, +* using the LU factorization computed by DGBTRF. +* +* An estimate is obtained for norm(inv(A)), and the reciprocal of the +* condition number is computed as +* RCOND = 1 / ( norm(A) * norm(inv(A)) ). +* +* Arguments +* ========= +* +* NORM (input) CHARACTER*1 +* Specifies whether the 1-norm condition number or the +* infinity-norm condition number is required: +* = '1' or 'O': 1-norm; +* = 'I': Infinity-norm. +* +* N (input) INTEGER +* 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) DOUBLE PRECISION array, dimension (LDAB,N) +* Details of the LU factorization of the band matrix A, as +* computed by DGBTRF. 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. +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. +* +* IPIV (input) INTEGER array, dimension (N) +* The pivot indices; for 1 <= i <= N, row i of the matrix was +* interchanged with row IPIV(i). +* +* ANORM (input) DOUBLE PRECISION +* If NORM = '1' or 'O', the 1-norm of the original matrix A. +* If NORM = 'I', the infinity-norm of the original matrix A. +* +* RCOND (output) DOUBLE PRECISION +* The reciprocal of the condition number of the matrix A, +* computed as RCOND = 1/(norm(A) * norm(inv(A))). +* +* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) +* +* IWORK (workspace) INTEGER array, dimension (N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LNOTI, ONENRM + CHARACTER NORMIN + INTEGER IX, J, JP, KASE, KASE1, KD, LM + DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER IDAMAX + DOUBLE PRECISION DDOT, DLAMCH + EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DLACON, DLATBS, DRSCL, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) + IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( KL.LT.0 ) THEN + INFO = -3 + ELSE IF( KU.LT.0 ) THEN + INFO = -4 + ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN + INFO = -6 + ELSE IF( ANORM.LT.ZERO ) THEN + INFO = -8 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGBCON', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + RCOND = ZERO + IF( N.EQ.0 ) THEN + RCOND = ONE + RETURN + ELSE IF( ANORM.EQ.ZERO ) THEN + RETURN + END IF +* + SMLNUM = DLAMCH( 'Safe minimum' ) +* +* Estimate the norm of inv(A). +* + AINVNM = ZERO + NORMIN = 'N' + IF( ONENRM ) THEN + KASE1 = 1 + ELSE + KASE1 = 2 + END IF + KD = KL + KU + 1 + LNOTI = KL.GT.0 + KASE = 0 + 10 CONTINUE + CALL DLACON( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE ) + IF( KASE.NE.0 ) THEN + IF( KASE.EQ.KASE1 ) THEN +* +* Multiply by inv(L). +* + IF( LNOTI ) THEN + DO 20 J = 1, N - 1 + LM = MIN( KL, N-J ) + JP = IPIV( J ) + T = WORK( JP ) + IF( JP.NE.J ) THEN + WORK( JP ) = WORK( J ) + WORK( J ) = T + END IF + CALL DAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 ) + 20 CONTINUE + END IF +* +* Multiply by inv(U). +* + CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, + $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), + $ INFO ) + ELSE +* +* Multiply by inv(U'). +* + CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, + $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), + $ INFO ) +* +* Multiply by inv(L'). +* + IF( LNOTI ) THEN + DO 30 J = N - 1, 1, -1 + LM = MIN( KL, N-J ) + WORK( J ) = WORK( J ) - DDOT( LM, AB( KD+1, J ), 1, + $ WORK( J+1 ), 1 ) + JP = IPIV( J ) + IF( JP.NE.J ) THEN + T = WORK( JP ) + WORK( JP ) = WORK( J ) + WORK( J ) = T + END IF + 30 CONTINUE + END IF + END IF +* +* Divide X by 1/SCALE if doing so will not cause overflow. +* + NORMIN = 'Y' + IF( SCALE.NE.ONE ) THEN + IX = IDAMAX( N, WORK, 1 ) + IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) + $ GO TO 40 + CALL DRSCL( N, SCALE, WORK, 1 ) + END IF + GO TO 10 + END IF +* +* Compute the estimate of the reciprocal condition number. +* + IF( AINVNM.NE.ZERO ) + $ RCOND = ( ONE / AINVNM ) / ANORM +* + 40 CONTINUE + RETURN +* +* End of DGBCON +* + END