Mercurial > octave-nkf
diff libcruft/lapack/zpbcon.f @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
author | jwe |
---|---|
date | Fri, 25 Feb 2005 19:55:28 +0000 |
parents | |
children | 68db500cb558 |
line wrap: on
line diff
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/zpbcon.f Fri Feb 25 19:55:28 2005 +0000 @@ -0,0 +1,194 @@ + SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, + $ RWORK, 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 UPLO + INTEGER INFO, KD, LDAB, N + DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. + DOUBLE PRECISION RWORK( * ) + COMPLEX*16 AB( LDAB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZPBCON estimates the reciprocal of the condition number (in the +* 1-norm) of a complex Hermitian positive definite band matrix using +* the Cholesky factorization A = U**H*U or A = L*L**H computed by +* ZPBTRF. +* +* An estimate is obtained for norm(inv(A)), and the reciprocal of the +* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangular factor stored in AB; +* = 'L': Lower triangular factor stored in AB. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* KD (input) INTEGER +* The number of superdiagonals of the matrix A if UPLO = 'U', +* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. +* +* AB (input) COMPLEX*16 array, dimension (LDAB,N) +* The triangular factor U or L from the Cholesky factorization +* A = U**H*U or A = L*L**H of the band matrix A, stored in the +* first KD+1 rows of the array. The j-th column of U or L is +* stored in the j-th column of the array AB as follows: +* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; +* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= KD+1. +* +* ANORM (input) DOUBLE PRECISION +* The 1-norm (or infinity-norm) of the Hermitian band matrix A. +* +* RCOND (output) DOUBLE PRECISION +* The reciprocal of the condition number of the matrix A, +* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an +* estimate of the 1-norm of inv(A) computed in this routine. +* +* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* +* RWORK (workspace) DOUBLE PRECISION 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 UPPER + CHARACTER NORMIN + INTEGER IX, KASE + DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM + COMPLEX*16 ZDUM +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER IZAMAX + DOUBLE PRECISION DLAMCH + EXTERNAL LSAME, IZAMAX, DLAMCH +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZDRSCL, ZLACON, ZLATBS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DIMAG +* .. +* .. Statement Functions .. + DOUBLE PRECISION CABS1 +* .. +* .. Statement Function definitions .. + CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( KD.LT.0 ) THEN + INFO = -3 + ELSE IF( LDAB.LT.KD+1 ) THEN + INFO = -5 + ELSE IF( ANORM.LT.ZERO ) THEN + INFO = -6 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZPBCON', -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 1-norm of the inverse. +* + KASE = 0 + NORMIN = 'N' + 10 CONTINUE + CALL ZLACON( N, WORK( N+1 ), WORK, AINVNM, KASE ) + IF( KASE.NE.0 ) THEN + IF( UPPER ) THEN +* +* Multiply by inv(U'). +* + CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit', + $ NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK, + $ INFO ) + NORMIN = 'Y' +* +* Multiply by inv(U). +* + CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, + $ KD, AB, LDAB, WORK, SCALEU, RWORK, INFO ) + ELSE +* +* Multiply by inv(L). +* + CALL ZLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, + $ KD, AB, LDAB, WORK, SCALEL, RWORK, INFO ) + NORMIN = 'Y' +* +* Multiply by inv(L'). +* + CALL ZLATBS( 'Lower', 'Conjugate transpose', 'Non-unit', + $ NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK, + $ INFO ) + END IF +* +* Multiply by 1/SCALE if doing so will not cause overflow. +* + SCALE = SCALEL*SCALEU + IF( SCALE.NE.ONE ) THEN + IX = IZAMAX( N, WORK, 1 ) + IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) + $ GO TO 20 + CALL ZDRSCL( 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 +* + 20 CONTINUE +* + RETURN +* +* End of ZPBCON +* + END