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SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
$ RWORK, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. * * .. 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 * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER IZAMAX DOUBLE PRECISION DLAMCH EXTERNAL LSAME, IZAMAX, DLAMCH * .. * .. External Subroutines .. EXTERNAL XERBLA, ZDRSCL, ZLACN2, 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 ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * * Multiply by inv(U**H). * 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**H). * 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 |