210 lines
6.1 KiB
FortranFixed
210 lines
6.1 KiB
FortranFixed
SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
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$ RWORK, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, NORM, UPLO
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INTEGER INFO, KD, LDAB, N
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DOUBLE PRECISION RCOND
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 AB( LDAB, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZTBCON estimates the reciprocal of the condition number of a
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* triangular band matrix A, in either the 1-norm or the infinity-norm.
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*
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* The norm of A is computed and an estimate is obtained for
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* norm(inv(A)), then the reciprocal of the condition number is
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* computed as
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* RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies whether the 1-norm condition number or the
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* infinity-norm condition number is required:
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* = '1' or 'O': 1-norm;
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* = 'I': Infinity-norm.
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*
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* UPLO (input) CHARACTER*1
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* = 'U': A is upper triangular;
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* = 'L': A is lower triangular.
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*
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* DIAG (input) CHARACTER*1
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* = 'N': A is non-unit triangular;
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* = 'U': A is unit triangular.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* KD (input) INTEGER
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* The number of superdiagonals or subdiagonals of the
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* triangular band matrix A. KD >= 0.
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*
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* AB (input) COMPLEX*16 array, dimension (LDAB,N)
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* The upper or lower triangular band matrix A, stored in the
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* first kd+1 rows of the array. The j-th column of A is stored
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* in the j-th column of the array AB as follows:
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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* If DIAG = 'U', the diagonal elements of A are not referenced
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* and are assumed to be 1.
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= KD+1.
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*
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* RCOND (output) DOUBLE PRECISION
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* The reciprocal of the condition number of the matrix A,
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* computed as RCOND = 1/(norm(A) * norm(inv(A))).
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*
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* WORK (workspace) COMPLEX*16 array, dimension (2*N)
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*
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* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT, ONENRM, UPPER
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CHARACTER NORMIN
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INTEGER IX, KASE, KASE1
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DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
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COMPLEX*16 ZDUM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IZAMAX
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DOUBLE PRECISION DLAMCH, ZLANTB
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EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DIMAG, MAX
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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NOUNIT = LSAME( DIAG, 'N' )
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*
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( KD.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTBCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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END IF
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*
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RCOND = ZERO
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SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) )
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*
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* Compute the 1-norm of the triangular matrix A or A'.
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*
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ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK )
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*
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* Continue only if ANORM > 0.
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*
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IF( ANORM.GT.ZERO ) THEN
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*
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* Estimate the 1-norm of the inverse of A.
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*
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AINVNM = ZERO
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NORMIN = 'N'
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KASE = 0
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10 CONTINUE
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CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(A).
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*
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CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
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$ AB, LDAB, WORK, SCALE, RWORK, INFO )
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ELSE
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*
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* Multiply by inv(A').
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*
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CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
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$ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO )
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END IF
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NORMIN = 'Y'
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*
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* Multiply by 1/SCALE if doing so will not cause overflow.
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*
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IF( SCALE.NE.ONE ) THEN
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IX = IZAMAX( N, WORK, 1 )
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XNORM = CABS1( WORK( IX ) )
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IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 20
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CALL ZDRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / ANORM ) / AINVNM
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END IF
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*
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20 CONTINUE
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RETURN
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*
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* End of ZTBCON
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*
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END
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