SUBROUTINE STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, \$ IWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO INTEGER INFO, KD, LDAB, N REAL RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL AB( LDAB, * ), WORK( * ) * .. * * Purpose * ======= * * STBCON estimates the reciprocal of the condition number of a * triangular band matrix A, in either the 1-norm or the infinity-norm. * * The norm of A is computed and an estimate is obtained for * norm(inv(A)), then 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. * * UPLO (input) CHARACTER*1 * = 'U': A is upper triangular; * = 'L': A is lower triangular. * * DIAG (input) CHARACTER*1 * = 'N': A is non-unit triangular; * = 'U': A is unit triangular. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of superdiagonals or subdiagonals of the * triangular band matrix A. KD >= 0. * * AB (input) REAL array, dimension (LDAB,N) * The upper or lower triangular band matrix A, stored in the * first kd+1 rows of the array. The j-th column of A is stored * in the j-th column of the array AB as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * If DIAG = 'U', the diagonal elements of A are not referenced * and are assumed to be 1. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD+1. * * RCOND (output) REAL * The reciprocal of the condition number of the matrix A, * computed as RCOND = 1/(norm(A) * norm(inv(A))). * * WORK (workspace) REAL 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 .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, ONENRM, UPPER CHARACTER NORMIN INTEGER IX, KASE, KASE1 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX REAL SLAMCH, SLANTB EXTERNAL LSAME, ISAMAX, SLAMCH, SLANTB * .. * .. External Subroutines .. EXTERNAL SLACN2, SLATBS, SRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) NOUNIT = LSAME( DIAG, 'N' ) * IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( KD.LT.0 ) THEN INFO = -5 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STBCON', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN RCOND = ONE RETURN END IF * RCOND = ZERO SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) ) * * Compute the norm of the triangular matrix A. * ANORM = SLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK ) * * Continue only if ANORM > 0. * IF( ANORM.GT.ZERO ) THEN * * Estimate the norm of the inverse of A. * AINVNM = ZERO NORMIN = 'N' IF( ONENRM ) THEN KASE1 = 1 ELSE KASE1 = 2 END IF KASE = 0 10 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(A). * CALL SLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, \$ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) ELSE * * Multiply by inv(A'). * CALL SLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB, \$ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) END IF NORMIN = 'Y' * * Multiply by 1/SCALE if doing so will not cause overflow. * IF( SCALE.NE.ONE ) THEN IX = ISAMAX( N, WORK, 1 ) XNORM = ABS( WORK( IX ) ) IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL SRSCL( 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 / ANORM ) / AINVNM END IF * 20 CONTINUE RETURN * * End of STBCON * END