Annotation of rpl/lapack/lapack/dtbcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
! 2: $ IWORK, INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER DIAG, NORM, UPLO
! 13: INTEGER INFO, KD, LDAB, N
! 14: DOUBLE PRECISION RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IWORK( * )
! 18: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DTBCON estimates the reciprocal of the condition number of a
! 25: * triangular band matrix A, in either the 1-norm or the infinity-norm.
! 26: *
! 27: * The norm of A is computed and an estimate is obtained for
! 28: * norm(inv(A)), then the reciprocal of the condition number is
! 29: * computed as
! 30: * RCOND = 1 / ( norm(A) * norm(inv(A)) ).
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * NORM (input) CHARACTER*1
! 36: * Specifies whether the 1-norm condition number or the
! 37: * infinity-norm condition number is required:
! 38: * = '1' or 'O': 1-norm;
! 39: * = 'I': Infinity-norm.
! 40: *
! 41: * UPLO (input) CHARACTER*1
! 42: * = 'U': A is upper triangular;
! 43: * = 'L': A is lower triangular.
! 44: *
! 45: * DIAG (input) CHARACTER*1
! 46: * = 'N': A is non-unit triangular;
! 47: * = 'U': A is unit triangular.
! 48: *
! 49: * N (input) INTEGER
! 50: * The order of the matrix A. N >= 0.
! 51: *
! 52: * KD (input) INTEGER
! 53: * The number of superdiagonals or subdiagonals of the
! 54: * triangular band matrix A. KD >= 0.
! 55: *
! 56: * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
! 57: * The upper or lower triangular band matrix A, stored in the
! 58: * first kd+1 rows of the array. The j-th column of A is stored
! 59: * in the j-th column of the array AB as follows:
! 60: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 61: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 62: * If DIAG = 'U', the diagonal elements of A are not referenced
! 63: * and are assumed to be 1.
! 64: *
! 65: * LDAB (input) INTEGER
! 66: * The leading dimension of the array AB. LDAB >= KD+1.
! 67: *
! 68: * RCOND (output) DOUBLE PRECISION
! 69: * The reciprocal of the condition number of the matrix A,
! 70: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 71: *
! 72: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 73: *
! 74: * IWORK (workspace) INTEGER array, dimension (N)
! 75: *
! 76: * INFO (output) INTEGER
! 77: * = 0: successful exit
! 78: * < 0: if INFO = -i, the i-th argument had an illegal value
! 79: *
! 80: * =====================================================================
! 81: *
! 82: * .. Parameters ..
! 83: DOUBLE PRECISION ONE, ZERO
! 84: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 85: * ..
! 86: * .. Local Scalars ..
! 87: LOGICAL NOUNIT, ONENRM, UPPER
! 88: CHARACTER NORMIN
! 89: INTEGER IX, KASE, KASE1
! 90: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
! 91: * ..
! 92: * .. Local Arrays ..
! 93: INTEGER ISAVE( 3 )
! 94: * ..
! 95: * .. External Functions ..
! 96: LOGICAL LSAME
! 97: INTEGER IDAMAX
! 98: DOUBLE PRECISION DLAMCH, DLANTB
! 99: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTB
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL DLACN2, DLATBS, DRSCL, XERBLA
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC ABS, DBLE, MAX
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: * Test the input parameters.
! 110: *
! 111: INFO = 0
! 112: UPPER = LSAME( UPLO, 'U' )
! 113: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 114: NOUNIT = LSAME( DIAG, 'N' )
! 115: *
! 116: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 117: INFO = -1
! 118: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 119: INFO = -2
! 120: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 121: INFO = -3
! 122: ELSE IF( N.LT.0 ) THEN
! 123: INFO = -4
! 124: ELSE IF( KD.LT.0 ) THEN
! 125: INFO = -5
! 126: ELSE IF( LDAB.LT.KD+1 ) THEN
! 127: INFO = -7
! 128: END IF
! 129: IF( INFO.NE.0 ) THEN
! 130: CALL XERBLA( 'DTBCON', -INFO )
! 131: RETURN
! 132: END IF
! 133: *
! 134: * Quick return if possible
! 135: *
! 136: IF( N.EQ.0 ) THEN
! 137: RCOND = ONE
! 138: RETURN
! 139: END IF
! 140: *
! 141: RCOND = ZERO
! 142: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
! 143: *
! 144: * Compute the norm of the triangular matrix A.
! 145: *
! 146: ANORM = DLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK )
! 147: *
! 148: * Continue only if ANORM > 0.
! 149: *
! 150: IF( ANORM.GT.ZERO ) THEN
! 151: *
! 152: * Estimate the norm of the inverse of A.
! 153: *
! 154: AINVNM = ZERO
! 155: NORMIN = 'N'
! 156: IF( ONENRM ) THEN
! 157: KASE1 = 1
! 158: ELSE
! 159: KASE1 = 2
! 160: END IF
! 161: KASE = 0
! 162: 10 CONTINUE
! 163: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 164: IF( KASE.NE.0 ) THEN
! 165: IF( KASE.EQ.KASE1 ) THEN
! 166: *
! 167: * Multiply by inv(A).
! 168: *
! 169: CALL DLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
! 170: $ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
! 171: ELSE
! 172: *
! 173: * Multiply by inv(A').
! 174: *
! 175: CALL DLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB,
! 176: $ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
! 177: END IF
! 178: NORMIN = 'Y'
! 179: *
! 180: * Multiply by 1/SCALE if doing so will not cause overflow.
! 181: *
! 182: IF( SCALE.NE.ONE ) THEN
! 183: IX = IDAMAX( N, WORK, 1 )
! 184: XNORM = ABS( WORK( IX ) )
! 185: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
! 186: $ GO TO 20
! 187: CALL DRSCL( N, SCALE, WORK, 1 )
! 188: END IF
! 189: GO TO 10
! 190: END IF
! 191: *
! 192: * Compute the estimate of the reciprocal condition number.
! 193: *
! 194: IF( AINVNM.NE.ZERO )
! 195: $ RCOND = ( ONE / ANORM ) / AINVNM
! 196: END IF
! 197: *
! 198: 20 CONTINUE
! 199: RETURN
! 200: *
! 201: * End of DTBCON
! 202: *
! 203: END
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