Annotation of rpl/lapack/lapack/dgbcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
! 2: $ WORK, 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 NORM
! 13: INTEGER INFO, KL, KU, LDAB, N
! 14: DOUBLE PRECISION ANORM, RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IPIV( * ), IWORK( * )
! 18: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DGBCON estimates the reciprocal of the condition number of a real
! 25: * general band matrix A, in either the 1-norm or the infinity-norm,
! 26: * using the LU factorization computed by DGBTRF.
! 27: *
! 28: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 29: * condition number is 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: * N (input) INTEGER
! 42: * The order of the matrix A. N >= 0.
! 43: *
! 44: * KL (input) INTEGER
! 45: * The number of subdiagonals within the band of A. KL >= 0.
! 46: *
! 47: * KU (input) INTEGER
! 48: * The number of superdiagonals within the band of A. KU >= 0.
! 49: *
! 50: * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
! 51: * Details of the LU factorization of the band matrix A, as
! 52: * computed by DGBTRF. U is stored as an upper triangular band
! 53: * matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
! 54: * the multipliers used during the factorization are stored in
! 55: * rows KL+KU+2 to 2*KL+KU+1.
! 56: *
! 57: * LDAB (input) INTEGER
! 58: * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
! 59: *
! 60: * IPIV (input) INTEGER array, dimension (N)
! 61: * The pivot indices; for 1 <= i <= N, row i of the matrix was
! 62: * interchanged with row IPIV(i).
! 63: *
! 64: * ANORM (input) DOUBLE PRECISION
! 65: * If NORM = '1' or 'O', the 1-norm of the original matrix A.
! 66: * If NORM = 'I', the infinity-norm of the original matrix A.
! 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 LNOTI, ONENRM
! 88: CHARACTER NORMIN
! 89: INTEGER IX, J, JP, KASE, KASE1, KD, LM
! 90: DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T
! 91: * ..
! 92: * .. Local Arrays ..
! 93: INTEGER ISAVE( 3 )
! 94: * ..
! 95: * .. External Functions ..
! 96: LOGICAL LSAME
! 97: INTEGER IDAMAX
! 98: DOUBLE PRECISION DDOT, DLAMCH
! 99: EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL DAXPY, DLACN2, DLATBS, DRSCL, XERBLA
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC ABS, MIN
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: * Test the input parameters.
! 110: *
! 111: INFO = 0
! 112: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 113: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 114: INFO = -1
! 115: ELSE IF( N.LT.0 ) THEN
! 116: INFO = -2
! 117: ELSE IF( KL.LT.0 ) THEN
! 118: INFO = -3
! 119: ELSE IF( KU.LT.0 ) THEN
! 120: INFO = -4
! 121: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
! 122: INFO = -6
! 123: ELSE IF( ANORM.LT.ZERO ) THEN
! 124: INFO = -8
! 125: END IF
! 126: IF( INFO.NE.0 ) THEN
! 127: CALL XERBLA( 'DGBCON', -INFO )
! 128: RETURN
! 129: END IF
! 130: *
! 131: * Quick return if possible
! 132: *
! 133: RCOND = ZERO
! 134: IF( N.EQ.0 ) THEN
! 135: RCOND = ONE
! 136: RETURN
! 137: ELSE IF( ANORM.EQ.ZERO ) THEN
! 138: RETURN
! 139: END IF
! 140: *
! 141: SMLNUM = DLAMCH( 'Safe minimum' )
! 142: *
! 143: * Estimate the norm of inv(A).
! 144: *
! 145: AINVNM = ZERO
! 146: NORMIN = 'N'
! 147: IF( ONENRM ) THEN
! 148: KASE1 = 1
! 149: ELSE
! 150: KASE1 = 2
! 151: END IF
! 152: KD = KL + KU + 1
! 153: LNOTI = KL.GT.0
! 154: KASE = 0
! 155: 10 CONTINUE
! 156: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 157: IF( KASE.NE.0 ) THEN
! 158: IF( KASE.EQ.KASE1 ) THEN
! 159: *
! 160: * Multiply by inv(L).
! 161: *
! 162: IF( LNOTI ) THEN
! 163: DO 20 J = 1, N - 1
! 164: LM = MIN( KL, N-J )
! 165: JP = IPIV( J )
! 166: T = WORK( JP )
! 167: IF( JP.NE.J ) THEN
! 168: WORK( JP ) = WORK( J )
! 169: WORK( J ) = T
! 170: END IF
! 171: CALL DAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
! 172: 20 CONTINUE
! 173: END IF
! 174: *
! 175: * Multiply by inv(U).
! 176: *
! 177: CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
! 178: $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
! 179: $ INFO )
! 180: ELSE
! 181: *
! 182: * Multiply by inv(U').
! 183: *
! 184: CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
! 185: $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
! 186: $ INFO )
! 187: *
! 188: * Multiply by inv(L').
! 189: *
! 190: IF( LNOTI ) THEN
! 191: DO 30 J = N - 1, 1, -1
! 192: LM = MIN( KL, N-J )
! 193: WORK( J ) = WORK( J ) - DDOT( LM, AB( KD+1, J ), 1,
! 194: $ WORK( J+1 ), 1 )
! 195: JP = IPIV( J )
! 196: IF( JP.NE.J ) THEN
! 197: T = WORK( JP )
! 198: WORK( JP ) = WORK( J )
! 199: WORK( J ) = T
! 200: END IF
! 201: 30 CONTINUE
! 202: END IF
! 203: END IF
! 204: *
! 205: * Divide X by 1/SCALE if doing so will not cause overflow.
! 206: *
! 207: NORMIN = 'Y'
! 208: IF( SCALE.NE.ONE ) THEN
! 209: IX = IDAMAX( N, WORK, 1 )
! 210: IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
! 211: $ GO TO 40
! 212: CALL DRSCL( N, SCALE, WORK, 1 )
! 213: END IF
! 214: GO TO 10
! 215: END IF
! 216: *
! 217: * Compute the estimate of the reciprocal condition number.
! 218: *
! 219: IF( AINVNM.NE.ZERO )
! 220: $ RCOND = ( ONE / AINVNM ) / ANORM
! 221: *
! 222: 40 CONTINUE
! 223: RETURN
! 224: *
! 225: * End of DGBCON
! 226: *
! 227: END
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