Annotation of rpl/lapack/lapack/zgbcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
! 2: $ WORK, RWORK, 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 ZLACN2 in place of ZLACON, 10 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( * )
! 18: DOUBLE PRECISION RWORK( * )
! 19: COMPLEX*16 AB( LDAB, * ), WORK( * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * ZGBCON estimates the reciprocal of the condition number of a complex
! 26: * general band matrix A, in either the 1-norm or the infinity-norm,
! 27: * using the LU factorization computed by ZGBTRF.
! 28: *
! 29: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 30: * condition number is computed as
! 31: * RCOND = 1 / ( norm(A) * norm(inv(A)) ).
! 32: *
! 33: * Arguments
! 34: * =========
! 35: *
! 36: * NORM (input) CHARACTER*1
! 37: * Specifies whether the 1-norm condition number or the
! 38: * infinity-norm condition number is required:
! 39: * = '1' or 'O': 1-norm;
! 40: * = 'I': Infinity-norm.
! 41: *
! 42: * N (input) INTEGER
! 43: * The order of the matrix A. N >= 0.
! 44: *
! 45: * KL (input) INTEGER
! 46: * The number of subdiagonals within the band of A. KL >= 0.
! 47: *
! 48: * KU (input) INTEGER
! 49: * The number of superdiagonals within the band of A. KU >= 0.
! 50: *
! 51: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 52: * Details of the LU factorization of the band matrix A, as
! 53: * computed by ZGBTRF. U is stored as an upper triangular band
! 54: * matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
! 55: * the multipliers used during the factorization are stored in
! 56: * rows KL+KU+2 to 2*KL+KU+1.
! 57: *
! 58: * LDAB (input) INTEGER
! 59: * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
! 60: *
! 61: * IPIV (input) INTEGER array, dimension (N)
! 62: * The pivot indices; for 1 <= i <= N, row i of the matrix was
! 63: * interchanged with row IPIV(i).
! 64: *
! 65: * ANORM (input) DOUBLE PRECISION
! 66: * If NORM = '1' or 'O', the 1-norm of the original matrix A.
! 67: * If NORM = 'I', the infinity-norm of the original matrix A.
! 68: *
! 69: * RCOND (output) DOUBLE PRECISION
! 70: * The reciprocal of the condition number of the matrix A,
! 71: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 72: *
! 73: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 74: *
! 75: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
! 76: *
! 77: * INFO (output) INTEGER
! 78: * = 0: successful exit
! 79: * < 0: if INFO = -i, the i-th argument had an illegal value
! 80: *
! 81: * =====================================================================
! 82: *
! 83: * .. Parameters ..
! 84: DOUBLE PRECISION ONE, ZERO
! 85: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 86: * ..
! 87: * .. Local Scalars ..
! 88: LOGICAL LNOTI, ONENRM
! 89: CHARACTER NORMIN
! 90: INTEGER IX, J, JP, KASE, KASE1, KD, LM
! 91: DOUBLE PRECISION AINVNM, SCALE, SMLNUM
! 92: COMPLEX*16 T, ZDUM
! 93: * ..
! 94: * .. Local Arrays ..
! 95: INTEGER ISAVE( 3 )
! 96: * ..
! 97: * .. External Functions ..
! 98: LOGICAL LSAME
! 99: INTEGER IZAMAX
! 100: DOUBLE PRECISION DLAMCH
! 101: COMPLEX*16 ZDOTC
! 102: EXTERNAL LSAME, IZAMAX, DLAMCH, ZDOTC
! 103: * ..
! 104: * .. External Subroutines ..
! 105: EXTERNAL XERBLA, ZAXPY, ZDRSCL, ZLACN2, ZLATBS
! 106: * ..
! 107: * .. Intrinsic Functions ..
! 108: INTRINSIC ABS, DBLE, DIMAG, MIN
! 109: * ..
! 110: * .. Statement Functions ..
! 111: DOUBLE PRECISION CABS1
! 112: * ..
! 113: * .. Statement Function definitions ..
! 114: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 115: * ..
! 116: * .. Executable Statements ..
! 117: *
! 118: * Test the input parameters.
! 119: *
! 120: INFO = 0
! 121: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 122: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 123: INFO = -1
! 124: ELSE IF( N.LT.0 ) THEN
! 125: INFO = -2
! 126: ELSE IF( KL.LT.0 ) THEN
! 127: INFO = -3
! 128: ELSE IF( KU.LT.0 ) THEN
! 129: INFO = -4
! 130: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
! 131: INFO = -6
! 132: ELSE IF( ANORM.LT.ZERO ) THEN
! 133: INFO = -8
! 134: END IF
! 135: IF( INFO.NE.0 ) THEN
! 136: CALL XERBLA( 'ZGBCON', -INFO )
! 137: RETURN
! 138: END IF
! 139: *
! 140: * Quick return if possible
! 141: *
! 142: RCOND = ZERO
! 143: IF( N.EQ.0 ) THEN
! 144: RCOND = ONE
! 145: RETURN
! 146: ELSE IF( ANORM.EQ.ZERO ) THEN
! 147: RETURN
! 148: END IF
! 149: *
! 150: SMLNUM = DLAMCH( 'Safe minimum' )
! 151: *
! 152: * Estimate the norm of inv(A).
! 153: *
! 154: AINVNM = ZERO
! 155: NORMIN = 'N'
! 156: IF( ONENRM ) THEN
! 157: KASE1 = 1
! 158: ELSE
! 159: KASE1 = 2
! 160: END IF
! 161: KD = KL + KU + 1
! 162: LNOTI = KL.GT.0
! 163: KASE = 0
! 164: 10 CONTINUE
! 165: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 166: IF( KASE.NE.0 ) THEN
! 167: IF( KASE.EQ.KASE1 ) THEN
! 168: *
! 169: * Multiply by inv(L).
! 170: *
! 171: IF( LNOTI ) THEN
! 172: DO 20 J = 1, N - 1
! 173: LM = MIN( KL, N-J )
! 174: JP = IPIV( J )
! 175: T = WORK( JP )
! 176: IF( JP.NE.J ) THEN
! 177: WORK( JP ) = WORK( J )
! 178: WORK( J ) = T
! 179: END IF
! 180: CALL ZAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
! 181: 20 CONTINUE
! 182: END IF
! 183: *
! 184: * Multiply by inv(U).
! 185: *
! 186: CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
! 187: $ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
! 188: ELSE
! 189: *
! 190: * Multiply by inv(U').
! 191: *
! 192: CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
! 193: $ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
! 194: $ INFO )
! 195: *
! 196: * Multiply by inv(L').
! 197: *
! 198: IF( LNOTI ) THEN
! 199: DO 30 J = N - 1, 1, -1
! 200: LM = MIN( KL, N-J )
! 201: WORK( J ) = WORK( J ) - ZDOTC( LM, AB( KD+1, J ), 1,
! 202: $ WORK( J+1 ), 1 )
! 203: JP = IPIV( J )
! 204: IF( JP.NE.J ) THEN
! 205: T = WORK( JP )
! 206: WORK( JP ) = WORK( J )
! 207: WORK( J ) = T
! 208: END IF
! 209: 30 CONTINUE
! 210: END IF
! 211: END IF
! 212: *
! 213: * Divide X by 1/SCALE if doing so will not cause overflow.
! 214: *
! 215: NORMIN = 'Y'
! 216: IF( SCALE.NE.ONE ) THEN
! 217: IX = IZAMAX( N, WORK, 1 )
! 218: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
! 219: $ GO TO 40
! 220: CALL ZDRSCL( N, SCALE, WORK, 1 )
! 221: END IF
! 222: GO TO 10
! 223: END IF
! 224: *
! 225: * Compute the estimate of the reciprocal condition number.
! 226: *
! 227: IF( AINVNM.NE.ZERO )
! 228: $ RCOND = ( ONE / AINVNM ) / ANORM
! 229: *
! 230: 40 CONTINUE
! 231: RETURN
! 232: *
! 233: * End of ZGBCON
! 234: *
! 235: END
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