Annotation of rpl/lapack/lapack/zla_gbrcond_x.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
! 2: $ LDAB, AFB, LDAFB, IPIV,
! 3: $ X, INFO, WORK, RWORK )
! 4: *
! 5: * -- LAPACK routine (version 3.2.1) --
! 6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 7: * -- Jason Riedy of Univ. of California Berkeley. --
! 8: * -- April 2009 --
! 9: *
! 10: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 11: * -- Univ. of California Berkeley and NAG Ltd. --
! 12: *
! 13: IMPLICIT NONE
! 14: * ..
! 15: * .. Scalar Arguments ..
! 16: CHARACTER TRANS
! 17: INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
! 18: * ..
! 19: * .. Array Arguments ..
! 20: INTEGER IPIV( * )
! 21: COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
! 22: $ X( * )
! 23: DOUBLE PRECISION RWORK( * )
! 24: *
! 25: *
! 26: * Purpose
! 27: * =======
! 28: *
! 29: * ZLA_GBRCOND_X Computes the infinity norm condition number of
! 30: * op(A) * diag(X) where X is a COMPLEX*16 vector.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * TRANS (input) CHARACTER*1
! 36: * Specifies the form of the system of equations:
! 37: * = 'N': A * X = B (No transpose)
! 38: * = 'T': A**T * X = B (Transpose)
! 39: * = 'C': A**H * X = B (Conjugate Transpose = Transpose)
! 40: *
! 41: * N (input) INTEGER
! 42: * The number of linear equations, i.e., the order of the
! 43: * 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: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 53: * The j-th column of A is stored in the j-th column of the
! 54: * array AB as follows:
! 55: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 56: *
! 57: * LDAB (input) INTEGER
! 58: * The leading dimension of the array AB. LDAB >= KL+KU+1.
! 59: *
! 60: * AFB (input) COMPLEX*16 array, dimension (LDAFB,N)
! 61: * Details of the LU factorization of the band matrix A, as
! 62: * computed by ZGBTRF. U is stored as an upper triangular
! 63: * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 64: * and the multipliers used during the factorization are stored
! 65: * in rows KL+KU+2 to 2*KL+KU+1.
! 66: *
! 67: * LDAFB (input) INTEGER
! 68: * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 69: *
! 70: * IPIV (input) INTEGER array, dimension (N)
! 71: * The pivot indices from the factorization A = P*L*U
! 72: * as computed by ZGBTRF; row i of the matrix was interchanged
! 73: * with row IPIV(i).
! 74: *
! 75: * X (input) COMPLEX*16 array, dimension (N)
! 76: * The vector X in the formula op(A) * diag(X).
! 77: *
! 78: * INFO (output) INTEGER
! 79: * = 0: Successful exit.
! 80: * i > 0: The ith argument is invalid.
! 81: *
! 82: * WORK (input) COMPLEX*16 array, dimension (2*N).
! 83: * Workspace.
! 84: *
! 85: * RWORK (input) DOUBLE PRECISION array, dimension (N).
! 86: * Workspace.
! 87: *
! 88: * =====================================================================
! 89: *
! 90: * .. Local Scalars ..
! 91: LOGICAL NOTRANS
! 92: INTEGER KASE, I, J
! 93: DOUBLE PRECISION AINVNM, ANORM, TMP
! 94: COMPLEX*16 ZDUM
! 95: * ..
! 96: * .. Local Arrays ..
! 97: INTEGER ISAVE( 3 )
! 98: * ..
! 99: * .. External Functions ..
! 100: LOGICAL LSAME
! 101: EXTERNAL LSAME
! 102: * ..
! 103: * .. External Subroutines ..
! 104: EXTERNAL ZLACN2, ZGBTRS, XERBLA
! 105: * ..
! 106: * .. Intrinsic Functions ..
! 107: INTRINSIC ABS, MAX
! 108: * ..
! 109: * .. Statement Functions ..
! 110: DOUBLE PRECISION CABS1
! 111: * ..
! 112: * .. Statement Function Definitions ..
! 113: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 114: * ..
! 115: * .. Executable Statements ..
! 116: *
! 117: ZLA_GBRCOND_X = 0.0D+0
! 118: *
! 119: INFO = 0
! 120: NOTRANS = LSAME( TRANS, 'N' )
! 121: IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT.
! 122: $ LSAME( TRANS, 'C' ) ) THEN
! 123: INFO = -1
! 124: ELSE IF( N.LT.0 ) THEN
! 125: INFO = -2
! 126: ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
! 127: INFO = -3
! 128: ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
! 129: INFO = -4
! 130: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
! 131: INFO = -6
! 132: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
! 133: INFO = -8
! 134: END IF
! 135: IF( INFO.NE.0 ) THEN
! 136: CALL XERBLA( 'ZLA_GBRCOND_X', -INFO )
! 137: RETURN
! 138: END IF
! 139: *
! 140: * Compute norm of op(A)*op2(C).
! 141: *
! 142: KD = KU + 1
! 143: KE = KL + 1
! 144: ANORM = 0.0D+0
! 145: IF ( NOTRANS ) THEN
! 146: DO I = 1, N
! 147: TMP = 0.0D+0
! 148: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 149: TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) )
! 150: END DO
! 151: RWORK( I ) = TMP
! 152: ANORM = MAX( ANORM, TMP )
! 153: END DO
! 154: ELSE
! 155: DO I = 1, N
! 156: TMP = 0.0D+0
! 157: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 158: TMP = TMP + CABS1( AB( KE-I+J, I ) * X( J ) )
! 159: END DO
! 160: RWORK( I ) = TMP
! 161: ANORM = MAX( ANORM, TMP )
! 162: END DO
! 163: END IF
! 164: *
! 165: * Quick return if possible.
! 166: *
! 167: IF( N.EQ.0 ) THEN
! 168: ZLA_GBRCOND_X = 1.0D+0
! 169: RETURN
! 170: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
! 171: RETURN
! 172: END IF
! 173: *
! 174: * Estimate the norm of inv(op(A)).
! 175: *
! 176: AINVNM = 0.0D+0
! 177: *
! 178: KASE = 0
! 179: 10 CONTINUE
! 180: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 181: IF( KASE.NE.0 ) THEN
! 182: IF( KASE.EQ.2 ) THEN
! 183: *
! 184: * Multiply by R.
! 185: *
! 186: DO I = 1, N
! 187: WORK( I ) = WORK( I ) * RWORK( I )
! 188: END DO
! 189: *
! 190: IF ( NOTRANS ) THEN
! 191: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
! 192: $ IPIV, WORK, N, INFO )
! 193: ELSE
! 194: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
! 195: $ LDAFB, IPIV, WORK, N, INFO )
! 196: ENDIF
! 197: *
! 198: * Multiply by inv(X).
! 199: *
! 200: DO I = 1, N
! 201: WORK( I ) = WORK( I ) / X( I )
! 202: END DO
! 203: ELSE
! 204: *
! 205: * Multiply by inv(X').
! 206: *
! 207: DO I = 1, N
! 208: WORK( I ) = WORK( I ) / X( I )
! 209: END DO
! 210: *
! 211: IF ( NOTRANS ) THEN
! 212: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
! 213: $ LDAFB, IPIV, WORK, N, INFO )
! 214: ELSE
! 215: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
! 216: $ IPIV, WORK, N, INFO )
! 217: END IF
! 218: *
! 219: * Multiply by R.
! 220: *
! 221: DO I = 1, N
! 222: WORK( I ) = WORK( I ) * RWORK( I )
! 223: END DO
! 224: END IF
! 225: GO TO 10
! 226: END IF
! 227: *
! 228: * Compute the estimate of the reciprocal condition number.
! 229: *
! 230: IF( AINVNM .NE. 0.0D+0 )
! 231: $ ZLA_GBRCOND_X = 1.0D+0 / AINVNM
! 232: *
! 233: RETURN
! 234: *
! 235: END
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