Annotation of rpl/lapack/lapack/dla_gbrcond.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB,
! 2: $ AFB, LDAFB, IPIV, CMODE, C,
! 3: $ INFO, WORK, IWORK )
! 4: *
! 5: * -- LAPACK routine (version 3.2.2) --
! 6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 7: * -- Jason Riedy of Univ. of California Berkeley. --
! 8: * -- June 2010 --
! 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, LDAB, LDAFB, INFO, KL, KU, CMODE
! 18: * ..
! 19: * .. Array Arguments ..
! 20: INTEGER IWORK( * ), IPIV( * )
! 21: DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
! 22: $ C( * )
! 23: * ..
! 24: *
! 25: * Purpose
! 26: * =======
! 27: *
! 28: * DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
! 29: * where op2 is determined by CMODE as follows
! 30: * CMODE = 1 op2(C) = C
! 31: * CMODE = 0 op2(C) = I
! 32: * CMODE = -1 op2(C) = inv(C)
! 33: * The Skeel condition number cond(A) = norminf( |inv(A)||A| )
! 34: * is computed by computing scaling factors R such that
! 35: * diag(R)*A*op2(C) is row equilibrated and computing the standard
! 36: * infinity-norm condition number.
! 37: *
! 38: * Arguments
! 39: * =========
! 40: *
! 41: * TRANS (input) CHARACTER*1
! 42: * Specifies the form of the system of equations:
! 43: * = 'N': A * X = B (No transpose)
! 44: * = 'T': A**T * X = B (Transpose)
! 45: * = 'C': A**H * X = B (Conjugate Transpose = Transpose)
! 46: *
! 47: * N (input) INTEGER
! 48: * The number of linear equations, i.e., the order of the
! 49: * matrix A. N >= 0.
! 50: *
! 51: * KL (input) INTEGER
! 52: * The number of subdiagonals within the band of A. KL >= 0.
! 53: *
! 54: * KU (input) INTEGER
! 55: * The number of superdiagonals within the band of A. KU >= 0.
! 56: *
! 57: * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
! 58: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 59: * The j-th column of A is stored in the j-th column of the
! 60: * array AB as follows:
! 61: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 62: *
! 63: * LDAB (input) INTEGER
! 64: * The leading dimension of the array AB. LDAB >= KL+KU+1.
! 65: *
! 66: * AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N)
! 67: * Details of the LU factorization of the band matrix A, as
! 68: * computed by DGBTRF. U is stored as an upper triangular
! 69: * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 70: * and the multipliers used during the factorization are stored
! 71: * in rows KL+KU+2 to 2*KL+KU+1.
! 72: *
! 73: * LDAFB (input) INTEGER
! 74: * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 75: *
! 76: * IPIV (input) INTEGER array, dimension (N)
! 77: * The pivot indices from the factorization A = P*L*U
! 78: * as computed by DGBTRF; row i of the matrix was interchanged
! 79: * with row IPIV(i).
! 80: *
! 81: * CMODE (input) INTEGER
! 82: * Determines op2(C) in the formula op(A) * op2(C) as follows:
! 83: * CMODE = 1 op2(C) = C
! 84: * CMODE = 0 op2(C) = I
! 85: * CMODE = -1 op2(C) = inv(C)
! 86: *
! 87: * C (input) DOUBLE PRECISION array, dimension (N)
! 88: * The vector C in the formula op(A) * op2(C).
! 89: *
! 90: * INFO (output) INTEGER
! 91: * = 0: Successful exit.
! 92: * i > 0: The ith argument is invalid.
! 93: *
! 94: * WORK (input) DOUBLE PRECISION array, dimension (5*N).
! 95: * Workspace.
! 96: *
! 97: * IWORK (input) INTEGER array, dimension (N).
! 98: * Workspace.
! 99: *
! 100: * =====================================================================
! 101: *
! 102: * .. Local Scalars ..
! 103: LOGICAL NOTRANS
! 104: INTEGER KASE, I, J, KD, KE
! 105: DOUBLE PRECISION AINVNM, TMP
! 106: * ..
! 107: * .. Local Arrays ..
! 108: INTEGER ISAVE( 3 )
! 109: * ..
! 110: * .. External Functions ..
! 111: LOGICAL LSAME
! 112: EXTERNAL LSAME
! 113: * ..
! 114: * .. External Subroutines ..
! 115: EXTERNAL DLACN2, DGBTRS, XERBLA
! 116: * ..
! 117: * .. Intrinsic Functions ..
! 118: INTRINSIC ABS, MAX
! 119: * ..
! 120: * .. Executable Statements ..
! 121: *
! 122: DLA_GBRCOND = 0.0D+0
! 123: *
! 124: INFO = 0
! 125: NOTRANS = LSAME( TRANS, 'N' )
! 126: IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T')
! 127: $ .AND. .NOT. LSAME(TRANS, 'C') ) THEN
! 128: INFO = -1
! 129: ELSE IF( N.LT.0 ) THEN
! 130: INFO = -2
! 131: ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
! 132: INFO = -3
! 133: ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
! 134: INFO = -4
! 135: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
! 136: INFO = -6
! 137: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
! 138: INFO = -8
! 139: END IF
! 140: IF( INFO.NE.0 ) THEN
! 141: CALL XERBLA( 'DLA_GBRCOND', -INFO )
! 142: RETURN
! 143: END IF
! 144: IF( N.EQ.0 ) THEN
! 145: DLA_GBRCOND = 1.0D+0
! 146: RETURN
! 147: END IF
! 148: *
! 149: * Compute the equilibration matrix R such that
! 150: * inv(R)*A*C has unit 1-norm.
! 151: *
! 152: KD = KU + 1
! 153: KE = KL + 1
! 154: IF ( NOTRANS ) THEN
! 155: DO I = 1, N
! 156: TMP = 0.0D+0
! 157: IF ( CMODE .EQ. 1 ) THEN
! 158: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 159: TMP = TMP + ABS( AB( KD+I-J, J ) * C( J ) )
! 160: END DO
! 161: ELSE IF ( CMODE .EQ. 0 ) THEN
! 162: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 163: TMP = TMP + ABS( AB( KD+I-J, J ) )
! 164: END DO
! 165: ELSE
! 166: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 167: TMP = TMP + ABS( AB( KD+I-J, J ) / C( J ) )
! 168: END DO
! 169: END IF
! 170: WORK( 2*N+I ) = TMP
! 171: END DO
! 172: ELSE
! 173: DO I = 1, N
! 174: TMP = 0.0D+0
! 175: IF ( CMODE .EQ. 1 ) THEN
! 176: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 177: TMP = TMP + ABS( AB( KE-I+J, I ) * C( J ) )
! 178: END DO
! 179: ELSE IF ( CMODE .EQ. 0 ) THEN
! 180: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 181: TMP = TMP + ABS( AB( KE-I+J, I ) )
! 182: END DO
! 183: ELSE
! 184: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
! 185: TMP = TMP + ABS( AB( KE-I+J, I ) / C( J ) )
! 186: END DO
! 187: END IF
! 188: WORK( 2*N+I ) = TMP
! 189: END DO
! 190: END IF
! 191: *
! 192: * Estimate the norm of inv(op(A)).
! 193: *
! 194: AINVNM = 0.0D+0
! 195:
! 196: KASE = 0
! 197: 10 CONTINUE
! 198: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 199: IF( KASE.NE.0 ) THEN
! 200: IF( KASE.EQ.2 ) THEN
! 201: *
! 202: * Multiply by R.
! 203: *
! 204: DO I = 1, N
! 205: WORK( I ) = WORK( I ) * WORK( 2*N+I )
! 206: END DO
! 207:
! 208: IF ( NOTRANS ) THEN
! 209: CALL DGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
! 210: $ IPIV, WORK, N, INFO )
! 211: ELSE
! 212: CALL DGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV,
! 213: $ WORK, N, INFO )
! 214: END IF
! 215: *
! 216: * Multiply by inv(C).
! 217: *
! 218: IF ( CMODE .EQ. 1 ) THEN
! 219: DO I = 1, N
! 220: WORK( I ) = WORK( I ) / C( I )
! 221: END DO
! 222: ELSE IF ( CMODE .EQ. -1 ) THEN
! 223: DO I = 1, N
! 224: WORK( I ) = WORK( I ) * C( I )
! 225: END DO
! 226: END IF
! 227: ELSE
! 228: *
! 229: * Multiply by inv(C').
! 230: *
! 231: IF ( CMODE .EQ. 1 ) THEN
! 232: DO I = 1, N
! 233: WORK( I ) = WORK( I ) / C( I )
! 234: END DO
! 235: ELSE IF ( CMODE .EQ. -1 ) THEN
! 236: DO I = 1, N
! 237: WORK( I ) = WORK( I ) * C( I )
! 238: END DO
! 239: END IF
! 240:
! 241: IF ( NOTRANS ) THEN
! 242: CALL DGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV,
! 243: $ WORK, N, INFO )
! 244: ELSE
! 245: CALL DGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
! 246: $ IPIV, WORK, N, INFO )
! 247: END IF
! 248: *
! 249: * Multiply by R.
! 250: *
! 251: DO I = 1, N
! 252: WORK( I ) = WORK( I ) * WORK( 2*N+I )
! 253: END DO
! 254: END IF
! 255: GO TO 10
! 256: END IF
! 257: *
! 258: * Compute the estimate of the reciprocal condition number.
! 259: *
! 260: IF( AINVNM .NE. 0.0D+0 )
! 261: $ DLA_GBRCOND = ( 1.0D+0 / AINVNM )
! 262: *
! 263: RETURN
! 264: *
! 265: END
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