Annotation of rpl/lapack/lapack/dgbsvx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
! 2: $ LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
! 3: $ RCOND, FERR, BERR, WORK, IWORK, INFO )
! 4: *
! 5: * -- LAPACK driver routine (version 3.2) --
! 6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 8: * November 2006
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER EQUED, FACT, TRANS
! 12: INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
! 13: DOUBLE PRECISION RCOND
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IPIV( * ), IWORK( * )
! 17: DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
! 18: $ BERR( * ), C( * ), FERR( * ), R( * ),
! 19: $ WORK( * ), X( LDX, * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * DGBSVX uses the LU factorization to compute the solution to a real
! 26: * system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
! 27: * where A is a band matrix of order N with KL subdiagonals and KU
! 28: * superdiagonals, and X and B are N-by-NRHS matrices.
! 29: *
! 30: * Error bounds on the solution and a condition estimate are also
! 31: * provided.
! 32: *
! 33: * Description
! 34: * ===========
! 35: *
! 36: * The following steps are performed by this subroutine:
! 37: *
! 38: * 1. If FACT = 'E', real scaling factors are computed to equilibrate
! 39: * the system:
! 40: * TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
! 41: * TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
! 42: * TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
! 43: * Whether or not the system will be equilibrated depends on the
! 44: * scaling of the matrix A, but if equilibration is used, A is
! 45: * overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
! 46: * or diag(C)*B (if TRANS = 'T' or 'C').
! 47: *
! 48: * 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
! 49: * matrix A (after equilibration if FACT = 'E') as
! 50: * A = L * U,
! 51: * where L is a product of permutation and unit lower triangular
! 52: * matrices with KL subdiagonals, and U is upper triangular with
! 53: * KL+KU superdiagonals.
! 54: *
! 55: * 3. If some U(i,i)=0, so that U is exactly singular, then the routine
! 56: * returns with INFO = i. Otherwise, the factored form of A is used
! 57: * to estimate the condition number of the matrix A. If the
! 58: * reciprocal of the condition number is less than machine precision,
! 59: * INFO = N+1 is returned as a warning, but the routine still goes on
! 60: * to solve for X and compute error bounds as described below.
! 61: *
! 62: * 4. The system of equations is solved for X using the factored form
! 63: * of A.
! 64: *
! 65: * 5. Iterative refinement is applied to improve the computed solution
! 66: * matrix and calculate error bounds and backward error estimates
! 67: * for it.
! 68: *
! 69: * 6. If equilibration was used, the matrix X is premultiplied by
! 70: * diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
! 71: * that it solves the original system before equilibration.
! 72: *
! 73: * Arguments
! 74: * =========
! 75: *
! 76: * FACT (input) CHARACTER*1
! 77: * Specifies whether or not the factored form of the matrix A is
! 78: * supplied on entry, and if not, whether the matrix A should be
! 79: * equilibrated before it is factored.
! 80: * = 'F': On entry, AFB and IPIV contain the factored form of
! 81: * A. If EQUED is not 'N', the matrix A has been
! 82: * equilibrated with scaling factors given by R and C.
! 83: * AB, AFB, and IPIV are not modified.
! 84: * = 'N': The matrix A will be copied to AFB and factored.
! 85: * = 'E': The matrix A will be equilibrated if necessary, then
! 86: * copied to AFB and factored.
! 87: *
! 88: * TRANS (input) CHARACTER*1
! 89: * Specifies the form of the system of equations.
! 90: * = 'N': A * X = B (No transpose)
! 91: * = 'T': A**T * X = B (Transpose)
! 92: * = 'C': A**H * X = B (Transpose)
! 93: *
! 94: * N (input) INTEGER
! 95: * The number of linear equations, i.e., the order of the
! 96: * matrix A. N >= 0.
! 97: *
! 98: * KL (input) INTEGER
! 99: * The number of subdiagonals within the band of A. KL >= 0.
! 100: *
! 101: * KU (input) INTEGER
! 102: * The number of superdiagonals within the band of A. KU >= 0.
! 103: *
! 104: * NRHS (input) INTEGER
! 105: * The number of right hand sides, i.e., the number of columns
! 106: * of the matrices B and X. NRHS >= 0.
! 107: *
! 108: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
! 109: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 110: * The j-th column of A is stored in the j-th column of the
! 111: * array AB as follows:
! 112: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 113: *
! 114: * If FACT = 'F' and EQUED is not 'N', then A must have been
! 115: * equilibrated by the scaling factors in R and/or C. AB is not
! 116: * modified if FACT = 'F' or 'N', or if FACT = 'E' and
! 117: * EQUED = 'N' on exit.
! 118: *
! 119: * On exit, if EQUED .ne. 'N', A is scaled as follows:
! 120: * EQUED = 'R': A := diag(R) * A
! 121: * EQUED = 'C': A := A * diag(C)
! 122: * EQUED = 'B': A := diag(R) * A * diag(C).
! 123: *
! 124: * LDAB (input) INTEGER
! 125: * The leading dimension of the array AB. LDAB >= KL+KU+1.
! 126: *
! 127: * AFB (input or output) DOUBLE PRECISION array, dimension (LDAFB,N)
! 128: * If FACT = 'F', then AFB is an input argument and on entry
! 129: * contains details of the LU factorization of the band matrix
! 130: * A, as computed by DGBTRF. U is stored as an upper triangular
! 131: * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 132: * and the multipliers used during the factorization are stored
! 133: * in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is
! 134: * the factored form of the equilibrated matrix A.
! 135: *
! 136: * If FACT = 'N', then AFB is an output argument and on exit
! 137: * returns details of the LU factorization of A.
! 138: *
! 139: * If FACT = 'E', then AFB is an output argument and on exit
! 140: * returns details of the LU factorization of the equilibrated
! 141: * matrix A (see the description of AB for the form of the
! 142: * equilibrated matrix).
! 143: *
! 144: * LDAFB (input) INTEGER
! 145: * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 146: *
! 147: * IPIV (input or output) INTEGER array, dimension (N)
! 148: * If FACT = 'F', then IPIV is an input argument and on entry
! 149: * contains the pivot indices from the factorization A = L*U
! 150: * as computed by DGBTRF; row i of the matrix was interchanged
! 151: * with row IPIV(i).
! 152: *
! 153: * If FACT = 'N', then IPIV is an output argument and on exit
! 154: * contains the pivot indices from the factorization A = L*U
! 155: * of the original matrix A.
! 156: *
! 157: * If FACT = 'E', then IPIV is an output argument and on exit
! 158: * contains the pivot indices from the factorization A = L*U
! 159: * of the equilibrated matrix A.
! 160: *
! 161: * EQUED (input or output) CHARACTER*1
! 162: * Specifies the form of equilibration that was done.
! 163: * = 'N': No equilibration (always true if FACT = 'N').
! 164: * = 'R': Row equilibration, i.e., A has been premultiplied by
! 165: * diag(R).
! 166: * = 'C': Column equilibration, i.e., A has been postmultiplied
! 167: * by diag(C).
! 168: * = 'B': Both row and column equilibration, i.e., A has been
! 169: * replaced by diag(R) * A * diag(C).
! 170: * EQUED is an input argument if FACT = 'F'; otherwise, it is an
! 171: * output argument.
! 172: *
! 173: * R (input or output) DOUBLE PRECISION array, dimension (N)
! 174: * The row scale factors for A. If EQUED = 'R' or 'B', A is
! 175: * multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
! 176: * is not accessed. R is an input argument if FACT = 'F';
! 177: * otherwise, R is an output argument. If FACT = 'F' and
! 178: * EQUED = 'R' or 'B', each element of R must be positive.
! 179: *
! 180: * C (input or output) DOUBLE PRECISION array, dimension (N)
! 181: * The column scale factors for A. If EQUED = 'C' or 'B', A is
! 182: * multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
! 183: * is not accessed. C is an input argument if FACT = 'F';
! 184: * otherwise, C is an output argument. If FACT = 'F' and
! 185: * EQUED = 'C' or 'B', each element of C must be positive.
! 186: *
! 187: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
! 188: * On entry, the right hand side matrix B.
! 189: * On exit,
! 190: * if EQUED = 'N', B is not modified;
! 191: * if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
! 192: * diag(R)*B;
! 193: * if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
! 194: * overwritten by diag(C)*B.
! 195: *
! 196: * LDB (input) INTEGER
! 197: * The leading dimension of the array B. LDB >= max(1,N).
! 198: *
! 199: * X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
! 200: * If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X
! 201: * to the original system of equations. Note that A and B are
! 202: * modified on exit if EQUED .ne. 'N', and the solution to the
! 203: * equilibrated system is inv(diag(C))*X if TRANS = 'N' and
! 204: * EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'
! 205: * and EQUED = 'R' or 'B'.
! 206: *
! 207: * LDX (input) INTEGER
! 208: * The leading dimension of the array X. LDX >= max(1,N).
! 209: *
! 210: * RCOND (output) DOUBLE PRECISION
! 211: * The estimate of the reciprocal condition number of the matrix
! 212: * A after equilibration (if done). If RCOND is less than the
! 213: * machine precision (in particular, if RCOND = 0), the matrix
! 214: * is singular to working precision. This condition is
! 215: * indicated by a return code of INFO > 0.
! 216: *
! 217: * FERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 218: * The estimated forward error bound for each solution vector
! 219: * X(j) (the j-th column of the solution matrix X).
! 220: * If XTRUE is the true solution corresponding to X(j), FERR(j)
! 221: * is an estimated upper bound for the magnitude of the largest
! 222: * element in (X(j) - XTRUE) divided by the magnitude of the
! 223: * largest element in X(j). The estimate is as reliable as
! 224: * the estimate for RCOND, and is almost always a slight
! 225: * overestimate of the true error.
! 226: *
! 227: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 228: * The componentwise relative backward error of each solution
! 229: * vector X(j) (i.e., the smallest relative change in
! 230: * any element of A or B that makes X(j) an exact solution).
! 231: *
! 232: * WORK (workspace/output) DOUBLE PRECISION array, dimension (3*N)
! 233: * On exit, WORK(1) contains the reciprocal pivot growth
! 234: * factor norm(A)/norm(U). The "max absolute element" norm is
! 235: * used. If WORK(1) is much less than 1, then the stability
! 236: * of the LU factorization of the (equilibrated) matrix A
! 237: * could be poor. This also means that the solution X, condition
! 238: * estimator RCOND, and forward error bound FERR could be
! 239: * unreliable. If factorization fails with 0<INFO<=N, then
! 240: * WORK(1) contains the reciprocal pivot growth factor for the
! 241: * leading INFO columns of A.
! 242: *
! 243: * IWORK (workspace) INTEGER array, dimension (N)
! 244: *
! 245: * INFO (output) INTEGER
! 246: * = 0: successful exit
! 247: * < 0: if INFO = -i, the i-th argument had an illegal value
! 248: * > 0: if INFO = i, and i is
! 249: * <= N: U(i,i) is exactly zero. The factorization
! 250: * has been completed, but the factor U is exactly
! 251: * singular, so the solution and error bounds
! 252: * could not be computed. RCOND = 0 is returned.
! 253: * = N+1: U is nonsingular, but RCOND is less than machine
! 254: * precision, meaning that the matrix is singular
! 255: * to working precision. Nevertheless, the
! 256: * solution and error bounds are computed because
! 257: * there are a number of situations where the
! 258: * computed solution can be more accurate than the
! 259: * value of RCOND would suggest.
! 260: *
! 261: * =====================================================================
! 262: *
! 263: * .. Parameters ..
! 264: DOUBLE PRECISION ZERO, ONE
! 265: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 266: * ..
! 267: * .. Local Scalars ..
! 268: LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
! 269: CHARACTER NORM
! 270: INTEGER I, INFEQU, J, J1, J2
! 271: DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
! 272: $ ROWCND, RPVGRW, SMLNUM
! 273: * ..
! 274: * .. External Functions ..
! 275: LOGICAL LSAME
! 276: DOUBLE PRECISION DLAMCH, DLANGB, DLANTB
! 277: EXTERNAL LSAME, DLAMCH, DLANGB, DLANTB
! 278: * ..
! 279: * .. External Subroutines ..
! 280: EXTERNAL DCOPY, DGBCON, DGBEQU, DGBRFS, DGBTRF, DGBTRS,
! 281: $ DLACPY, DLAQGB, XERBLA
! 282: * ..
! 283: * .. Intrinsic Functions ..
! 284: INTRINSIC ABS, MAX, MIN
! 285: * ..
! 286: * .. Executable Statements ..
! 287: *
! 288: INFO = 0
! 289: NOFACT = LSAME( FACT, 'N' )
! 290: EQUIL = LSAME( FACT, 'E' )
! 291: NOTRAN = LSAME( TRANS, 'N' )
! 292: IF( NOFACT .OR. EQUIL ) THEN
! 293: EQUED = 'N'
! 294: ROWEQU = .FALSE.
! 295: COLEQU = .FALSE.
! 296: ELSE
! 297: ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
! 298: COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
! 299: SMLNUM = DLAMCH( 'Safe minimum' )
! 300: BIGNUM = ONE / SMLNUM
! 301: END IF
! 302: *
! 303: * Test the input parameters.
! 304: *
! 305: IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.LSAME( FACT, 'F' ) )
! 306: $ THEN
! 307: INFO = -1
! 308: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
! 309: $ LSAME( TRANS, 'C' ) ) THEN
! 310: INFO = -2
! 311: ELSE IF( N.LT.0 ) THEN
! 312: INFO = -3
! 313: ELSE IF( KL.LT.0 ) THEN
! 314: INFO = -4
! 315: ELSE IF( KU.LT.0 ) THEN
! 316: INFO = -5
! 317: ELSE IF( NRHS.LT.0 ) THEN
! 318: INFO = -6
! 319: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
! 320: INFO = -8
! 321: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
! 322: INFO = -10
! 323: ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
! 324: $ ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
! 325: INFO = -12
! 326: ELSE
! 327: IF( ROWEQU ) THEN
! 328: RCMIN = BIGNUM
! 329: RCMAX = ZERO
! 330: DO 10 J = 1, N
! 331: RCMIN = MIN( RCMIN, R( J ) )
! 332: RCMAX = MAX( RCMAX, R( J ) )
! 333: 10 CONTINUE
! 334: IF( RCMIN.LE.ZERO ) THEN
! 335: INFO = -13
! 336: ELSE IF( N.GT.0 ) THEN
! 337: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 338: ELSE
! 339: ROWCND = ONE
! 340: END IF
! 341: END IF
! 342: IF( COLEQU .AND. INFO.EQ.0 ) THEN
! 343: RCMIN = BIGNUM
! 344: RCMAX = ZERO
! 345: DO 20 J = 1, N
! 346: RCMIN = MIN( RCMIN, C( J ) )
! 347: RCMAX = MAX( RCMAX, C( J ) )
! 348: 20 CONTINUE
! 349: IF( RCMIN.LE.ZERO ) THEN
! 350: INFO = -14
! 351: ELSE IF( N.GT.0 ) THEN
! 352: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 353: ELSE
! 354: COLCND = ONE
! 355: END IF
! 356: END IF
! 357: IF( INFO.EQ.0 ) THEN
! 358: IF( LDB.LT.MAX( 1, N ) ) THEN
! 359: INFO = -16
! 360: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
! 361: INFO = -18
! 362: END IF
! 363: END IF
! 364: END IF
! 365: *
! 366: IF( INFO.NE.0 ) THEN
! 367: CALL XERBLA( 'DGBSVX', -INFO )
! 368: RETURN
! 369: END IF
! 370: *
! 371: IF( EQUIL ) THEN
! 372: *
! 373: * Compute row and column scalings to equilibrate the matrix A.
! 374: *
! 375: CALL DGBEQU( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 376: $ AMAX, INFEQU )
! 377: IF( INFEQU.EQ.0 ) THEN
! 378: *
! 379: * Equilibrate the matrix.
! 380: *
! 381: CALL DLAQGB( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 382: $ AMAX, EQUED )
! 383: ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
! 384: COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
! 385: END IF
! 386: END IF
! 387: *
! 388: * Scale the right hand side.
! 389: *
! 390: IF( NOTRAN ) THEN
! 391: IF( ROWEQU ) THEN
! 392: DO 40 J = 1, NRHS
! 393: DO 30 I = 1, N
! 394: B( I, J ) = R( I )*B( I, J )
! 395: 30 CONTINUE
! 396: 40 CONTINUE
! 397: END IF
! 398: ELSE IF( COLEQU ) THEN
! 399: DO 60 J = 1, NRHS
! 400: DO 50 I = 1, N
! 401: B( I, J ) = C( I )*B( I, J )
! 402: 50 CONTINUE
! 403: 60 CONTINUE
! 404: END IF
! 405: *
! 406: IF( NOFACT .OR. EQUIL ) THEN
! 407: *
! 408: * Compute the LU factorization of the band matrix A.
! 409: *
! 410: DO 70 J = 1, N
! 411: J1 = MAX( J-KU, 1 )
! 412: J2 = MIN( J+KL, N )
! 413: CALL DCOPY( J2-J1+1, AB( KU+1-J+J1, J ), 1,
! 414: $ AFB( KL+KU+1-J+J1, J ), 1 )
! 415: 70 CONTINUE
! 416: *
! 417: CALL DGBTRF( N, N, KL, KU, AFB, LDAFB, IPIV, INFO )
! 418: *
! 419: * Return if INFO is non-zero.
! 420: *
! 421: IF( INFO.GT.0 ) THEN
! 422: *
! 423: * Compute the reciprocal pivot growth factor of the
! 424: * leading rank-deficient INFO columns of A.
! 425: *
! 426: ANORM = ZERO
! 427: DO 90 J = 1, INFO
! 428: DO 80 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
! 429: ANORM = MAX( ANORM, ABS( AB( I, J ) ) )
! 430: 80 CONTINUE
! 431: 90 CONTINUE
! 432: RPVGRW = DLANTB( 'M', 'U', 'N', INFO, MIN( INFO-1, KL+KU ),
! 433: $ AFB( MAX( 1, KL+KU+2-INFO ), 1 ), LDAFB,
! 434: $ WORK )
! 435: IF( RPVGRW.EQ.ZERO ) THEN
! 436: RPVGRW = ONE
! 437: ELSE
! 438: RPVGRW = ANORM / RPVGRW
! 439: END IF
! 440: WORK( 1 ) = RPVGRW
! 441: RCOND = ZERO
! 442: RETURN
! 443: END IF
! 444: END IF
! 445: *
! 446: * Compute the norm of the matrix A and the
! 447: * reciprocal pivot growth factor RPVGRW.
! 448: *
! 449: IF( NOTRAN ) THEN
! 450: NORM = '1'
! 451: ELSE
! 452: NORM = 'I'
! 453: END IF
! 454: ANORM = DLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
! 455: RPVGRW = DLANTB( 'M', 'U', 'N', N, KL+KU, AFB, LDAFB, WORK )
! 456: IF( RPVGRW.EQ.ZERO ) THEN
! 457: RPVGRW = ONE
! 458: ELSE
! 459: RPVGRW = DLANGB( 'M', N, KL, KU, AB, LDAB, WORK ) / RPVGRW
! 460: END IF
! 461: *
! 462: * Compute the reciprocal of the condition number of A.
! 463: *
! 464: CALL DGBCON( NORM, N, KL, KU, AFB, LDAFB, IPIV, ANORM, RCOND,
! 465: $ WORK, IWORK, INFO )
! 466: *
! 467: * Compute the solution matrix X.
! 468: *
! 469: CALL DLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
! 470: CALL DGBTRS( TRANS, N, KL, KU, NRHS, AFB, LDAFB, IPIV, X, LDX,
! 471: $ INFO )
! 472: *
! 473: * Use iterative refinement to improve the computed solution and
! 474: * compute error bounds and backward error estimates for it.
! 475: *
! 476: CALL DGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
! 477: $ B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
! 478: *
! 479: * Transform the solution matrix X to a solution of the original
! 480: * system.
! 481: *
! 482: IF( NOTRAN ) THEN
! 483: IF( COLEQU ) THEN
! 484: DO 110 J = 1, NRHS
! 485: DO 100 I = 1, N
! 486: X( I, J ) = C( I )*X( I, J )
! 487: 100 CONTINUE
! 488: 110 CONTINUE
! 489: DO 120 J = 1, NRHS
! 490: FERR( J ) = FERR( J ) / COLCND
! 491: 120 CONTINUE
! 492: END IF
! 493: ELSE IF( ROWEQU ) THEN
! 494: DO 140 J = 1, NRHS
! 495: DO 130 I = 1, N
! 496: X( I, J ) = R( I )*X( I, J )
! 497: 130 CONTINUE
! 498: 140 CONTINUE
! 499: DO 150 J = 1, NRHS
! 500: FERR( J ) = FERR( J ) / ROWCND
! 501: 150 CONTINUE
! 502: END IF
! 503: *
! 504: * Set INFO = N+1 if the matrix is singular to working precision.
! 505: *
! 506: IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
! 507: $ INFO = N + 1
! 508: *
! 509: WORK( 1 ) = RPVGRW
! 510: RETURN
! 511: *
! 512: * End of DGBSVX
! 513: *
! 514: END
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