Annotation of rpl/lapack/lapack/zgbsvx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
! 2: $ LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
! 3: $ RCOND, FERR, BERR, WORK, RWORK, 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( * )
! 17: DOUBLE PRECISION BERR( * ), C( * ), FERR( * ), R( * ),
! 18: $ RWORK( * )
! 19: COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
! 20: $ WORK( * ), X( LDX, * )
! 21: * ..
! 22: *
! 23: * Purpose
! 24: * =======
! 25: *
! 26: * ZGBSVX uses the LU factorization to compute the solution to a complex
! 27: * system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
! 28: * where A is a band matrix of order N with KL subdiagonals and KU
! 29: * superdiagonals, and X and B are N-by-NRHS matrices.
! 30: *
! 31: * Error bounds on the solution and a condition estimate are also
! 32: * provided.
! 33: *
! 34: * Description
! 35: * ===========
! 36: *
! 37: * The following steps are performed by this subroutine:
! 38: *
! 39: * 1. If FACT = 'E', real scaling factors are computed to equilibrate
! 40: * the system:
! 41: * TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
! 42: * TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
! 43: * TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
! 44: * Whether or not the system will be equilibrated depends on the
! 45: * scaling of the matrix A, but if equilibration is used, A is
! 46: * overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
! 47: * or diag(C)*B (if TRANS = 'T' or 'C').
! 48: *
! 49: * 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
! 50: * matrix A (after equilibration if FACT = 'E') as
! 51: * A = L * U,
! 52: * where L is a product of permutation and unit lower triangular
! 53: * matrices with KL subdiagonals, and U is upper triangular with
! 54: * KL+KU superdiagonals.
! 55: *
! 56: * 3. If some U(i,i)=0, so that U is exactly singular, then the routine
! 57: * returns with INFO = i. Otherwise, the factored form of A is used
! 58: * to estimate the condition number of the matrix A. If the
! 59: * reciprocal of the condition number is less than machine precision,
! 60: * INFO = N+1 is returned as a warning, but the routine still goes on
! 61: * to solve for X and compute error bounds as described below.
! 62: *
! 63: * 4. The system of equations is solved for X using the factored form
! 64: * of A.
! 65: *
! 66: * 5. Iterative refinement is applied to improve the computed solution
! 67: * matrix and calculate error bounds and backward error estimates
! 68: * for it.
! 69: *
! 70: * 6. If equilibration was used, the matrix X is premultiplied by
! 71: * diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
! 72: * that it solves the original system before equilibration.
! 73: *
! 74: * Arguments
! 75: * =========
! 76: *
! 77: * FACT (input) CHARACTER*1
! 78: * Specifies whether or not the factored form of the matrix A is
! 79: * supplied on entry, and if not, whether the matrix A should be
! 80: * equilibrated before it is factored.
! 81: * = 'F': On entry, AFB and IPIV contain the factored form of
! 82: * A. If EQUED is not 'N', the matrix A has been
! 83: * equilibrated with scaling factors given by R and C.
! 84: * AB, AFB, and IPIV are not modified.
! 85: * = 'N': The matrix A will be copied to AFB and factored.
! 86: * = 'E': The matrix A will be equilibrated if necessary, then
! 87: * copied to AFB and factored.
! 88: *
! 89: * TRANS (input) CHARACTER*1
! 90: * Specifies the form of the system of equations.
! 91: * = 'N': A * X = B (No transpose)
! 92: * = 'T': A**T * X = B (Transpose)
! 93: * = 'C': A**H * X = B (Conjugate transpose)
! 94: *
! 95: * N (input) INTEGER
! 96: * The number of linear equations, i.e., the order of the
! 97: * matrix A. N >= 0.
! 98: *
! 99: * KL (input) INTEGER
! 100: * The number of subdiagonals within the band of A. KL >= 0.
! 101: *
! 102: * KU (input) INTEGER
! 103: * The number of superdiagonals within the band of A. KU >= 0.
! 104: *
! 105: * NRHS (input) INTEGER
! 106: * The number of right hand sides, i.e., the number of columns
! 107: * of the matrices B and X. NRHS >= 0.
! 108: *
! 109: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
! 110: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 111: * The j-th column of A is stored in the j-th column of the
! 112: * array AB as follows:
! 113: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 114: *
! 115: * If FACT = 'F' and EQUED is not 'N', then A must have been
! 116: * equilibrated by the scaling factors in R and/or C. AB is not
! 117: * modified if FACT = 'F' or 'N', or if FACT = 'E' and
! 118: * EQUED = 'N' on exit.
! 119: *
! 120: * On exit, if EQUED .ne. 'N', A is scaled as follows:
! 121: * EQUED = 'R': A := diag(R) * A
! 122: * EQUED = 'C': A := A * diag(C)
! 123: * EQUED = 'B': A := diag(R) * A * diag(C).
! 124: *
! 125: * LDAB (input) INTEGER
! 126: * The leading dimension of the array AB. LDAB >= KL+KU+1.
! 127: *
! 128: * AFB (input or output) COMPLEX*16 array, dimension (LDAFB,N)
! 129: * If FACT = 'F', then AFB is an input argument and on entry
! 130: * contains details of the LU factorization of the band matrix
! 131: * A, as computed by ZGBTRF. U is stored as an upper triangular
! 132: * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 133: * and the multipliers used during the factorization are stored
! 134: * in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is
! 135: * the factored form of the equilibrated matrix A.
! 136: *
! 137: * If FACT = 'N', then AFB is an output argument and on exit
! 138: * returns details of the LU factorization of A.
! 139: *
! 140: * If FACT = 'E', then AFB is an output argument and on exit
! 141: * returns details of the LU factorization of the equilibrated
! 142: * matrix A (see the description of AB for the form of the
! 143: * equilibrated matrix).
! 144: *
! 145: * LDAFB (input) INTEGER
! 146: * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 147: *
! 148: * IPIV (input or output) INTEGER array, dimension (N)
! 149: * If FACT = 'F', then IPIV is an input argument and on entry
! 150: * contains the pivot indices from the factorization A = L*U
! 151: * as computed by ZGBTRF; row i of the matrix was interchanged
! 152: * with row IPIV(i).
! 153: *
! 154: * If FACT = 'N', then IPIV is an output argument and on exit
! 155: * contains the pivot indices from the factorization A = L*U
! 156: * of the original matrix A.
! 157: *
! 158: * If FACT = 'E', then IPIV is an output argument and on exit
! 159: * contains the pivot indices from the factorization A = L*U
! 160: * of the equilibrated matrix A.
! 161: *
! 162: * EQUED (input or output) CHARACTER*1
! 163: * Specifies the form of equilibration that was done.
! 164: * = 'N': No equilibration (always true if FACT = 'N').
! 165: * = 'R': Row equilibration, i.e., A has been premultiplied by
! 166: * diag(R).
! 167: * = 'C': Column equilibration, i.e., A has been postmultiplied
! 168: * by diag(C).
! 169: * = 'B': Both row and column equilibration, i.e., A has been
! 170: * replaced by diag(R) * A * diag(C).
! 171: * EQUED is an input argument if FACT = 'F'; otherwise, it is an
! 172: * output argument.
! 173: *
! 174: * R (input or output) DOUBLE PRECISION array, dimension (N)
! 175: * The row scale factors for A. If EQUED = 'R' or 'B', A is
! 176: * multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
! 177: * is not accessed. R is an input argument if FACT = 'F';
! 178: * otherwise, R is an output argument. If FACT = 'F' and
! 179: * EQUED = 'R' or 'B', each element of R must be positive.
! 180: *
! 181: * C (input or output) DOUBLE PRECISION array, dimension (N)
! 182: * The column scale factors for A. If EQUED = 'C' or 'B', A is
! 183: * multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
! 184: * is not accessed. C is an input argument if FACT = 'F';
! 185: * otherwise, C is an output argument. If FACT = 'F' and
! 186: * EQUED = 'C' or 'B', each element of C must be positive.
! 187: *
! 188: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 189: * On entry, the right hand side matrix B.
! 190: * On exit,
! 191: * if EQUED = 'N', B is not modified;
! 192: * if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
! 193: * diag(R)*B;
! 194: * if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
! 195: * overwritten by diag(C)*B.
! 196: *
! 197: * LDB (input) INTEGER
! 198: * The leading dimension of the array B. LDB >= max(1,N).
! 199: *
! 200: * X (output) COMPLEX*16 array, dimension (LDX,NRHS)
! 201: * If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X
! 202: * to the original system of equations. Note that A and B are
! 203: * modified on exit if EQUED .ne. 'N', and the solution to the
! 204: * equilibrated system is inv(diag(C))*X if TRANS = 'N' and
! 205: * EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'
! 206: * and EQUED = 'R' or 'B'.
! 207: *
! 208: * LDX (input) INTEGER
! 209: * The leading dimension of the array X. LDX >= max(1,N).
! 210: *
! 211: * RCOND (output) DOUBLE PRECISION
! 212: * The estimate of the reciprocal condition number of the matrix
! 213: * A after equilibration (if done). If RCOND is less than the
! 214: * machine precision (in particular, if RCOND = 0), the matrix
! 215: * is singular to working precision. This condition is
! 216: * indicated by a return code of INFO > 0.
! 217: *
! 218: * FERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 219: * The estimated forward error bound for each solution vector
! 220: * X(j) (the j-th column of the solution matrix X).
! 221: * If XTRUE is the true solution corresponding to X(j), FERR(j)
! 222: * is an estimated upper bound for the magnitude of the largest
! 223: * element in (X(j) - XTRUE) divided by the magnitude of the
! 224: * largest element in X(j). The estimate is as reliable as
! 225: * the estimate for RCOND, and is almost always a slight
! 226: * overestimate of the true error.
! 227: *
! 228: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 229: * The componentwise relative backward error of each solution
! 230: * vector X(j) (i.e., the smallest relative change in
! 231: * any element of A or B that makes X(j) an exact solution).
! 232: *
! 233: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 234: *
! 235: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (N)
! 236: * On exit, RWORK(1) contains the reciprocal pivot growth
! 237: * factor norm(A)/norm(U). The "max absolute element" norm is
! 238: * used. If RWORK(1) is much less than 1, then the stability
! 239: * of the LU factorization of the (equilibrated) matrix A
! 240: * could be poor. This also means that the solution X, condition
! 241: * estimator RCOND, and forward error bound FERR could be
! 242: * unreliable. If factorization fails with 0<INFO<=N, then
! 243: * RWORK(1) contains the reciprocal pivot growth factor for the
! 244: * leading INFO columns of A.
! 245: *
! 246: * INFO (output) INTEGER
! 247: * = 0: successful exit
! 248: * < 0: if INFO = -i, the i-th argument had an illegal value
! 249: * > 0: if INFO = i, and i is
! 250: * <= N: U(i,i) is exactly zero. The factorization
! 251: * has been completed, but the factor U is exactly
! 252: * singular, so the solution and error bounds
! 253: * could not be computed. RCOND = 0 is returned.
! 254: * = N+1: U is nonsingular, but RCOND is less than machine
! 255: * precision, meaning that the matrix is singular
! 256: * to working precision. Nevertheless, the
! 257: * solution and error bounds are computed because
! 258: * there are a number of situations where the
! 259: * computed solution can be more accurate than the
! 260: * value of RCOND would suggest.
! 261: *
! 262: * =====================================================================
! 263: * Moved setting of INFO = N+1 so INFO does not subsequently get
! 264: * overwritten. Sven, 17 Mar 05.
! 265: * =====================================================================
! 266: *
! 267: * .. Parameters ..
! 268: DOUBLE PRECISION ZERO, ONE
! 269: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 270: * ..
! 271: * .. Local Scalars ..
! 272: LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
! 273: CHARACTER NORM
! 274: INTEGER I, INFEQU, J, J1, J2
! 275: DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
! 276: $ ROWCND, RPVGRW, SMLNUM
! 277: * ..
! 278: * .. External Functions ..
! 279: LOGICAL LSAME
! 280: DOUBLE PRECISION DLAMCH, ZLANGB, ZLANTB
! 281: EXTERNAL LSAME, DLAMCH, ZLANGB, ZLANTB
! 282: * ..
! 283: * .. External Subroutines ..
! 284: EXTERNAL XERBLA, ZCOPY, ZGBCON, ZGBEQU, ZGBRFS, ZGBTRF,
! 285: $ ZGBTRS, ZLACPY, ZLAQGB
! 286: * ..
! 287: * .. Intrinsic Functions ..
! 288: INTRINSIC ABS, MAX, MIN
! 289: * ..
! 290: * .. Executable Statements ..
! 291: *
! 292: INFO = 0
! 293: NOFACT = LSAME( FACT, 'N' )
! 294: EQUIL = LSAME( FACT, 'E' )
! 295: NOTRAN = LSAME( TRANS, 'N' )
! 296: IF( NOFACT .OR. EQUIL ) THEN
! 297: EQUED = 'N'
! 298: ROWEQU = .FALSE.
! 299: COLEQU = .FALSE.
! 300: ELSE
! 301: ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
! 302: COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
! 303: SMLNUM = DLAMCH( 'Safe minimum' )
! 304: BIGNUM = ONE / SMLNUM
! 305: END IF
! 306: *
! 307: * Test the input parameters.
! 308: *
! 309: IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.LSAME( FACT, 'F' ) )
! 310: $ THEN
! 311: INFO = -1
! 312: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
! 313: $ LSAME( TRANS, 'C' ) ) THEN
! 314: INFO = -2
! 315: ELSE IF( N.LT.0 ) THEN
! 316: INFO = -3
! 317: ELSE IF( KL.LT.0 ) THEN
! 318: INFO = -4
! 319: ELSE IF( KU.LT.0 ) THEN
! 320: INFO = -5
! 321: ELSE IF( NRHS.LT.0 ) THEN
! 322: INFO = -6
! 323: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
! 324: INFO = -8
! 325: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
! 326: INFO = -10
! 327: ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
! 328: $ ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
! 329: INFO = -12
! 330: ELSE
! 331: IF( ROWEQU ) THEN
! 332: RCMIN = BIGNUM
! 333: RCMAX = ZERO
! 334: DO 10 J = 1, N
! 335: RCMIN = MIN( RCMIN, R( J ) )
! 336: RCMAX = MAX( RCMAX, R( J ) )
! 337: 10 CONTINUE
! 338: IF( RCMIN.LE.ZERO ) THEN
! 339: INFO = -13
! 340: ELSE IF( N.GT.0 ) THEN
! 341: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 342: ELSE
! 343: ROWCND = ONE
! 344: END IF
! 345: END IF
! 346: IF( COLEQU .AND. INFO.EQ.0 ) THEN
! 347: RCMIN = BIGNUM
! 348: RCMAX = ZERO
! 349: DO 20 J = 1, N
! 350: RCMIN = MIN( RCMIN, C( J ) )
! 351: RCMAX = MAX( RCMAX, C( J ) )
! 352: 20 CONTINUE
! 353: IF( RCMIN.LE.ZERO ) THEN
! 354: INFO = -14
! 355: ELSE IF( N.GT.0 ) THEN
! 356: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 357: ELSE
! 358: COLCND = ONE
! 359: END IF
! 360: END IF
! 361: IF( INFO.EQ.0 ) THEN
! 362: IF( LDB.LT.MAX( 1, N ) ) THEN
! 363: INFO = -16
! 364: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
! 365: INFO = -18
! 366: END IF
! 367: END IF
! 368: END IF
! 369: *
! 370: IF( INFO.NE.0 ) THEN
! 371: CALL XERBLA( 'ZGBSVX', -INFO )
! 372: RETURN
! 373: END IF
! 374: *
! 375: IF( EQUIL ) THEN
! 376: *
! 377: * Compute row and column scalings to equilibrate the matrix A.
! 378: *
! 379: CALL ZGBEQU( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 380: $ AMAX, INFEQU )
! 381: IF( INFEQU.EQ.0 ) THEN
! 382: *
! 383: * Equilibrate the matrix.
! 384: *
! 385: CALL ZLAQGB( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 386: $ AMAX, EQUED )
! 387: ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
! 388: COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
! 389: END IF
! 390: END IF
! 391: *
! 392: * Scale the right hand side.
! 393: *
! 394: IF( NOTRAN ) THEN
! 395: IF( ROWEQU ) THEN
! 396: DO 40 J = 1, NRHS
! 397: DO 30 I = 1, N
! 398: B( I, J ) = R( I )*B( I, J )
! 399: 30 CONTINUE
! 400: 40 CONTINUE
! 401: END IF
! 402: ELSE IF( COLEQU ) THEN
! 403: DO 60 J = 1, NRHS
! 404: DO 50 I = 1, N
! 405: B( I, J ) = C( I )*B( I, J )
! 406: 50 CONTINUE
! 407: 60 CONTINUE
! 408: END IF
! 409: *
! 410: IF( NOFACT .OR. EQUIL ) THEN
! 411: *
! 412: * Compute the LU factorization of the band matrix A.
! 413: *
! 414: DO 70 J = 1, N
! 415: J1 = MAX( J-KU, 1 )
! 416: J2 = MIN( J+KL, N )
! 417: CALL ZCOPY( J2-J1+1, AB( KU+1-J+J1, J ), 1,
! 418: $ AFB( KL+KU+1-J+J1, J ), 1 )
! 419: 70 CONTINUE
! 420: *
! 421: CALL ZGBTRF( N, N, KL, KU, AFB, LDAFB, IPIV, INFO )
! 422: *
! 423: * Return if INFO is non-zero.
! 424: *
! 425: IF( INFO.GT.0 ) THEN
! 426: *
! 427: * Compute the reciprocal pivot growth factor of the
! 428: * leading rank-deficient INFO columns of A.
! 429: *
! 430: ANORM = ZERO
! 431: DO 90 J = 1, INFO
! 432: DO 80 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
! 433: ANORM = MAX( ANORM, ABS( AB( I, J ) ) )
! 434: 80 CONTINUE
! 435: 90 CONTINUE
! 436: RPVGRW = ZLANTB( 'M', 'U', 'N', INFO, MIN( INFO-1, KL+KU ),
! 437: $ AFB( MAX( 1, KL+KU+2-INFO ), 1 ), LDAFB,
! 438: $ RWORK )
! 439: IF( RPVGRW.EQ.ZERO ) THEN
! 440: RPVGRW = ONE
! 441: ELSE
! 442: RPVGRW = ANORM / RPVGRW
! 443: END IF
! 444: RWORK( 1 ) = RPVGRW
! 445: RCOND = ZERO
! 446: RETURN
! 447: END IF
! 448: END IF
! 449: *
! 450: * Compute the norm of the matrix A and the
! 451: * reciprocal pivot growth factor RPVGRW.
! 452: *
! 453: IF( NOTRAN ) THEN
! 454: NORM = '1'
! 455: ELSE
! 456: NORM = 'I'
! 457: END IF
! 458: ANORM = ZLANGB( NORM, N, KL, KU, AB, LDAB, RWORK )
! 459: RPVGRW = ZLANTB( 'M', 'U', 'N', N, KL+KU, AFB, LDAFB, RWORK )
! 460: IF( RPVGRW.EQ.ZERO ) THEN
! 461: RPVGRW = ONE
! 462: ELSE
! 463: RPVGRW = ZLANGB( 'M', N, KL, KU, AB, LDAB, RWORK ) / RPVGRW
! 464: END IF
! 465: *
! 466: * Compute the reciprocal of the condition number of A.
! 467: *
! 468: CALL ZGBCON( NORM, N, KL, KU, AFB, LDAFB, IPIV, ANORM, RCOND,
! 469: $ WORK, RWORK, INFO )
! 470: *
! 471: * Compute the solution matrix X.
! 472: *
! 473: CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
! 474: CALL ZGBTRS( TRANS, N, KL, KU, NRHS, AFB, LDAFB, IPIV, X, LDX,
! 475: $ INFO )
! 476: *
! 477: * Use iterative refinement to improve the computed solution and
! 478: * compute error bounds and backward error estimates for it.
! 479: *
! 480: CALL ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
! 481: $ B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
! 482: *
! 483: * Transform the solution matrix X to a solution of the original
! 484: * system.
! 485: *
! 486: IF( NOTRAN ) THEN
! 487: IF( COLEQU ) THEN
! 488: DO 110 J = 1, NRHS
! 489: DO 100 I = 1, N
! 490: X( I, J ) = C( I )*X( I, J )
! 491: 100 CONTINUE
! 492: 110 CONTINUE
! 493: DO 120 J = 1, NRHS
! 494: FERR( J ) = FERR( J ) / COLCND
! 495: 120 CONTINUE
! 496: END IF
! 497: ELSE IF( ROWEQU ) THEN
! 498: DO 140 J = 1, NRHS
! 499: DO 130 I = 1, N
! 500: X( I, J ) = R( I )*X( I, J )
! 501: 130 CONTINUE
! 502: 140 CONTINUE
! 503: DO 150 J = 1, NRHS
! 504: FERR( J ) = FERR( J ) / ROWCND
! 505: 150 CONTINUE
! 506: END IF
! 507: *
! 508: * Set INFO = N+1 if the matrix is singular to working precision.
! 509: *
! 510: IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
! 511: $ INFO = N + 1
! 512: *
! 513: RWORK( 1 ) = RPVGRW
! 514: RETURN
! 515: *
! 516: * End of ZGBSVX
! 517: *
! 518: END
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