1: SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
2: $ AF, LDAF, IPIV, COLEQU, C, B, LDB,
3: $ Y, LDY, BERR_OUT, N_NORMS,
4: $ ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
5: $ AYB, DY, Y_TAIL, RCOND, ITHRESH,
6: $ RTHRESH, DZ_UB, IGNORE_CWISE,
7: $ INFO )
8: *
9: * -- LAPACK routine (version 3.2.2) --
10: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
11: * -- Jason Riedy of Univ. of California Berkeley. --
12: * -- June 2010 --
13: *
14: * -- LAPACK is a software package provided by Univ. of Tennessee, --
15: * -- Univ. of California Berkeley and NAG Ltd. --
16: *
17: IMPLICIT NONE
18: * ..
19: * .. Scalar Arguments ..
20: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
21: $ N_NORMS, ITHRESH
22: CHARACTER UPLO
23: LOGICAL COLEQU, IGNORE_CWISE
24: DOUBLE PRECISION RTHRESH, DZ_UB
25: * ..
26: * .. Array Arguments ..
27: INTEGER IPIV( * )
28: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
29: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
30: DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
31: $ ERR_BNDS_NORM( NRHS, * ),
32: $ ERR_BNDS_COMP( NRHS, * )
33: * ..
34: *
35: * Purpose
36: * =======
37: *
38: * DLA_SYRFSX_EXTENDED improves the computed solution to a system of
39: * linear equations by performing extra-precise iterative refinement
40: * and provides error bounds and backward error estimates for the solution.
41: * This subroutine is called by DSYRFSX to perform iterative refinement.
42: * In addition to normwise error bound, the code provides maximum
43: * componentwise error bound if possible. See comments for ERR_BNDS_NORM
44: * and ERR_BNDS_COMP for details of the error bounds. Note that this
45: * subroutine is only resonsible for setting the second fields of
46: * ERR_BNDS_NORM and ERR_BNDS_COMP.
47: *
48: * Arguments
49: * =========
50: *
51: * PREC_TYPE (input) INTEGER
52: * Specifies the intermediate precision to be used in refinement.
53: * The value is defined by ILAPREC(P) where P is a CHARACTER and
54: * P = 'S': Single
55: * = 'D': Double
56: * = 'I': Indigenous
57: * = 'X', 'E': Extra
58: *
59: * UPLO (input) CHARACTER*1
60: * = 'U': Upper triangle of A is stored;
61: * = 'L': Lower triangle of A is stored.
62: *
63: * N (input) INTEGER
64: * The number of linear equations, i.e., the order of the
65: * matrix A. N >= 0.
66: *
67: * NRHS (input) INTEGER
68: * The number of right-hand-sides, i.e., the number of columns of the
69: * matrix B.
70: *
71: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
72: * On entry, the N-by-N matrix A.
73: *
74: * LDA (input) INTEGER
75: * The leading dimension of the array A. LDA >= max(1,N).
76: *
77: * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
78: * The block diagonal matrix D and the multipliers used to
79: * obtain the factor U or L as computed by DSYTRF.
80: *
81: * LDAF (input) INTEGER
82: * The leading dimension of the array AF. LDAF >= max(1,N).
83: *
84: * IPIV (input) INTEGER array, dimension (N)
85: * Details of the interchanges and the block structure of D
86: * as determined by DSYTRF.
87: *
88: * COLEQU (input) LOGICAL
89: * If .TRUE. then column equilibration was done to A before calling
90: * this routine. This is needed to compute the solution and error
91: * bounds correctly.
92: *
93: * C (input) DOUBLE PRECISION array, dimension (N)
94: * The column scale factors for A. If COLEQU = .FALSE., C
95: * is not accessed. If C is input, each element of C should be a power
96: * of the radix to ensure a reliable solution and error estimates.
97: * Scaling by powers of the radix does not cause rounding errors unless
98: * the result underflows or overflows. Rounding errors during scaling
99: * lead to refining with a matrix that is not equivalent to the
100: * input matrix, producing error estimates that may not be
101: * reliable.
102: *
103: * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
104: * The right-hand-side matrix B.
105: *
106: * LDB (input) INTEGER
107: * The leading dimension of the array B. LDB >= max(1,N).
108: *
109: * Y (input/output) DOUBLE PRECISION array, dimension
110: * (LDY,NRHS)
111: * On entry, the solution matrix X, as computed by DSYTRS.
112: * On exit, the improved solution matrix Y.
113: *
114: * LDY (input) INTEGER
115: * The leading dimension of the array Y. LDY >= max(1,N).
116: *
117: * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS)
118: * On exit, BERR_OUT(j) contains the componentwise relative backward
119: * error for right-hand-side j from the formula
120: * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
121: * where abs(Z) is the componentwise absolute value of the matrix
122: * or vector Z. This is computed by DLA_LIN_BERR.
123: *
124: * N_NORMS (input) INTEGER
125: * Determines which error bounds to return (see ERR_BNDS_NORM
126: * and ERR_BNDS_COMP).
127: * If N_NORMS >= 1 return normwise error bounds.
128: * If N_NORMS >= 2 return componentwise error bounds.
129: *
130: * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension
131: * (NRHS, N_ERR_BNDS)
132: * For each right-hand side, this array contains information about
133: * various error bounds and condition numbers corresponding to the
134: * normwise relative error, which is defined as follows:
135: *
136: * Normwise relative error in the ith solution vector:
137: * max_j (abs(XTRUE(j,i) - X(j,i)))
138: * ------------------------------
139: * max_j abs(X(j,i))
140: *
141: * The array is indexed by the type of error information as described
142: * below. There currently are up to three pieces of information
143: * returned.
144: *
145: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
146: * right-hand side.
147: *
148: * The second index in ERR_BNDS_NORM(:,err) contains the following
149: * three fields:
150: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
151: * reciprocal condition number is less than the threshold
152: * sqrt(n) * slamch('Epsilon').
153: *
154: * err = 2 "Guaranteed" error bound: The estimated forward error,
155: * almost certainly within a factor of 10 of the true error
156: * so long as the next entry is greater than the threshold
157: * sqrt(n) * slamch('Epsilon'). This error bound should only
158: * be trusted if the previous boolean is true.
159: *
160: * err = 3 Reciprocal condition number: Estimated normwise
161: * reciprocal condition number. Compared with the threshold
162: * sqrt(n) * slamch('Epsilon') to determine if the error
163: * estimate is "guaranteed". These reciprocal condition
164: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
165: * appropriately scaled matrix Z.
166: * Let Z = S*A, where S scales each row by a power of the
167: * radix so all absolute row sums of Z are approximately 1.
168: *
169: * This subroutine is only responsible for setting the second field
170: * above.
171: * See Lapack Working Note 165 for further details and extra
172: * cautions.
173: *
174: * ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension
175: * (NRHS, N_ERR_BNDS)
176: * For each right-hand side, this array contains information about
177: * various error bounds and condition numbers corresponding to the
178: * componentwise relative error, which is defined as follows:
179: *
180: * Componentwise relative error in the ith solution vector:
181: * abs(XTRUE(j,i) - X(j,i))
182: * max_j ----------------------
183: * abs(X(j,i))
184: *
185: * The array is indexed by the right-hand side i (on which the
186: * componentwise relative error depends), and the type of error
187: * information as described below. There currently are up to three
188: * pieces of information returned for each right-hand side. If
189: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
190: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
191: * the first (:,N_ERR_BNDS) entries are returned.
192: *
193: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
194: * right-hand side.
195: *
196: * The second index in ERR_BNDS_COMP(:,err) contains the following
197: * three fields:
198: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
199: * reciprocal condition number is less than the threshold
200: * sqrt(n) * slamch('Epsilon').
201: *
202: * err = 2 "Guaranteed" error bound: The estimated forward error,
203: * almost certainly within a factor of 10 of the true error
204: * so long as the next entry is greater than the threshold
205: * sqrt(n) * slamch('Epsilon'). This error bound should only
206: * be trusted if the previous boolean is true.
207: *
208: * err = 3 Reciprocal condition number: Estimated componentwise
209: * reciprocal condition number. Compared with the threshold
210: * sqrt(n) * slamch('Epsilon') to determine if the error
211: * estimate is "guaranteed". These reciprocal condition
212: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
213: * appropriately scaled matrix Z.
214: * Let Z = S*(A*diag(x)), where x is the solution for the
215: * current right-hand side and S scales each row of
216: * A*diag(x) by a power of the radix so all absolute row
217: * sums of Z are approximately 1.
218: *
219: * This subroutine is only responsible for setting the second field
220: * above.
221: * See Lapack Working Note 165 for further details and extra
222: * cautions.
223: *
224: * RES (input) DOUBLE PRECISION array, dimension (N)
225: * Workspace to hold the intermediate residual.
226: *
227: * AYB (input) DOUBLE PRECISION array, dimension (N)
228: * Workspace. This can be the same workspace passed for Y_TAIL.
229: *
230: * DY (input) DOUBLE PRECISION array, dimension (N)
231: * Workspace to hold the intermediate solution.
232: *
233: * Y_TAIL (input) DOUBLE PRECISION array, dimension (N)
234: * Workspace to hold the trailing bits of the intermediate solution.
235: *
236: * RCOND (input) DOUBLE PRECISION
237: * Reciprocal scaled condition number. This is an estimate of the
238: * reciprocal Skeel condition number of the matrix A after
239: * equilibration (if done). If this is less than the machine
240: * precision (in particular, if it is zero), the matrix is singular
241: * to working precision. Note that the error may still be small even
242: * if this number is very small and the matrix appears ill-
243: * conditioned.
244: *
245: * ITHRESH (input) INTEGER
246: * The maximum number of residual computations allowed for
247: * refinement. The default is 10. For 'aggressive' set to 100 to
248: * permit convergence using approximate factorizations or
249: * factorizations other than LU. If the factorization uses a
250: * technique other than Gaussian elimination, the guarantees in
251: * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
252: *
253: * RTHRESH (input) DOUBLE PRECISION
254: * Determines when to stop refinement if the error estimate stops
255: * decreasing. Refinement will stop when the next solution no longer
256: * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
257: * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
258: * default value is 0.5. For 'aggressive' set to 0.9 to permit
259: * convergence on extremely ill-conditioned matrices. See LAWN 165
260: * for more details.
261: *
262: * DZ_UB (input) DOUBLE PRECISION
263: * Determines when to start considering componentwise convergence.
264: * Componentwise convergence is only considered after each component
265: * of the solution Y is stable, which we definte as the relative
266: * change in each component being less than DZ_UB. The default value
267: * is 0.25, requiring the first bit to be stable. See LAWN 165 for
268: * more details.
269: *
270: * IGNORE_CWISE (input) LOGICAL
271: * If .TRUE. then ignore componentwise convergence. Default value
272: * is .FALSE..
273: *
274: * INFO (output) INTEGER
275: * = 0: Successful exit.
276: * < 0: if INFO = -i, the ith argument to DSYTRS had an illegal
277: * value
278: *
279: * =====================================================================
280: *
281: * .. Local Scalars ..
282: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE
283: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
284: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
285: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
286: $ EPS, HUGEVAL, INCR_THRESH
287: LOGICAL INCR_PREC
288: * ..
289: * .. Parameters ..
290: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
291: $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
292: $ EXTRA_RESIDUAL, EXTRA_Y
293: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
294: $ CONV_STATE = 2, NOPROG_STATE = 3 )
295: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
296: $ EXTRA_Y = 2 )
297: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
298: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
299: INTEGER CMP_ERR_I, PIV_GROWTH_I
300: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
301: $ BERR_I = 3 )
302: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
303: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
304: $ PIV_GROWTH_I = 9 )
305: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
306: $ LA_LINRX_CWISE_I
307: PARAMETER ( LA_LINRX_ITREF_I = 1,
308: $ LA_LINRX_ITHRESH_I = 2 )
309: PARAMETER ( LA_LINRX_CWISE_I = 3 )
310: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
311: $ LA_LINRX_RCOND_I
312: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
313: PARAMETER ( LA_LINRX_RCOND_I = 3 )
314: * ..
315: * .. External Functions ..
316: LOGICAL LSAME
317: EXTERNAL ILAUPLO
318: INTEGER ILAUPLO
319: * ..
320: * .. External Subroutines ..
321: EXTERNAL DAXPY, DCOPY, DSYTRS, DSYMV, BLAS_DSYMV_X,
322: $ BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
323: $ DLA_LIN_BERR
324: DOUBLE PRECISION DLAMCH
325: * ..
326: * .. Intrinsic Functions ..
327: INTRINSIC ABS, MAX, MIN
328: * ..
329: * .. Executable Statements ..
330: *
331: IF ( INFO.NE.0 ) RETURN
332: EPS = DLAMCH( 'Epsilon' )
333: HUGEVAL = DLAMCH( 'Overflow' )
334: * Force HUGEVAL to Inf
335: HUGEVAL = HUGEVAL * HUGEVAL
336: * Using HUGEVAL may lead to spurious underflows.
337: INCR_THRESH = DBLE( N )*EPS
338:
339: IF ( LSAME ( UPLO, 'L' ) ) THEN
340: UPLO2 = ILAUPLO( 'L' )
341: ELSE
342: UPLO2 = ILAUPLO( 'U' )
343: ENDIF
344:
345: DO J = 1, NRHS
346: Y_PREC_STATE = EXTRA_RESIDUAL
347: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
348: DO I = 1, N
349: Y_TAIL( I ) = 0.0D+0
350: END DO
351: END IF
352:
353: DXRAT = 0.0D+0
354: DXRATMAX = 0.0D+0
355: DZRAT = 0.0D+0
356: DZRATMAX = 0.0D+0
357: FINAL_DX_X = HUGEVAL
358: FINAL_DZ_Z = HUGEVAL
359: PREVNORMDX = HUGEVAL
360: PREV_DZ_Z = HUGEVAL
361: DZ_Z = HUGEVAL
362: DX_X = HUGEVAL
363:
364: X_STATE = WORKING_STATE
365: Z_STATE = UNSTABLE_STATE
366: INCR_PREC = .FALSE.
367:
368: DO CNT = 1, ITHRESH
369: *
370: * Compute residual RES = B_s - op(A_s) * Y,
371: * op(A) = A, A**T, or A**H depending on TRANS (and type).
372: *
373: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
374: IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN
375: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
376: $ 1.0D+0, RES, 1 )
377: ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
378: CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
379: $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
380: ELSE
381: CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
382: $ Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
383: END IF
384:
385: ! XXX: RES is no longer needed.
386: CALL DCOPY( N, RES, 1, DY, 1 )
387: CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
388: *
389: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
390: *
391: NORMX = 0.0D+0
392: NORMY = 0.0D+0
393: NORMDX = 0.0D+0
394: DZ_Z = 0.0D+0
395: YMIN = HUGEVAL
396:
397: DO I = 1, N
398: YK = ABS( Y( I, J ) )
399: DYK = ABS( DY( I ) )
400:
401: IF ( YK .NE. 0.0D+0 ) THEN
402: DZ_Z = MAX( DZ_Z, DYK / YK )
403: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
404: DZ_Z = HUGEVAL
405: END IF
406:
407: YMIN = MIN( YMIN, YK )
408:
409: NORMY = MAX( NORMY, YK )
410:
411: IF ( COLEQU ) THEN
412: NORMX = MAX( NORMX, YK * C( I ) )
413: NORMDX = MAX( NORMDX, DYK * C( I ) )
414: ELSE
415: NORMX = NORMY
416: NORMDX = MAX(NORMDX, DYK)
417: END IF
418: END DO
419:
420: IF ( NORMX .NE. 0.0D+0 ) THEN
421: DX_X = NORMDX / NORMX
422: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
423: DX_X = 0.0D+0
424: ELSE
425: DX_X = HUGEVAL
426: END IF
427:
428: DXRAT = NORMDX / PREVNORMDX
429: DZRAT = DZ_Z / PREV_DZ_Z
430: *
431: * Check termination criteria.
432: *
433: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
434: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
435: $ INCR_PREC = .TRUE.
436:
437: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
438: $ X_STATE = WORKING_STATE
439: IF ( X_STATE .EQ. WORKING_STATE ) THEN
440: IF ( DX_X .LE. EPS ) THEN
441: X_STATE = CONV_STATE
442: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
443: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
444: INCR_PREC = .TRUE.
445: ELSE
446: X_STATE = NOPROG_STATE
447: END IF
448: ELSE
449: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
450: END IF
451: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
452: END IF
453:
454: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
455: $ Z_STATE = WORKING_STATE
456: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
457: $ Z_STATE = WORKING_STATE
458: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
459: IF ( DZ_Z .LE. EPS ) THEN
460: Z_STATE = CONV_STATE
461: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
462: Z_STATE = UNSTABLE_STATE
463: DZRATMAX = 0.0D+0
464: FINAL_DZ_Z = HUGEVAL
465: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
466: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
467: INCR_PREC = .TRUE.
468: ELSE
469: Z_STATE = NOPROG_STATE
470: END IF
471: ELSE
472: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
473: END IF
474: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
475: END IF
476:
477: IF ( X_STATE.NE.WORKING_STATE.AND.
478: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
479: $ GOTO 666
480:
481: IF ( INCR_PREC ) THEN
482: INCR_PREC = .FALSE.
483: Y_PREC_STATE = Y_PREC_STATE + 1
484: DO I = 1, N
485: Y_TAIL( I ) = 0.0D+0
486: END DO
487: END IF
488:
489: PREVNORMDX = NORMDX
490: PREV_DZ_Z = DZ_Z
491: *
492: * Update soluton.
493: *
494: IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
495: CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
496: ELSE
497: CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
498: END IF
499:
500: END DO
501: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
502: 666 CONTINUE
503: *
504: * Set final_* when cnt hits ithresh.
505: *
506: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
507: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
508: *
509: * Compute error bounds.
510: *
511: IF ( N_NORMS .GE. 1 ) THEN
512: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
513: $ FINAL_DX_X / (1 - DXRATMAX)
514: END IF
515: IF ( N_NORMS .GE. 2 ) THEN
516: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
517: $ FINAL_DZ_Z / (1 - DZRATMAX)
518: END IF
519: *
520: * Compute componentwise relative backward error from formula
521: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
522: * where abs(Z) is the componentwise absolute value of the matrix
523: * or vector Z.
524: *
525: * Compute residual RES = B_s - op(A_s) * Y,
526: * op(A) = A, A**T, or A**H depending on TRANS (and type).
527: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
528: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
529: $ 1 )
530:
531: DO I = 1, N
532: AYB( I ) = ABS( B( I, J ) )
533: END DO
534: *
535: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
536: *
537: CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
538: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
539:
540: CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
541: *
542: * End of loop for each RHS.
543: *
544: END DO
545: *
546: RETURN
547: END
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