Annotation of rpl/lapack/lapack/zla_syrfsx_extended.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZLA_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: COMPLEX*16 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: * ZLA_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 ZSYRFSX 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) COMPLEX*16 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) COMPLEX*16 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 ZSYTRF.
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 ZSYTRF.
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) COMPLEX*16 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) COMPLEX*16 array, dimension
110: * (LDY,NRHS)
111: * On entry, the solution matrix X, as computed by ZSYTRS.
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 ZLA_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) COMPLEX*16 array, dimension (N)
225: * Workspace to hold the intermediate residual.
226: *
227: * AYB (input) DOUBLE PRECISION array, dimension (N)
228: * Workspace.
229: *
230: * DY (input) COMPLEX*16 array, dimension (N)
231: * Workspace to hold the intermediate solution.
232: *
233: * Y_TAIL (input) COMPLEX*16 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 ZSYTRS had an illegal
277: * value
278: *
279: * =====================================================================
280: *
281: * .. Local Scalars ..
282: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE,
283: $ Y_PREC_STATE
284: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
285: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
286: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
287: $ EPS, HUGEVAL, INCR_THRESH
288: LOGICAL INCR_PREC
289: COMPLEX*16 ZDUM
290: * ..
291: * .. Parameters ..
292: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
293: $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
294: $ EXTRA_Y
295: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
296: $ CONV_STATE = 2, NOPROG_STATE = 3 )
297: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
298: $ EXTRA_Y = 2 )
299: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
300: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
301: INTEGER CMP_ERR_I, PIV_GROWTH_I
302: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
303: $ BERR_I = 3 )
304: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
305: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
306: $ PIV_GROWTH_I = 9 )
307: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
308: $ LA_LINRX_CWISE_I
309: PARAMETER ( LA_LINRX_ITREF_I = 1,
310: $ LA_LINRX_ITHRESH_I = 2 )
311: PARAMETER ( LA_LINRX_CWISE_I = 3 )
312: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
313: $ LA_LINRX_RCOND_I
314: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
315: PARAMETER ( LA_LINRX_RCOND_I = 3 )
316: * ..
317: * .. External Functions ..
318: LOGICAL LSAME
319: EXTERNAL ILAUPLO
320: INTEGER ILAUPLO
321: * ..
322: * .. External Subroutines ..
323: EXTERNAL ZAXPY, ZCOPY, ZSYTRS, ZSYMV, BLAS_ZSYMV_X,
324: $ BLAS_ZSYMV2_X, ZLA_SYAMV, ZLA_WWADDW,
325: $ ZLA_LIN_BERR
326: DOUBLE PRECISION DLAMCH
327: * ..
328: * .. Intrinsic Functions ..
329: INTRINSIC ABS, REAL, DIMAG, MAX, MIN
330: * ..
331: * .. Statement Functions ..
332: DOUBLE PRECISION CABS1
333: * ..
334: * .. Statement Function Definitions ..
335: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
336: * ..
337: * .. Executable Statements ..
338: *
339: IF ( INFO.NE.0 ) RETURN
340: EPS = DLAMCH( 'Epsilon' )
341: HUGEVAL = DLAMCH( 'Overflow' )
342: * Force HUGEVAL to Inf
343: HUGEVAL = HUGEVAL * HUGEVAL
344: * Using HUGEVAL may lead to spurious underflows.
345: INCR_THRESH = DBLE( N ) * EPS
346:
347: IF ( LSAME ( UPLO, 'L' ) ) THEN
348: UPLO2 = ILAUPLO( 'L' )
349: ELSE
350: UPLO2 = ILAUPLO( 'U' )
351: ENDIF
352:
353: DO J = 1, NRHS
354: Y_PREC_STATE = EXTRA_RESIDUAL
355: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
356: DO I = 1, N
357: Y_TAIL( I ) = 0.0D+0
358: END DO
359: END IF
360:
361: DXRAT = 0.0D+0
362: DXRATMAX = 0.0D+0
363: DZRAT = 0.0D+0
364: DZRATMAX = 0.0D+0
365: FINAL_DX_X = HUGEVAL
366: FINAL_DZ_Z = HUGEVAL
367: PREVNORMDX = HUGEVAL
368: PREV_DZ_Z = HUGEVAL
369: DZ_Z = HUGEVAL
370: DX_X = HUGEVAL
371:
372: X_STATE = WORKING_STATE
373: Z_STATE = UNSTABLE_STATE
374: INCR_PREC = .FALSE.
375:
376: DO CNT = 1, ITHRESH
377: *
378: * Compute residual RES = B_s - op(A_s) * Y,
379: * op(A) = A, A**T, or A**H depending on TRANS (and type).
380: *
381: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
382: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
383: CALL ZSYMV( UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
384: $ DCMPLX(1.0D+0), RES, 1 )
385: ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
386: CALL BLAS_ZSYMV_X( UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
387: $ Y( 1, J ), 1, DCMPLX(1.0D+0), RES, 1, PREC_TYPE )
388: ELSE
389: CALL BLAS_ZSYMV2_X(UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
390: $ Y(1, J), Y_TAIL, 1, DCMPLX(1.0D+0), RES, 1,
391: $ PREC_TYPE)
392: END IF
393:
394: ! XXX: RES is no longer needed.
395: CALL ZCOPY( N, RES, 1, DY, 1 )
396: CALL ZSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
397: *
398: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
399: *
400: NORMX = 0.0D+0
401: NORMY = 0.0D+0
402: NORMDX = 0.0D+0
403: DZ_Z = 0.0D+0
404: YMIN = HUGEVAL
405:
406: DO I = 1, N
407: YK = CABS1( Y( I, J ) )
408: DYK = CABS1( DY( I ) )
409:
410: IF ( YK .NE. 0.0D+0 ) THEN
411: DZ_Z = MAX( DZ_Z, DYK / YK )
412: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
413: DZ_Z = HUGEVAL
414: END IF
415:
416: YMIN = MIN( YMIN, YK )
417:
418: NORMY = MAX( NORMY, YK )
419:
420: IF ( COLEQU ) THEN
421: NORMX = MAX( NORMX, YK * C( I ) )
422: NORMDX = MAX( NORMDX, DYK * C( I ) )
423: ELSE
424: NORMX = NORMY
425: NORMDX = MAX( NORMDX, DYK )
426: END IF
427: END DO
428:
429: IF ( NORMX .NE. 0.0D+0 ) THEN
430: DX_X = NORMDX / NORMX
431: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
432: DX_X = 0.0D+0
433: ELSE
434: DX_X = HUGEVAL
435: END IF
436:
437: DXRAT = NORMDX / PREVNORMDX
438: DZRAT = DZ_Z / PREV_DZ_Z
439: *
440: * Check termination criteria.
441: *
442: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
443: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
444: $ INCR_PREC = .TRUE.
445:
446: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
447: $ X_STATE = WORKING_STATE
448: IF ( X_STATE .EQ. WORKING_STATE ) THEN
449: IF ( DX_X .LE. EPS ) THEN
450: X_STATE = CONV_STATE
451: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
452: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
453: INCR_PREC = .TRUE.
454: ELSE
455: X_STATE = NOPROG_STATE
456: END IF
457: ELSE
458: IF (DXRAT .GT. DXRATMAX) DXRATMAX = DXRAT
459: END IF
460: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
461: END IF
462:
463: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
464: $ Z_STATE = WORKING_STATE
465: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
466: $ Z_STATE = WORKING_STATE
467: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
468: IF ( DZ_Z .LE. EPS ) THEN
469: Z_STATE = CONV_STATE
470: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
471: Z_STATE = UNSTABLE_STATE
472: DZRATMAX = 0.0D+0
473: FINAL_DZ_Z = HUGEVAL
474: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
475: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
476: INCR_PREC = .TRUE.
477: ELSE
478: Z_STATE = NOPROG_STATE
479: END IF
480: ELSE
481: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
482: END IF
483: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
484: END IF
485:
486: IF ( X_STATE.NE.WORKING_STATE.AND.
487: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
488: $ GOTO 666
489:
490: IF ( INCR_PREC ) THEN
491: INCR_PREC = .FALSE.
492: Y_PREC_STATE = Y_PREC_STATE + 1
493: DO I = 1, N
494: Y_TAIL( I ) = 0.0D+0
495: END DO
496: END IF
497:
498: PREVNORMDX = NORMDX
499: PREV_DZ_Z = DZ_Z
500: *
501: * Update soluton.
502: *
503: IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
504: CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
505: ELSE
506: CALL ZLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
507: END IF
508:
509: END DO
510: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
511: 666 CONTINUE
512: *
513: * Set final_* when cnt hits ithresh.
514: *
515: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
516: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
517: *
518: * Compute error bounds.
519: *
520: IF ( N_NORMS .GE. 1 ) THEN
521: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
522: $ FINAL_DX_X / (1 - DXRATMAX)
523: END IF
524: IF ( N_NORMS .GE. 2 ) THEN
525: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
526: $ FINAL_DZ_Z / (1 - DZRATMAX)
527: END IF
528: *
529: * Compute componentwise relative backward error from formula
530: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
531: * where abs(Z) is the componentwise absolute value of the matrix
532: * or vector Z.
533: *
534: * Compute residual RES = B_s - op(A_s) * Y,
535: * op(A) = A, A**T, or A**H depending on TRANS (and type).
536: *
537: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
538: CALL ZSYMV( UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
539: $ DCMPLX(1.0D+0), RES, 1 )
540:
541: DO I = 1, N
542: AYB( I ) = CABS1( B( I, J ) )
543: END DO
544: *
545: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
546: *
547: CALL ZLA_SYAMV ( UPLO2, N, 1.0D+0,
548: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
549:
550: CALL ZLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
551: *
552: * End of loop for each RHS.
553: *
554: END DO
555: *
556: RETURN
557: END
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