1       SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
  2 *
  3 *  -- LAPACK routine (version 3.3.1)                                    --
  4 *
  5 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
  6 *  -- April 2011                                                      --
  7 *
  8 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  9 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 10 *
 11 *     ..
 12 *     .. Scalar Arguments ..
 13       CHARACTER          TRANSR, UPLO
 14       INTEGER            INFO, N
 15 *     ..
 16 *     .. Array Arguments ..
 17       COMPLEX*16         AP( 0* ), ARF( 0* )
 18 *
 19 *  Purpose
 20 *  =======
 21 *
 22 *  ZTPTTF copies a triangular matrix A from standard packed format (TP)
 23 *  to rectangular full packed format (TF).
 24 *
 25 *  Arguments
 26 *  =========
 27 *
 28 *  TRANSR   (input) CHARACTER*1
 29 *          = 'N':  ARF in Normal format is wanted;
 30 *          = 'C':  ARF in Conjugate-transpose format is wanted.
 31 *
 32 *  UPLO    (input) CHARACTER*1
 33 *          = 'U':  A is upper triangular;
 34 *          = 'L':  A is lower triangular.
 35 *
 36 *  N       (input) INTEGER
 37 *          The order of the matrix A.  N >= 0.
 38 *
 39 *  AP      (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
 40 *          On entry, the upper or lower triangular matrix A, packed
 41 *          columnwise in a linear array. The j-th column of A is stored
 42 *          in the array AP as follows:
 43 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
 44 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
 45 *
 46 *  ARF     (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
 47 *          On exit, the upper or lower triangular matrix A stored in
 48 *          RFP format. For a further discussion see Notes below.
 49 *
 50 *  INFO    (output) INTEGER
 51 *          = 0:  successful exit
 52 *          < 0:  if INFO = -i, the i-th argument had an illegal value
 53 *
 54 *  Further Details
 55 *  ===============
 56 *
 57 *  We first consider Standard Packed Format when N is even.
 58 *  We give an example where N = 6.
 59 *
 60 *      AP is Upper             AP is Lower
 61 *
 62 *   00 01 02 03 04 05       00
 63 *      11 12 13 14 15       10 11
 64 *         22 23 24 25       20 21 22
 65 *            33 34 35       30 31 32 33
 66 *               44 45       40 41 42 43 44
 67 *                  55       50 51 52 53 54 55
 68 *
 69 *
 70 *  Let TRANSR = 'N'. RFP holds AP as follows:
 71 *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
 72 *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
 73 *  conjugate-transpose of the first three columns of AP upper.
 74 *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
 75 *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
 76 *  conjugate-transpose of the last three columns of AP lower.
 77 *  To denote conjugate we place -- above the element. This covers the
 78 *  case N even and TRANSR = 'N'.
 79 *
 80 *         RFP A                   RFP A
 81 *
 82 *                                -- -- --
 83 *        03 04 05                33 43 53
 84 *                                   -- --
 85 *        13 14 15                00 44 54
 86 *                                      --
 87 *        23 24 25                10 11 55
 88 *
 89 *        33 34 35                20 21 22
 90 *        --
 91 *        00 44 45                30 31 32
 92 *        -- --
 93 *        01 11 55                40 41 42
 94 *        -- -- --
 95 *        02 12 22                50 51 52
 96 *
 97 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
 98 *  transpose of RFP A above. One therefore gets:
 99 *
100 *
101 *           RFP A                   RFP A
102 *
103 *     -- -- -- --                -- -- -- -- -- --
104 *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
105 *     -- -- -- -- --                -- -- -- -- --
106 *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
107 *     -- -- -- -- -- --                -- -- -- --
108 *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
109 *
110 *
111 *  We next  consider Standard Packed Format when N is odd.
112 *  We give an example where N = 5.
113 *
114 *     AP is Upper                 AP is Lower
115 *
116 *   00 01 02 03 04              00
117 *      11 12 13 14              10 11
118 *         22 23 24              20 21 22
119 *            33 34              30 31 32 33
120 *               44              40 41 42 43 44
121 *
122 *
123 *  Let TRANSR = 'N'. RFP holds AP as follows:
124 *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
125 *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
126 *  conjugate-transpose of the first two   columns of AP upper.
127 *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
128 *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
129 *  conjugate-transpose of the last two   columns of AP lower.
130 *  To denote conjugate we place -- above the element. This covers the
131 *  case N odd  and TRANSR = 'N'.
132 *
133 *         RFP A                   RFP A
134 *
135 *                                   -- --
136 *        02 03 04                00 33 43
137 *                                      --
138 *        12 13 14                10 11 44
139 *
140 *        22 23 24                20 21 22
141 *        --
142 *        00 33 34                30 31 32
143 *        -- --
144 *        01 11 44                40 41 42
145 *
146 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
147 *  transpose of RFP A above. One therefore gets:
148 *
149 *
150 *           RFP A                   RFP A
151 *
152 *     -- -- --                   -- -- -- -- -- --
153 *     02 12 22 00 01             00 10 20 30 40 50
154 *     -- -- -- --                   -- -- -- -- --
155 *     03 13 23 33 11             33 11 21 31 41 51
156 *     -- -- -- -- --                   -- -- -- --
157 *     04 14 24 34 44             43 44 22 32 42 52
158 *
159 *  =====================================================================
160 *
161 *     .. Parameters ..
162 *     ..
163 *     .. Local Scalars ..
164       LOGICAL            LOWER, NISODD, NORMALTRANSR
165       INTEGER            N1, N2, K, NT
166       INTEGER            I, J, IJ
167       INTEGER            IJP, JP, LDA, JS
168 *     ..
169 *     .. External Functions ..
170       LOGICAL            LSAME
171       EXTERNAL           LSAME
172 *     ..
173 *     .. External Subroutines ..
174       EXTERNAL           XERBLA
175 *     ..
176 *     .. Intrinsic Functions ..
177       INTRINSIC          DCONJGMOD
178 *     ..
179 *     .. Executable Statements ..
180 *
181 *     Test the input parameters.
182 *
183       INFO = 0
184       NORMALTRANSR = LSAME( TRANSR, 'N' )
185       LOWER = LSAME( UPLO, 'L' )
186       IF.NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
187          INFO = -1
188       ELSE IF.NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
189          INFO = -2
190       ELSE IF( N.LT.0 ) THEN
191          INFO = -3
192       END IF
193       IF( INFO.NE.0 ) THEN
194          CALL XERBLA( 'ZTPTTF'-INFO )
195          RETURN
196       END IF
197 *
198 *     Quick return if possible
199 *
200       IF( N.EQ.0 )
201      $   RETURN
202 *
203       IF( N.EQ.1 ) THEN
204          IF( NORMALTRANSR ) THEN
205             ARF( 0 ) = AP( 0 )
206          ELSE
207             ARF( 0 ) = DCONJG( AP( 0 ) )
208          END IF
209          RETURN
210       END IF
211 *
212 *     Size of array ARF(0:NT-1)
213 *
214       NT = N*( N+1 ) / 2
215 *
216 *     Set N1 and N2 depending on LOWER
217 *
218       IF( LOWER ) THEN
219          N2 = N / 2
220          N1 = N - N2
221       ELSE
222          N1 = N / 2
223          N2 = N - N1
224       END IF
225 *
226 *     If N is odd, set NISODD = .TRUE.
227 *     If N is even, set K = N/2 and NISODD = .FALSE.
228 *
229 *     set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
230 *     where noe = 0 if n is even, noe = 1 if n is odd
231 *
232       IFMOD( N, 2 ).EQ.0 ) THEN
233          K = N / 2
234          NISODD = .FALSE.
235          LDA = N + 1
236       ELSE
237          NISODD = .TRUE.
238          LDA = N
239       END IF
240 *
241 *     ARF^C has lda rows and n+1-noe cols
242 *
243       IF.NOT.NORMALTRANSR )
244      $   LDA = ( N+1 ) / 2
245 *
246 *     start execution: there are eight cases
247 *
248       IF( NISODD ) THEN
249 *
250 *        N is odd
251 *
252          IF( NORMALTRANSR ) THEN
253 *
254 *           N is odd and TRANSR = 'N'
255 *
256             IF( LOWER ) THEN
257 *
258 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
259 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
260 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
261 *
262                IJP = 0
263                JP = 0
264                DO J = 0, N2
265                   DO I = J, N - 1
266                      IJ = I + JP
267                      ARF( IJ ) = AP( IJP )
268                      IJP = IJP + 1
269                   END DO
270                   JP = JP + LDA
271                END DO
272                DO I = 0, N2 - 1
273                   DO J = 1 + I, N2
274                      IJ = I + J*LDA
275                      ARF( IJ ) = DCONJG( AP( IJP ) )
276                      IJP = IJP + 1
277                   END DO
278                END DO
279 *
280             ELSE
281 *
282 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
283 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
284 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
285 *
286                IJP = 0
287                DO J = 0, N1 - 1
288                   IJ = N2 + J
289                   DO I = 0, J
290                      ARF( IJ ) = DCONJG( AP( IJP ) )
291                      IJP = IJP + 1
292                      IJ = IJ + LDA
293                   END DO
294                END DO
295                JS = 0
296                DO J = N1, N - 1
297                   IJ = JS
298                   DO IJ = JS, JS + J
299                      ARF( IJ ) = AP( IJP )
300                      IJP = IJP + 1
301                   END DO
302                   JS = JS + LDA
303                END DO
304 *
305             END IF
306 *
307          ELSE
308 *
309 *           N is odd and TRANSR = 'C'
310 *
311             IF( LOWER ) THEN
312 *
313 *              SRPA for LOWER, TRANSPOSE and N is odd
314 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
315 *              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
316 *
317                IJP = 0
318                DO I = 0, N2
319                   DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
320                      ARF( IJ ) = DCONJG( AP( IJP ) )
321                      IJP = IJP + 1
322                   END DO
323                END DO
324                JS = 1
325                DO J = 0, N2 - 1
326                   DO IJ = JS, JS + N2 - J - 1
327                      ARF( IJ ) = AP( IJP )
328                      IJP = IJP + 1
329                   END DO
330                   JS = JS + LDA + 1
331                END DO
332 *
333             ELSE
334 *
335 *              SRPA for UPPER, TRANSPOSE and N is odd
336 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
337 *              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
338 *
339                IJP = 0
340                JS = N2*LDA
341                DO J = 0, N1 - 1
342                   DO IJ = JS, JS + J
343                      ARF( IJ ) = AP( IJP )
344                      IJP = IJP + 1
345                   END DO
346                   JS = JS + LDA
347                END DO
348                DO I = 0, N1
349                   DO IJ = I, I + ( N1+I )*LDA, LDA
350                      ARF( IJ ) = DCONJG( AP( IJP ) )
351                      IJP = IJP + 1
352                   END DO
353                END DO
354 *
355             END IF
356 *
357          END IF
358 *
359       ELSE
360 *
361 *        N is even
362 *
363          IF( NORMALTRANSR ) THEN
364 *
365 *           N is even and TRANSR = 'N'
366 *
367             IF( LOWER ) THEN
368 *
369 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
370 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
371 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
372 *
373                IJP = 0
374                JP = 0
375                DO J = 0, K - 1
376                   DO I = J, N - 1
377                      IJ = 1 + I + JP
378                      ARF( IJ ) = AP( IJP )
379                      IJP = IJP + 1
380                   END DO
381                   JP = JP + LDA
382                END DO
383                DO I = 0, K - 1
384                   DO J = I, K - 1
385                      IJ = I + J*LDA
386                      ARF( IJ ) = DCONJG( AP( IJP ) )
387                      IJP = IJP + 1
388                   END DO
389                END DO
390 *
391             ELSE
392 *
393 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
394 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
395 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
396 *
397                IJP = 0
398                DO J = 0, K - 1
399                   IJ = K + 1 + J
400                   DO I = 0, J
401                      ARF( IJ ) = DCONJG( AP( IJP ) )
402                      IJP = IJP + 1
403                      IJ = IJ + LDA
404                   END DO
405                END DO
406                JS = 0
407                DO J = K, N - 1
408                   IJ = JS
409                   DO IJ = JS, JS + J
410                      ARF( IJ ) = AP( IJP )
411                      IJP = IJP + 1
412                   END DO
413                   JS = JS + LDA
414                END DO
415 *
416             END IF
417 *
418          ELSE
419 *
420 *           N is even and TRANSR = 'C'
421 *
422             IF( LOWER ) THEN
423 *
424 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
425 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
426 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
427 *
428                IJP = 0
429                DO I = 0, K - 1
430                   DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
431                      ARF( IJ ) = DCONJG( AP( IJP ) )
432                      IJP = IJP + 1
433                   END DO
434                END DO
435                JS = 0
436                DO J = 0, K - 1
437                   DO IJ = JS, JS + K - J - 1
438                      ARF( IJ ) = AP( IJP )
439                      IJP = IJP + 1
440                   END DO
441                   JS = JS + LDA + 1
442                END DO
443 *
444             ELSE
445 *
446 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
447 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
448 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
449 *
450                IJP = 0
451                JS = ( K+1 )*LDA
452                DO J = 0, K - 1
453                   DO IJ = JS, JS + J
454                      ARF( IJ ) = AP( IJP )
455                      IJP = IJP + 1
456                   END DO
457                   JS = JS + LDA
458                END DO
459                DO I = 0, K - 1
460                   DO IJ = I, I + ( K+I )*LDA, LDA
461                      ARF( IJ ) = DCONJG( AP( IJP ) )
462                      IJP = IJP + 1
463                   END DO
464                END DO
465 *
466             END IF
467 *
468          END IF
469 *
470       END IF
471 *
472       RETURN
473 *
474 *     End of ZTPTTF
475 *
476       END