Annotation of rpl/lapack/lapack/ztpttf.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b ZTPTTF
1.1 bertrand 2: *
1.7 ! bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.7 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 ! bertrand 8: *> \htmlonly
! 9: *> Download ZTPTTF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztpttf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztpttf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpttf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANSR, UPLO
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AP( 0: * ), ARF( 0: * )
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZTPTTF copies a triangular matrix A from standard packed format (TP)
! 37: *> to rectangular full packed format (TF).
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] TRANSR
! 44: *> \verbatim
! 45: *> TRANSR is CHARACTER*1
! 46: *> = 'N': ARF in Normal format is wanted;
! 47: *> = 'C': ARF in Conjugate-transpose format is wanted.
! 48: *> \endverbatim
! 49: *>
! 50: *> \param[in] UPLO
! 51: *> \verbatim
! 52: *> UPLO is CHARACTER*1
! 53: *> = 'U': A is upper triangular;
! 54: *> = 'L': A is lower triangular.
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in] N
! 58: *> \verbatim
! 59: *> N is INTEGER
! 60: *> The order of the matrix A. N >= 0.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] AP
! 64: *> \verbatim
! 65: *> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 66: *> On entry, the upper or lower triangular matrix A, packed
! 67: *> columnwise in a linear array. The j-th column of A is stored
! 68: *> in the array AP as follows:
! 69: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 70: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[out] ARF
! 74: *> \verbatim
! 75: *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 76: *> On exit, the upper or lower triangular matrix A stored in
! 77: *> RFP format. For a further discussion see Notes below.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[out] INFO
! 81: *> \verbatim
! 82: *> INFO is INTEGER
! 83: *> = 0: successful exit
! 84: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 85: *> \endverbatim
! 86: *
! 87: * Authors:
! 88: * ========
! 89: *
! 90: *> \author Univ. of Tennessee
! 91: *> \author Univ. of California Berkeley
! 92: *> \author Univ. of Colorado Denver
! 93: *> \author NAG Ltd.
! 94: *
! 95: *> \date November 2011
! 96: *
! 97: *> \ingroup complex16OTHERcomputational
! 98: *
! 99: *> \par Further Details:
! 100: * =====================
! 101: *>
! 102: *> \verbatim
! 103: *>
! 104: *> We first consider Standard Packed Format when N is even.
! 105: *> We give an example where N = 6.
! 106: *>
! 107: *> AP is Upper AP is Lower
! 108: *>
! 109: *> 00 01 02 03 04 05 00
! 110: *> 11 12 13 14 15 10 11
! 111: *> 22 23 24 25 20 21 22
! 112: *> 33 34 35 30 31 32 33
! 113: *> 44 45 40 41 42 43 44
! 114: *> 55 50 51 52 53 54 55
! 115: *>
! 116: *>
! 117: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 118: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 119: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 120: *> conjugate-transpose of the first three columns of AP upper.
! 121: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 122: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 123: *> conjugate-transpose of the last three columns of AP lower.
! 124: *> To denote conjugate we place -- above the element. This covers the
! 125: *> case N even and TRANSR = 'N'.
! 126: *>
! 127: *> RFP A RFP A
! 128: *>
! 129: *> -- -- --
! 130: *> 03 04 05 33 43 53
! 131: *> -- --
! 132: *> 13 14 15 00 44 54
! 133: *> --
! 134: *> 23 24 25 10 11 55
! 135: *>
! 136: *> 33 34 35 20 21 22
! 137: *> --
! 138: *> 00 44 45 30 31 32
! 139: *> -- --
! 140: *> 01 11 55 40 41 42
! 141: *> -- -- --
! 142: *> 02 12 22 50 51 52
! 143: *>
! 144: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 145: *> transpose of RFP A above. One therefore gets:
! 146: *>
! 147: *>
! 148: *> RFP A RFP A
! 149: *>
! 150: *> -- -- -- -- -- -- -- -- -- --
! 151: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 152: *> -- -- -- -- -- -- -- -- -- --
! 153: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 154: *> -- -- -- -- -- -- -- -- -- --
! 155: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 156: *>
! 157: *>
! 158: *> We next consider Standard Packed Format when N is odd.
! 159: *> We give an example where N = 5.
! 160: *>
! 161: *> AP is Upper AP is Lower
! 162: *>
! 163: *> 00 01 02 03 04 00
! 164: *> 11 12 13 14 10 11
! 165: *> 22 23 24 20 21 22
! 166: *> 33 34 30 31 32 33
! 167: *> 44 40 41 42 43 44
! 168: *>
! 169: *>
! 170: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 171: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 172: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 173: *> conjugate-transpose of the first two columns of AP upper.
! 174: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 175: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 176: *> conjugate-transpose of the last two columns of AP lower.
! 177: *> To denote conjugate we place -- above the element. This covers the
! 178: *> case N odd and TRANSR = 'N'.
! 179: *>
! 180: *> RFP A RFP A
! 181: *>
! 182: *> -- --
! 183: *> 02 03 04 00 33 43
! 184: *> --
! 185: *> 12 13 14 10 11 44
! 186: *>
! 187: *> 22 23 24 20 21 22
! 188: *> --
! 189: *> 00 33 34 30 31 32
! 190: *> -- --
! 191: *> 01 11 44 40 41 42
! 192: *>
! 193: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 194: *> transpose of RFP A above. One therefore gets:
! 195: *>
! 196: *>
! 197: *> RFP A RFP A
! 198: *>
! 199: *> -- -- -- -- -- -- -- -- --
! 200: *> 02 12 22 00 01 00 10 20 30 40 50
! 201: *> -- -- -- -- -- -- -- -- --
! 202: *> 03 13 23 33 11 33 11 21 31 41 51
! 203: *> -- -- -- -- -- -- -- -- --
! 204: *> 04 14 24 34 44 43 44 22 32 42 52
! 205: *> \endverbatim
! 206: *>
! 207: * =====================================================================
! 208: SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
! 209: *
! 210: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 211: * -- LAPACK is a software package provided by Univ. of Tennessee, --
212: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 213: * November 2011
1.1 bertrand 214: *
215: * .. Scalar Arguments ..
216: CHARACTER TRANSR, UPLO
217: INTEGER INFO, N
218: * ..
219: * .. Array Arguments ..
220: COMPLEX*16 AP( 0: * ), ARF( 0: * )
221: *
222: * =====================================================================
223: *
224: * .. Parameters ..
225: * ..
226: * .. Local Scalars ..
227: LOGICAL LOWER, NISODD, NORMALTRANSR
228: INTEGER N1, N2, K, NT
229: INTEGER I, J, IJ
230: INTEGER IJP, JP, LDA, JS
231: * ..
232: * .. External Functions ..
233: LOGICAL LSAME
234: EXTERNAL LSAME
235: * ..
236: * .. External Subroutines ..
237: EXTERNAL XERBLA
238: * ..
239: * .. Intrinsic Functions ..
240: INTRINSIC DCONJG, MOD
241: * ..
242: * .. Executable Statements ..
243: *
244: * Test the input parameters.
245: *
246: INFO = 0
247: NORMALTRANSR = LSAME( TRANSR, 'N' )
248: LOWER = LSAME( UPLO, 'L' )
249: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
250: INFO = -1
251: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
252: INFO = -2
253: ELSE IF( N.LT.0 ) THEN
254: INFO = -3
255: END IF
256: IF( INFO.NE.0 ) THEN
257: CALL XERBLA( 'ZTPTTF', -INFO )
258: RETURN
259: END IF
260: *
261: * Quick return if possible
262: *
263: IF( N.EQ.0 )
1.6 bertrand 264: $ RETURN
1.1 bertrand 265: *
266: IF( N.EQ.1 ) THEN
267: IF( NORMALTRANSR ) THEN
268: ARF( 0 ) = AP( 0 )
269: ELSE
270: ARF( 0 ) = DCONJG( AP( 0 ) )
271: END IF
272: RETURN
273: END IF
274: *
275: * Size of array ARF(0:NT-1)
276: *
277: NT = N*( N+1 ) / 2
278: *
279: * Set N1 and N2 depending on LOWER
280: *
281: IF( LOWER ) THEN
282: N2 = N / 2
283: N1 = N - N2
284: ELSE
285: N1 = N / 2
286: N2 = N - N1
287: END IF
288: *
289: * If N is odd, set NISODD = .TRUE.
290: * If N is even, set K = N/2 and NISODD = .FALSE.
291: *
292: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
293: * where noe = 0 if n is even, noe = 1 if n is odd
294: *
295: IF( MOD( N, 2 ).EQ.0 ) THEN
296: K = N / 2
297: NISODD = .FALSE.
298: LDA = N + 1
299: ELSE
300: NISODD = .TRUE.
301: LDA = N
302: END IF
303: *
304: * ARF^C has lda rows and n+1-noe cols
305: *
306: IF( .NOT.NORMALTRANSR )
1.6 bertrand 307: $ LDA = ( N+1 ) / 2
1.1 bertrand 308: *
309: * start execution: there are eight cases
310: *
311: IF( NISODD ) THEN
312: *
313: * N is odd
314: *
315: IF( NORMALTRANSR ) THEN
316: *
317: * N is odd and TRANSR = 'N'
318: *
319: IF( LOWER ) THEN
320: *
321: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
322: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
323: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
324: *
325: IJP = 0
326: JP = 0
327: DO J = 0, N2
328: DO I = J, N - 1
329: IJ = I + JP
330: ARF( IJ ) = AP( IJP )
331: IJP = IJP + 1
332: END DO
333: JP = JP + LDA
334: END DO
335: DO I = 0, N2 - 1
336: DO J = 1 + I, N2
337: IJ = I + J*LDA
338: ARF( IJ ) = DCONJG( AP( IJP ) )
339: IJP = IJP + 1
340: END DO
341: END DO
342: *
343: ELSE
344: *
345: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
346: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
347: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
348: *
349: IJP = 0
350: DO J = 0, N1 - 1
351: IJ = N2 + J
352: DO I = 0, J
353: ARF( IJ ) = DCONJG( AP( IJP ) )
354: IJP = IJP + 1
355: IJ = IJ + LDA
356: END DO
357: END DO
358: JS = 0
359: DO J = N1, N - 1
360: IJ = JS
361: DO IJ = JS, JS + J
362: ARF( IJ ) = AP( IJP )
363: IJP = IJP + 1
364: END DO
365: JS = JS + LDA
366: END DO
367: *
368: END IF
369: *
370: ELSE
371: *
372: * N is odd and TRANSR = 'C'
373: *
374: IF( LOWER ) THEN
375: *
376: * SRPA for LOWER, TRANSPOSE and N is odd
377: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
378: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
379: *
380: IJP = 0
381: DO I = 0, N2
382: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
383: ARF( IJ ) = DCONJG( AP( IJP ) )
384: IJP = IJP + 1
385: END DO
386: END DO
387: JS = 1
388: DO J = 0, N2 - 1
389: DO IJ = JS, JS + N2 - J - 1
390: ARF( IJ ) = AP( IJP )
391: IJP = IJP + 1
392: END DO
393: JS = JS + LDA + 1
394: END DO
395: *
396: ELSE
397: *
398: * SRPA for UPPER, TRANSPOSE and N is odd
399: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
400: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
401: *
402: IJP = 0
403: JS = N2*LDA
404: DO J = 0, N1 - 1
405: DO IJ = JS, JS + J
406: ARF( IJ ) = AP( IJP )
407: IJP = IJP + 1
408: END DO
409: JS = JS + LDA
410: END DO
411: DO I = 0, N1
412: DO IJ = I, I + ( N1+I )*LDA, LDA
413: ARF( IJ ) = DCONJG( AP( IJP ) )
414: IJP = IJP + 1
415: END DO
416: END DO
417: *
418: END IF
419: *
420: END IF
421: *
422: ELSE
423: *
424: * N is even
425: *
426: IF( NORMALTRANSR ) THEN
427: *
428: * N is even and TRANSR = 'N'
429: *
430: IF( LOWER ) THEN
431: *
432: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
433: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
434: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
435: *
436: IJP = 0
437: JP = 0
438: DO J = 0, K - 1
439: DO I = J, N - 1
440: IJ = 1 + I + JP
441: ARF( IJ ) = AP( IJP )
442: IJP = IJP + 1
443: END DO
444: JP = JP + LDA
445: END DO
446: DO I = 0, K - 1
447: DO J = I, K - 1
448: IJ = I + J*LDA
449: ARF( IJ ) = DCONJG( AP( IJP ) )
450: IJP = IJP + 1
451: END DO
452: END DO
453: *
454: ELSE
455: *
456: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
457: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
458: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
459: *
460: IJP = 0
461: DO J = 0, K - 1
462: IJ = K + 1 + J
463: DO I = 0, J
464: ARF( IJ ) = DCONJG( AP( IJP ) )
465: IJP = IJP + 1
466: IJ = IJ + LDA
467: END DO
468: END DO
469: JS = 0
470: DO J = K, N - 1
471: IJ = JS
472: DO IJ = JS, JS + J
473: ARF( IJ ) = AP( IJP )
474: IJP = IJP + 1
475: END DO
476: JS = JS + LDA
477: END DO
478: *
479: END IF
480: *
481: ELSE
482: *
483: * N is even and TRANSR = 'C'
484: *
485: IF( LOWER ) THEN
486: *
487: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
488: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
489: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
490: *
491: IJP = 0
492: DO I = 0, K - 1
493: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
494: ARF( IJ ) = DCONJG( AP( IJP ) )
495: IJP = IJP + 1
496: END DO
497: END DO
498: JS = 0
499: DO J = 0, K - 1
500: DO IJ = JS, JS + K - J - 1
501: ARF( IJ ) = AP( IJP )
502: IJP = IJP + 1
503: END DO
504: JS = JS + LDA + 1
505: END DO
506: *
507: ELSE
508: *
509: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
510: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
511: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
512: *
513: IJP = 0
514: JS = ( K+1 )*LDA
515: DO J = 0, K - 1
516: DO IJ = JS, JS + J
517: ARF( IJ ) = AP( IJP )
518: IJP = IJP + 1
519: END DO
520: JS = JS + LDA
521: END DO
522: DO I = 0, K - 1
523: DO IJ = I, I + ( K+I )*LDA, LDA
524: ARF( IJ ) = DCONJG( AP( IJP ) )
525: IJP = IJP + 1
526: END DO
527: END DO
528: *
529: END IF
530: *
531: END IF
532: *
533: END IF
534: *
535: RETURN
536: *
537: * End of ZTPTTF
538: *
539: END
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