Annotation of rpl/lapack/lapack/ztfttp.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b ZTFTTP
! 2: *
! 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 ZTFTTP + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfttp.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfttp.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfttp.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, 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: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZTFTTP copies a triangular matrix A from rectangular full packed
! 38: *> format (TF) to standard packed format (TP).
! 39: *> \endverbatim
! 40: *
! 41: * Arguments:
! 42: * ==========
! 43: *
! 44: *> \param[in] TRANSR
! 45: *> \verbatim
! 46: *> TRANSR is CHARACTER*1
! 47: *> = 'N': ARF is in Normal format;
! 48: *> = 'C': ARF is in Conjugate-transpose format;
! 49: *> \endverbatim
! 50: *>
! 51: *> \param[in] UPLO
! 52: *> \verbatim
! 53: *> UPLO is CHARACTER*1
! 54: *> = 'U': A is upper triangular;
! 55: *> = 'L': A is lower triangular.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The order of the matrix A. N >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] ARF
! 65: *> \verbatim
! 66: *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 67: *> On entry, the upper or lower triangular matrix A stored in
! 68: *> RFP format. For a further discussion see Notes below.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[out] AP
! 72: *> \verbatim
! 73: *> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 74: *> On exit, the upper or lower triangular matrix A, packed
! 75: *> columnwise in a linear array. The j-th column of A is stored
! 76: *> in the array AP as follows:
! 77: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 78: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[out] INFO
! 82: *> \verbatim
! 83: *> INFO is INTEGER
! 84: *> = 0: successful exit
! 85: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 86: *> \endverbatim
! 87: *
! 88: * Authors:
! 89: * ========
! 90: *
! 91: *> \author Univ. of Tennessee
! 92: *> \author Univ. of California Berkeley
! 93: *> \author Univ. of Colorado Denver
! 94: *> \author NAG Ltd.
! 95: *
! 96: *> \date November 2011
! 97: *
! 98: *> \ingroup complex16OTHERcomputational
! 99: *
! 100: *> \par Further Details:
! 101: * =====================
! 102: *>
! 103: *> \verbatim
! 104: *>
! 105: *> We first consider Standard Packed Format when N is even.
! 106: *> We give an example where N = 6.
! 107: *>
! 108: *> AP is Upper AP is Lower
! 109: *>
! 110: *> 00 01 02 03 04 05 00
! 111: *> 11 12 13 14 15 10 11
! 112: *> 22 23 24 25 20 21 22
! 113: *> 33 34 35 30 31 32 33
! 114: *> 44 45 40 41 42 43 44
! 115: *> 55 50 51 52 53 54 55
! 116: *>
! 117: *>
! 118: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 119: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 120: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 121: *> conjugate-transpose of the first three columns of AP upper.
! 122: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 123: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 124: *> conjugate-transpose of the last three columns of AP lower.
! 125: *> To denote conjugate we place -- above the element. This covers the
! 126: *> case N even and TRANSR = 'N'.
! 127: *>
! 128: *> RFP A RFP A
! 129: *>
! 130: *> -- -- --
! 131: *> 03 04 05 33 43 53
! 132: *> -- --
! 133: *> 13 14 15 00 44 54
! 134: *> --
! 135: *> 23 24 25 10 11 55
! 136: *>
! 137: *> 33 34 35 20 21 22
! 138: *> --
! 139: *> 00 44 45 30 31 32
! 140: *> -- --
! 141: *> 01 11 55 40 41 42
! 142: *> -- -- --
! 143: *> 02 12 22 50 51 52
! 144: *>
! 145: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 146: *> transpose of RFP A above. One therefore gets:
! 147: *>
! 148: *>
! 149: *> RFP A RFP A
! 150: *>
! 151: *> -- -- -- -- -- -- -- -- -- --
! 152: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 153: *> -- -- -- -- -- -- -- -- -- --
! 154: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 155: *> -- -- -- -- -- -- -- -- -- --
! 156: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 157: *>
! 158: *>
! 159: *> We next consider Standard Packed Format when N is odd.
! 160: *> We give an example where N = 5.
! 161: *>
! 162: *> AP is Upper AP is Lower
! 163: *>
! 164: *> 00 01 02 03 04 00
! 165: *> 11 12 13 14 10 11
! 166: *> 22 23 24 20 21 22
! 167: *> 33 34 30 31 32 33
! 168: *> 44 40 41 42 43 44
! 169: *>
! 170: *>
! 171: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 172: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 173: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 174: *> conjugate-transpose of the first two columns of AP upper.
! 175: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 176: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 177: *> conjugate-transpose of the last two columns of AP lower.
! 178: *> To denote conjugate we place -- above the element. This covers the
! 179: *> case N odd and TRANSR = 'N'.
! 180: *>
! 181: *> RFP A RFP A
! 182: *>
! 183: *> -- --
! 184: *> 02 03 04 00 33 43
! 185: *> --
! 186: *> 12 13 14 10 11 44
! 187: *>
! 188: *> 22 23 24 20 21 22
! 189: *> --
! 190: *> 00 33 34 30 31 32
! 191: *> -- --
! 192: *> 01 11 44 40 41 42
! 193: *>
! 194: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 195: *> transpose of RFP A above. One therefore gets:
! 196: *>
! 197: *>
! 198: *> RFP A RFP A
! 199: *>
! 200: *> -- -- -- -- -- -- -- -- --
! 201: *> 02 12 22 00 01 00 10 20 30 40 50
! 202: *> -- -- -- -- -- -- -- -- --
! 203: *> 03 13 23 33 11 33 11 21 31 41 51
! 204: *> -- -- -- -- -- -- -- -- --
! 205: *> 04 14 24 34 44 43 44 22 32 42 52
! 206: *> \endverbatim
! 207: *>
! 208: * =====================================================================
! 209: SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
1.1 bertrand 210: *
1.7 ! bertrand 211: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 212: * -- LAPACK is a software package provided by Univ. of Tennessee, --
213: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 214: * November 2011
1.1 bertrand 215: *
216: * .. Scalar Arguments ..
217: CHARACTER TRANSR, UPLO
218: INTEGER INFO, N
219: * ..
220: * .. Array Arguments ..
221: COMPLEX*16 AP( 0: * ), ARF( 0: * )
222: * ..
223: *
224: * =====================================================================
225: *
226: * .. Parameters ..
227: * ..
228: * .. Local Scalars ..
229: LOGICAL LOWER, NISODD, NORMALTRANSR
230: INTEGER N1, N2, K, NT
231: INTEGER I, J, IJ
232: INTEGER IJP, JP, LDA, JS
233: * ..
234: * .. External Functions ..
235: LOGICAL LSAME
236: EXTERNAL LSAME
237: * ..
238: * .. External Subroutines ..
239: EXTERNAL XERBLA
240: * ..
241: * .. Intrinsic Functions ..
242: INTRINSIC DCONJG
243: * ..
244: * .. Intrinsic Functions ..
245: * ..
246: * .. Executable Statements ..
247: *
248: * Test the input parameters.
249: *
250: INFO = 0
251: NORMALTRANSR = LSAME( TRANSR, 'N' )
252: LOWER = LSAME( UPLO, 'L' )
253: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
254: INFO = -1
255: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
256: INFO = -2
257: ELSE IF( N.LT.0 ) THEN
258: INFO = -3
259: END IF
260: IF( INFO.NE.0 ) THEN
261: CALL XERBLA( 'ZTFTTP', -INFO )
262: RETURN
263: END IF
264: *
265: * Quick return if possible
266: *
267: IF( N.EQ.0 )
1.6 bertrand 268: $ RETURN
1.1 bertrand 269: *
270: IF( N.EQ.1 ) THEN
271: IF( NORMALTRANSR ) THEN
272: AP( 0 ) = ARF( 0 )
273: ELSE
274: AP( 0 ) = DCONJG( ARF( 0 ) )
275: END IF
276: RETURN
277: END IF
278: *
279: * Size of array ARF(0:NT-1)
280: *
281: NT = N*( N+1 ) / 2
282: *
283: * Set N1 and N2 depending on LOWER
284: *
285: IF( LOWER ) THEN
286: N2 = N / 2
287: N1 = N - N2
288: ELSE
289: N1 = N / 2
290: N2 = N - N1
291: END IF
292: *
293: * If N is odd, set NISODD = .TRUE.
294: * If N is even, set K = N/2 and NISODD = .FALSE.
295: *
296: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
297: * where noe = 0 if n is even, noe = 1 if n is odd
298: *
299: IF( MOD( N, 2 ).EQ.0 ) THEN
300: K = N / 2
301: NISODD = .FALSE.
302: LDA = N + 1
303: ELSE
304: NISODD = .TRUE.
305: LDA = N
306: END IF
307: *
308: * ARF^C has lda rows and n+1-noe cols
309: *
310: IF( .NOT.NORMALTRANSR )
1.6 bertrand 311: $ LDA = ( N+1 ) / 2
1.1 bertrand 312: *
313: * start execution: there are eight cases
314: *
315: IF( NISODD ) THEN
316: *
317: * N is odd
318: *
319: IF( NORMALTRANSR ) THEN
320: *
321: * N is odd and TRANSR = 'N'
322: *
323: IF( LOWER ) THEN
324: *
325: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
326: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
327: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
328: *
329: IJP = 0
330: JP = 0
331: DO J = 0, N2
332: DO I = J, N - 1
333: IJ = I + JP
334: AP( IJP ) = ARF( IJ )
335: IJP = IJP + 1
336: END DO
337: JP = JP + LDA
338: END DO
339: DO I = 0, N2 - 1
340: DO J = 1 + I, N2
341: IJ = I + J*LDA
342: AP( IJP ) = DCONJG( ARF( IJ ) )
343: IJP = IJP + 1
344: END DO
345: END DO
346: *
347: ELSE
348: *
349: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
350: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
351: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
352: *
353: IJP = 0
354: DO J = 0, N1 - 1
355: IJ = N2 + J
356: DO I = 0, J
357: AP( IJP ) = DCONJG( ARF( IJ ) )
358: IJP = IJP + 1
359: IJ = IJ + LDA
360: END DO
361: END DO
362: JS = 0
363: DO J = N1, N - 1
364: IJ = JS
365: DO IJ = JS, JS + J
366: AP( IJP ) = ARF( IJ )
367: IJP = IJP + 1
368: END DO
369: JS = JS + LDA
370: END DO
371: *
372: END IF
373: *
374: ELSE
375: *
376: * N is odd and TRANSR = 'C'
377: *
378: IF( LOWER ) THEN
379: *
380: * SRPA for LOWER, TRANSPOSE and N is odd
381: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
382: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
383: *
384: IJP = 0
385: DO I = 0, N2
386: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
387: AP( IJP ) = DCONJG( ARF( IJ ) )
388: IJP = IJP + 1
389: END DO
390: END DO
391: JS = 1
392: DO J = 0, N2 - 1
393: DO IJ = JS, JS + N2 - J - 1
394: AP( IJP ) = ARF( IJ )
395: IJP = IJP + 1
396: END DO
397: JS = JS + LDA + 1
398: END DO
399: *
400: ELSE
401: *
402: * SRPA for UPPER, TRANSPOSE and N is odd
403: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
404: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
405: *
406: IJP = 0
407: JS = N2*LDA
408: DO J = 0, N1 - 1
409: DO IJ = JS, JS + J
410: AP( IJP ) = ARF( IJ )
411: IJP = IJP + 1
412: END DO
413: JS = JS + LDA
414: END DO
415: DO I = 0, N1
416: DO IJ = I, I + ( N1+I )*LDA, LDA
417: AP( IJP ) = DCONJG( ARF( IJ ) )
418: IJP = IJP + 1
419: END DO
420: END DO
421: *
422: END IF
423: *
424: END IF
425: *
426: ELSE
427: *
428: * N is even
429: *
430: IF( NORMALTRANSR ) THEN
431: *
432: * N is even and TRANSR = 'N'
433: *
434: IF( LOWER ) THEN
435: *
436: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
437: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
438: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
439: *
440: IJP = 0
441: JP = 0
442: DO J = 0, K - 1
443: DO I = J, N - 1
444: IJ = 1 + I + JP
445: AP( IJP ) = ARF( IJ )
446: IJP = IJP + 1
447: END DO
448: JP = JP + LDA
449: END DO
450: DO I = 0, K - 1
451: DO J = I, K - 1
452: IJ = I + J*LDA
453: AP( IJP ) = DCONJG( ARF( IJ ) )
454: IJP = IJP + 1
455: END DO
456: END DO
457: *
458: ELSE
459: *
460: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
461: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
462: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
463: *
464: IJP = 0
465: DO J = 0, K - 1
466: IJ = K + 1 + J
467: DO I = 0, J
468: AP( IJP ) = DCONJG( ARF( IJ ) )
469: IJP = IJP + 1
470: IJ = IJ + LDA
471: END DO
472: END DO
473: JS = 0
474: DO J = K, N - 1
475: IJ = JS
476: DO IJ = JS, JS + J
477: AP( IJP ) = ARF( IJ )
478: IJP = IJP + 1
479: END DO
480: JS = JS + LDA
481: END DO
482: *
483: END IF
484: *
485: ELSE
486: *
487: * N is even and TRANSR = 'C'
488: *
489: IF( LOWER ) THEN
490: *
491: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
492: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
493: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
494: *
495: IJP = 0
496: DO I = 0, K - 1
497: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
498: AP( IJP ) = DCONJG( ARF( IJ ) )
499: IJP = IJP + 1
500: END DO
501: END DO
502: JS = 0
503: DO J = 0, K - 1
504: DO IJ = JS, JS + K - J - 1
505: AP( IJP ) = ARF( IJ )
506: IJP = IJP + 1
507: END DO
508: JS = JS + LDA + 1
509: END DO
510: *
511: ELSE
512: *
513: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
514: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
515: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
516: *
517: IJP = 0
518: JS = ( K+1 )*LDA
519: DO J = 0, K - 1
520: DO IJ = JS, JS + J
521: AP( IJP ) = ARF( IJ )
522: IJP = IJP + 1
523: END DO
524: JS = JS + LDA
525: END DO
526: DO I = 0, K - 1
527: DO IJ = I, I + ( K+I )*LDA, LDA
528: AP( IJP ) = DCONJG( ARF( IJ ) )
529: IJP = IJP + 1
530: END DO
531: END DO
532: *
533: END IF
534: *
535: END IF
536: *
537: END IF
538: *
539: RETURN
540: *
541: * End of ZTFTTP
542: *
543: END
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