Annotation of rpl/lapack/lapack/dtpttf.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b DTPTTF
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 DTPTTF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpttf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpttf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpttf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANSR, UPLO
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DTPTTF 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: *> = 'T': 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleOTHERcomputational
! 98: *
! 99: *> \par Further Details:
! 100: * =====================
! 101: *>
! 102: *> \verbatim
! 103: *>
! 104: *> We first consider Rectangular Full Packed (RFP) Format when N is
! 105: *> even. 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: *> the 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: *> the transpose of the last three columns of AP lower.
! 124: *> This covers the case N even and TRANSR = 'N'.
! 125: *>
! 126: *> RFP A RFP A
! 127: *>
! 128: *> 03 04 05 33 43 53
! 129: *> 13 14 15 00 44 54
! 130: *> 23 24 25 10 11 55
! 131: *> 33 34 35 20 21 22
! 132: *> 00 44 45 30 31 32
! 133: *> 01 11 55 40 41 42
! 134: *> 02 12 22 50 51 52
! 135: *>
! 136: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 137: *> transpose of RFP A above. One therefore gets:
! 138: *>
! 139: *>
! 140: *> RFP A RFP A
! 141: *>
! 142: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 143: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 144: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 145: *>
! 146: *>
! 147: *> We then consider Rectangular Full Packed (RFP) Format when N is
! 148: *> odd. We give an example where N = 5.
! 149: *>
! 150: *> AP is Upper AP is Lower
! 151: *>
! 152: *> 00 01 02 03 04 00
! 153: *> 11 12 13 14 10 11
! 154: *> 22 23 24 20 21 22
! 155: *> 33 34 30 31 32 33
! 156: *> 44 40 41 42 43 44
! 157: *>
! 158: *>
! 159: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 160: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 161: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 162: *> the transpose of the first two columns of AP upper.
! 163: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 164: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 165: *> the transpose of the last two columns of AP lower.
! 166: *> This covers the case N odd and TRANSR = 'N'.
! 167: *>
! 168: *> RFP A RFP A
! 169: *>
! 170: *> 02 03 04 00 33 43
! 171: *> 12 13 14 10 11 44
! 172: *> 22 23 24 20 21 22
! 173: *> 00 33 34 30 31 32
! 174: *> 01 11 44 40 41 42
! 175: *>
! 176: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 177: *> transpose of RFP A above. One therefore gets:
! 178: *>
! 179: *> RFP A RFP A
! 180: *>
! 181: *> 02 12 22 00 01 00 10 20 30 40 50
! 182: *> 03 13 23 33 11 33 11 21 31 41 51
! 183: *> 04 14 24 34 44 43 44 22 32 42 52
! 184: *> \endverbatim
! 185: *>
! 186: * =====================================================================
! 187: SUBROUTINE DTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
! 188: *
! 189: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 190: * -- LAPACK is a software package provided by Univ. of Tennessee, --
191: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 192: * November 2011
1.1 bertrand 193: *
194: * .. Scalar Arguments ..
195: CHARACTER TRANSR, UPLO
196: INTEGER INFO, N
197: * ..
198: * .. Array Arguments ..
199: DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
200: *
201: * =====================================================================
202: *
203: * .. Parameters ..
204: * ..
205: * .. Local Scalars ..
206: LOGICAL LOWER, NISODD, NORMALTRANSR
207: INTEGER N1, N2, K, NT
208: INTEGER I, J, IJ
209: INTEGER IJP, JP, LDA, JS
210: * ..
211: * .. External Functions ..
212: LOGICAL LSAME
213: EXTERNAL LSAME
214: * ..
215: * .. External Subroutines ..
216: EXTERNAL XERBLA
217: * ..
218: * .. Intrinsic Functions ..
219: INTRINSIC MOD
220: * ..
221: * .. Executable Statements ..
222: *
223: * Test the input parameters.
224: *
225: INFO = 0
226: NORMALTRANSR = LSAME( TRANSR, 'N' )
227: LOWER = LSAME( UPLO, 'L' )
228: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
229: INFO = -1
230: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
231: INFO = -2
232: ELSE IF( N.LT.0 ) THEN
233: INFO = -3
234: END IF
235: IF( INFO.NE.0 ) THEN
236: CALL XERBLA( 'DTPTTF', -INFO )
237: RETURN
238: END IF
239: *
240: * Quick return if possible
241: *
242: IF( N.EQ.0 )
1.6 bertrand 243: $ RETURN
1.1 bertrand 244: *
245: IF( N.EQ.1 ) THEN
246: IF( NORMALTRANSR ) THEN
247: ARF( 0 ) = AP( 0 )
248: ELSE
249: ARF( 0 ) = AP( 0 )
250: END IF
251: RETURN
252: END IF
253: *
254: * Size of array ARF(0:NT-1)
255: *
256: NT = N*( N+1 ) / 2
257: *
258: * Set N1 and N2 depending on LOWER
259: *
260: IF( LOWER ) THEN
261: N2 = N / 2
262: N1 = N - N2
263: ELSE
264: N1 = N / 2
265: N2 = N - N1
266: END IF
267: *
268: * If N is odd, set NISODD = .TRUE.
269: * If N is even, set K = N/2 and NISODD = .FALSE.
270: *
271: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
272: * where noe = 0 if n is even, noe = 1 if n is odd
273: *
274: IF( MOD( N, 2 ).EQ.0 ) THEN
275: K = N / 2
276: NISODD = .FALSE.
277: LDA = N + 1
278: ELSE
279: NISODD = .TRUE.
280: LDA = N
281: END IF
282: *
283: * ARF^C has lda rows and n+1-noe cols
284: *
285: IF( .NOT.NORMALTRANSR )
1.6 bertrand 286: $ LDA = ( N+1 ) / 2
1.1 bertrand 287: *
288: * start execution: there are eight cases
289: *
290: IF( NISODD ) THEN
291: *
292: * N is odd
293: *
294: IF( NORMALTRANSR ) THEN
295: *
296: * N is odd and TRANSR = 'N'
297: *
298: IF( LOWER ) THEN
299: *
300: * N is odd, TRANSR = 'N', and UPLO = 'L'
301: *
302: IJP = 0
303: JP = 0
304: DO J = 0, N2
305: DO I = J, N - 1
306: IJ = I + JP
307: ARF( IJ ) = AP( IJP )
308: IJP = IJP + 1
309: END DO
310: JP = JP + LDA
311: END DO
312: DO I = 0, N2 - 1
313: DO J = 1 + I, N2
314: IJ = I + J*LDA
315: ARF( IJ ) = AP( IJP )
316: IJP = IJP + 1
317: END DO
318: END DO
319: *
320: ELSE
321: *
322: * N is odd, TRANSR = 'N', and UPLO = 'U'
323: *
324: IJP = 0
325: DO J = 0, N1 - 1
326: IJ = N2 + J
327: DO I = 0, J
328: ARF( IJ ) = AP( IJP )
329: IJP = IJP + 1
330: IJ = IJ + LDA
331: END DO
332: END DO
333: JS = 0
334: DO J = N1, N - 1
335: IJ = JS
336: DO IJ = JS, JS + J
337: ARF( IJ ) = AP( IJP )
338: IJP = IJP + 1
339: END DO
340: JS = JS + LDA
341: END DO
342: *
343: END IF
344: *
345: ELSE
346: *
347: * N is odd and TRANSR = 'T'
348: *
349: IF( LOWER ) THEN
350: *
351: * N is odd, TRANSR = 'T', and UPLO = 'L'
352: *
353: IJP = 0
354: DO I = 0, N2
355: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
356: ARF( IJ ) = AP( IJP )
357: IJP = IJP + 1
358: END DO
359: END DO
360: JS = 1
361: DO J = 0, N2 - 1
362: DO IJ = JS, JS + N2 - J - 1
363: ARF( IJ ) = AP( IJP )
364: IJP = IJP + 1
365: END DO
366: JS = JS + LDA + 1
367: END DO
368: *
369: ELSE
370: *
371: * N is odd, TRANSR = 'T', and UPLO = 'U'
372: *
373: IJP = 0
374: JS = N2*LDA
375: DO J = 0, N1 - 1
376: DO IJ = JS, JS + J
377: ARF( IJ ) = AP( IJP )
378: IJP = IJP + 1
379: END DO
380: JS = JS + LDA
381: END DO
382: DO I = 0, N1
383: DO IJ = I, I + ( N1+I )*LDA, LDA
384: ARF( IJ ) = AP( IJP )
385: IJP = IJP + 1
386: END DO
387: END DO
388: *
389: END IF
390: *
391: END IF
392: *
393: ELSE
394: *
395: * N is even
396: *
397: IF( NORMALTRANSR ) THEN
398: *
399: * N is even and TRANSR = 'N'
400: *
401: IF( LOWER ) THEN
402: *
403: * N is even, TRANSR = 'N', and UPLO = 'L'
404: *
405: IJP = 0
406: JP = 0
407: DO J = 0, K - 1
408: DO I = J, N - 1
409: IJ = 1 + I + JP
410: ARF( IJ ) = AP( IJP )
411: IJP = IJP + 1
412: END DO
413: JP = JP + LDA
414: END DO
415: DO I = 0, K - 1
416: DO J = I, K - 1
417: IJ = I + J*LDA
418: ARF( IJ ) = AP( IJP )
419: IJP = IJP + 1
420: END DO
421: END DO
422: *
423: ELSE
424: *
425: * N is even, TRANSR = 'N', and UPLO = 'U'
426: *
427: IJP = 0
428: DO J = 0, K - 1
429: IJ = K + 1 + J
430: DO I = 0, J
431: ARF( IJ ) = AP( IJP )
432: IJP = IJP + 1
433: IJ = IJ + LDA
434: END DO
435: END DO
436: JS = 0
437: DO J = K, N - 1
438: IJ = JS
439: DO IJ = JS, JS + J
440: ARF( IJ ) = AP( IJP )
441: IJP = IJP + 1
442: END DO
443: JS = JS + LDA
444: END DO
445: *
446: END IF
447: *
448: ELSE
449: *
450: * N is even and TRANSR = 'T'
451: *
452: IF( LOWER ) THEN
453: *
454: * N is even, TRANSR = 'T', and UPLO = 'L'
455: *
456: IJP = 0
457: DO I = 0, K - 1
458: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
459: ARF( IJ ) = AP( IJP )
460: IJP = IJP + 1
461: END DO
462: END DO
463: JS = 0
464: DO J = 0, K - 1
465: DO IJ = JS, JS + K - J - 1
466: ARF( IJ ) = AP( IJP )
467: IJP = IJP + 1
468: END DO
469: JS = JS + LDA + 1
470: END DO
471: *
472: ELSE
473: *
474: * N is even, TRANSR = 'T', and UPLO = 'U'
475: *
476: IJP = 0
477: JS = ( K+1 )*LDA
478: DO J = 0, K - 1
479: DO IJ = JS, JS + J
480: ARF( IJ ) = AP( IJP )
481: IJP = IJP + 1
482: END DO
483: JS = JS + LDA
484: END DO
485: DO I = 0, K - 1
486: DO IJ = I, I + ( K+I )*LDA, LDA
487: ARF( IJ ) = AP( IJP )
488: IJP = IJP + 1
489: END DO
490: END DO
491: *
492: END IF
493: *
494: END IF
495: *
496: END IF
497: *
498: RETURN
499: *
500: * End of DTPTTF
501: *
502: END
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