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54: -- N - INTEGER.
55: -- On entry, N specifies the number of elements of the vectors X and Y.
56: -- N must be at least zero.
57: -- Unchanged on exit.
58: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
59: -- ( 1 + ( n - 1 )*abs( INCX ) )
60: -- INCX - INTEGER.
61: -- On entry, INCX specifies the increment for the elements of
62: -- X. INCX must not be zero.
60: -- INCX - INTEGER.
61: -- On entry, INCX specifies the increment for the elements of
62: -- X. INCX must not be zero.
63: -- Unchanged on exit.
64: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
65: -- ( 1 + ( n - 1 )*abs( INCY ) )
66: -- INCY - INTEGER.
67: -- On entry, INCY specifies the increment for the elements of
68: -- Y. INCY must not be zero.
74: y IN OUT utl_nla_array_dbl,
75: incy IN POSITIVEN);
76:
77: PROCEDURE blas_swap(n IN POSITIVEN,
78: x IN OUT UTL_NLA_ARRAY_FLT,
79: incx IN POSITIVEN,
80: y IN OUT UTL_NLA_ARRAY_FLT,
81: incy IN POSITIVEN);
82:
76:
77: PROCEDURE blas_swap(n IN POSITIVEN,
78: x IN OUT UTL_NLA_ARRAY_FLT,
79: incx IN POSITIVEN,
80: y IN OUT UTL_NLA_ARRAY_FLT,
81: incy IN POSITIVEN);
82:
83: -- Purpose
84: -- =======
94: -- Unchanged on exit.
95: -- ALPHA - SCALAR_FLOAT/DOUBLE .
96: -- On entry, ALPHA specifies the scalar alpha.
97: -- Unchanged on exit.
98: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
99: -- ( 1 + ( n - 1 )*abs( INCX ) )
100: -- INCX - INTEGER.
101: -- On entry, INCX specifies the increment for the elements of
102: -- X. INCX must not be zero.
108: incx IN POSITIVEN);
109:
110: PROCEDURE blas_scal(n IN POSITIVEN,
111: alpha IN scalar_float,
112: x IN OUT UTL_NLA_ARRAY_FLT,
113: incx IN POSITIVEN);
114:
115: -- Purpose
116: -- =======
123: -- N - INTEGER.
124: -- On entry, N specifies the number of elements of the vectors X and Y.
125: -- N must be at least zero.
126: -- Unchanged on exit.
127: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
128: -- ( 1 + ( n - 1 )*abs( INCX ) )
129: -- INCX - INTEGER.
130: -- On entry, INCX specifies the increment for the elements of
131: -- X. INCX must not be zero.
129: -- INCX - INTEGER.
130: -- On entry, INCX specifies the increment for the elements of
131: -- X. INCX must not be zero.
132: -- Unchanged on exit.
133: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
134: -- ( 1 + ( n - 1 )*abs( INCY ) )
135: -- INCY - INTEGER.
136: -- On entry, INCY specifies the increment for the elements of
137: -- Y. INCY must not be zero.
143: y IN OUT utl_nla_array_dbl,
144: incy IN POSITIVEN);
145:
146: PROCEDURE blas_copy(n IN POSITIVEN,
147: x IN UTL_NLA_ARRAY_FLT,
148: incx IN POSITIVEN,
149: y IN OUT UTL_NLA_ARRAY_FLT,
150: incy IN POSITIVEN);
151:
145:
146: PROCEDURE blas_copy(n IN POSITIVEN,
147: x IN UTL_NLA_ARRAY_FLT,
148: incx IN POSITIVEN,
149: y IN OUT UTL_NLA_ARRAY_FLT,
150: incy IN POSITIVEN);
151:
152: -- Purpose
153: -- =======
163: -- Unchanged on exit.
164: -- ALPHA - SCALAR_FLOAT/DOUBLE .
165: -- On entry, ALPHA specifies the scalar alpha.
166: -- Unchanged on exit.
167: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
168: -- ( 1 + ( n - 1 )*abs( INCX ) )
169: -- Unchanged on exit.
170: -- INCX - INTEGER.
171: -- On entry, INCX specifies the increment for the elements of
170: -- INCX - INTEGER.
171: -- On entry, INCX specifies the increment for the elements of
172: -- X. INCX must not be zero.
173: -- Unchanged on exit.
174: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
175: -- ( 1 + ( n - 1 )*abs( INCY ) )
176: -- INCY - INTEGER.
177: -- On entry, INCY specifies the increment for the elements of
178: -- Y. INCY must not be zero.
186: incy IN POSITIVEN);
187:
188: PROCEDURE blas_axpy(n IN POSITIVEN,
189: alpha IN scalar_float,
190: x IN UTL_NLA_ARRAY_FLT,
191: incx IN POSITIVEN,
192: y IN OUT UTL_NLA_ARRAY_FLT,
193: incy IN POSITIVEN);
194:
188: PROCEDURE blas_axpy(n IN POSITIVEN,
189: alpha IN scalar_float,
190: x IN UTL_NLA_ARRAY_FLT,
191: incx IN POSITIVEN,
192: y IN OUT UTL_NLA_ARRAY_FLT,
193: incy IN POSITIVEN);
194:
195: -- Purpose
196: -- =======
203: -- N - INTEGER.
204: -- On entry, N specifies the number of elements of the vectors X and Y.
205: -- N must be at least zero.
206: -- Unchanged on exit.
207: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
208: -- ( 1 + ( n - 1 )*abs( INCX ) )
209: -- Unchanged on exit.
210: -- INCX - INTEGER.
211: -- On entry, INCX specifies the increment for the elements of
210: -- INCX - INTEGER.
211: -- On entry, INCX specifies the increment for the elements of
212: -- X. INCX must not be zero.
213: -- Unchanged on exit.
214: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
215: -- ( 1 + ( n - 1 )*abs( INCY ) )
216: -- Unchanged on exit.
217: -- INCY - INTEGER.
218: -- On entry, INCY specifies the increment for the elements of
225: y IN utl_nla_array_dbl,
226: incy IN POSITIVEN) RETURN BINARY_DOUBLE;
227:
228: FUNCTION blas_dot(n IN POSITIVEN,
229: x IN UTL_NLA_ARRAY_FLT,
230: incx IN POSITIVEN,
231: y IN UTL_NLA_ARRAY_FLT,
232: incy IN POSITIVEN) RETURN BINARY_FLOAT;
233:
227:
228: FUNCTION blas_dot(n IN POSITIVEN,
229: x IN UTL_NLA_ARRAY_FLT,
230: incx IN POSITIVEN,
231: y IN UTL_NLA_ARRAY_FLT,
232: incy IN POSITIVEN) RETURN BINARY_FLOAT;
233:
234: -- Purpose
235: -- =======
242: -- N - INTEGER.
243: -- On entry, N specifies the number of elements of the vectors X and Y.
244: -- N must be at least zero.
245: -- Unchanged on exit.
246: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
247: -- ( 1 + ( n - 1 )*abs( INCX ) )
248: -- Unchanged on exit.
249: -- INCX - INTEGER.
250: -- On entry, INCX specifies the increment for the elements of
255: x IN utl_nla_array_dbl,
256: incx IN POSITIVEN) RETURN BINARY_DOUBLE;
257:
258: FUNCTION blas_nrm2(n IN POSITIVEN,
259: x IN UTL_NLA_ARRAY_FLT,
260: incx IN POSITIVEN) RETURN BINARY_FLOAT;
261:
262: -- Purpose
263: -- =======
270: -- N - INTEGER.
271: -- On entry, N specifies the number of elements of the vectors X and Y.
272: -- N must be at least zero.
273: -- Unchanged on exit.
274: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
275: -- ( 1 + ( n - 1 )*abs( INCX ) )
276: -- Unchanged on exit.
277: -- INCX - INTEGER.
278: -- On entry, INCX specifies the increment for the elements of
283: x IN utl_nla_array_dbl,
284: incx IN POSITIVEN) RETURN BINARY_DOUBLE;
285:
286: FUNCTION blas_asum(n IN POSITIVEN,
287: x IN UTL_NLA_ARRAY_FLT,
288: incx IN POSITIVEN) RETURN BINARY_FLOAT;
289:
290: -- Purpose
291: -- =======
299: -- N - INTEGER.
300: -- On entry, N specifies the number of elements of the vectors X and Y.
301: -- N must be at least zero.
302: -- Unchanged on exit.
303: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
304: -- ( 1 + ( n - 1 )*abs( INCX ) )
305: -- Unchanged on exit.
306: -- INCX - INTEGER.
307: -- On entry, INCX specifies the increment for the elements of
312: x IN utl_nla_array_dbl,
313: incx IN POSITIVEN) RETURN POSITIVEN;
314:
315: FUNCTION blas_iamax(n IN POSITIVEN,
316: x IN UTL_NLA_ARRAY_FLT,
317: incx IN POSITIVEN) RETURN POSITIVEN;
318:
319: -- Purpose
320: -- =======
327: -- N - INTEGER.
328: -- On entry, N specifies the number of elements of the vectors X and Y.
329: -- N must be at least zero.
330: -- Unchanged on exit.
331: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
332: -- ( 1 + ( n - 1 )*abs( INCX ) )
333: -- INCX - INTEGER.
334: -- On entry, INCX specifies the increment for the elements of
335: -- X. INCX must not be zero.
333: -- INCX - INTEGER.
334: -- On entry, INCX specifies the increment for the elements of
335: -- X. INCX must not be zero.
336: -- Unchanged on exit.
337: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
338: -- ( 1 + ( n - 1 )*abs( INCY ) )
339: -- INCY - INTEGER.
340: -- On entry, INCY specifies the increment for the elements of
341: -- Y. INCY must not be zero.
355: c IN scalar_double,
356: s IN scalar_double);
357:
358: PROCEDURE blas_rot(n IN POSITIVEN,
359: x IN OUT UTL_NLA_ARRAY_FLT,
360: incx IN POSITIVEN,
361: y IN OUT UTL_NLA_ARRAY_FLT,
362: incy IN POSITIVEN,
363: c IN scalar_float,
357:
358: PROCEDURE blas_rot(n IN POSITIVEN,
359: x IN OUT UTL_NLA_ARRAY_FLT,
360: incx IN POSITIVEN,
361: y IN OUT UTL_NLA_ARRAY_FLT,
362: incy IN POSITIVEN,
363: c IN scalar_float,
364: s IN scalar_float);
365:
422: -- Unchanged on exit.
423: -- ALPHA - SCALAR_FLOAT/DOUBLE .
424: -- On entry, ALPHA specifies the scalar alpha.
425: -- Unchanged on exit.
426: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
427: -- Before entry, the leading m by n part of the array A must
428: -- contain the matrix of coefficients.
429: -- Unchanged on exit.
430: -- LDA - INTEGER.
431: -- On entry, LDA specifies the first dimension of A as declared
432: -- in the calling (sub) program. LDA must be at least
433: -- max( 1, m ).
434: -- Unchanged on exit.
435: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
436: -- ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
437: -- and at least
438: -- ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
439: -- Before entry, the incremented array X must contain the
446: -- BETA - SCALAR_FLOAT/DOUBLE .
447: -- On entry, BETA specifies the scalar beta. When BETA is
448: -- supplied as zero then Y need not be set on input.
449: -- Unchanged on exit.
450: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
451: -- ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
452: -- and at least
453: -- ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
454: -- Before entry with BETA non-zero, the incremented array Y
479: PROCEDURE blas_gemv(trans IN flag,
480: m IN POSITIVEN,
481: n IN POSITIVEN,
482: alpha IN scalar_float,
483: a IN UTL_NLA_ARRAY_FLT,
484: lda IN POSITIVEN,
485: x IN UTL_NLA_ARRAY_FLT,
486: incx IN POSITIVEN,
487: beta IN scalar_float,
481: n IN POSITIVEN,
482: alpha IN scalar_float,
483: a IN UTL_NLA_ARRAY_FLT,
484: lda IN POSITIVEN,
485: x IN UTL_NLA_ARRAY_FLT,
486: incx IN POSITIVEN,
487: beta IN scalar_float,
488: y IN OUT UTL_NLA_ARRAY_FLT,
489: incy IN POSITIVEN,
484: lda IN POSITIVEN,
485: x IN UTL_NLA_ARRAY_FLT,
486: incx IN POSITIVEN,
487: beta IN scalar_float,
488: y IN OUT UTL_NLA_ARRAY_FLT,
489: incy IN POSITIVEN,
490: pack IN flag DEFAULT 'C');
491:
492: -- Purpose
525: -- Unchanged on exit.
526: -- ALPHA - SCALAR_FLOAT/DOUBLE .
527: -- On entry, ALPHA specifies the scalar alpha.
528: -- Unchanged on exit.
529: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
530: -- Before entry, the leading ( kl + ku + 1 ) by n part of the
531: -- array A must contain the matrix of coefficients, supplied
532: -- column by column, with the leading diagonal of the matrix in
533: -- row ( ku + 1 ) of the array, the first super-diagonal
541: -- On entry, LDA specifies the first dimension of A as declared
542: -- in the calling (sub) program. LDA must be at least
543: -- ( kl + ku + 1 ).
544: -- Unchanged on exit.
545: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
546: -- ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
547: -- and at least
548: -- ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
549: -- Before entry, the incremented array X must contain the
556: -- BETA - SCALAR_FLOAT/DOUBLE .
557: -- On entry, BETA specifies the scalar beta. When BETA is
558: -- supplied as zero then Y need not be set on input.
559: -- Unchanged on exit.
560: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
561: -- ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
562: -- and at least
563: -- ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
564: -- Before entry, the incremented array Y must contain the
592: n IN POSITIVEN,
593: kl IN NATURALN,
594: ku IN NATURALN,
595: alpha IN scalar_float,
596: a IN UTL_NLA_ARRAY_FLT,
597: lda IN POSITIVEN,
598: x IN UTL_NLA_ARRAY_FLT,
599: incx IN POSITIVEN,
600: beta IN scalar_float,
594: ku IN NATURALN,
595: alpha IN scalar_float,
596: a IN UTL_NLA_ARRAY_FLT,
597: lda IN POSITIVEN,
598: x IN UTL_NLA_ARRAY_FLT,
599: incx IN POSITIVEN,
600: beta IN scalar_float,
601: y IN OUT UTL_NLA_ARRAY_FLT,
602: incy IN POSITIVEN,
597: lda IN POSITIVEN,
598: x IN UTL_NLA_ARRAY_FLT,
599: incx IN POSITIVEN,
600: beta IN scalar_float,
601: y IN OUT UTL_NLA_ARRAY_FLT,
602: incy IN POSITIVEN,
603: pack IN flag DEFAULT 'C');
604:
605: -- Purpose
628: -- Unchanged on exit.
629: -- ALPHA - SCALAR_FLOAT/DOUBLE .
630: -- On entry, ALPHA specifies the scalar alpha.
631: -- Unchanged on exit.
632: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
633: -- Before entry with UPLO = 'U' or 'u', the leading n by n
634: -- upper triangular part of the array A must contain the upper
635: -- triangular part of the symmetric matrix and the strictly
636: -- lower triangular part of A is not referenced.
643: -- On entry, LDA specifies the first dimension of A as declared
644: -- in the calling (sub) program. LDA must be at least
645: -- max( 1, n ).
646: -- Unchanged on exit.
647: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
648: -- ( 1 + ( n - 1 )*abs( INCX ) ).
649: -- Before entry, the incremented array X must contain the n
650: -- element vector x.
651: -- Unchanged on exit.
656: -- BETA - SCALAR_FLOAT/DOUBLE .
657: -- On entry, BETA specifies the scalar beta. When BETA is
658: -- supplied as zero then Y need not be set on input.
659: -- Unchanged on exit.
660: -- Y - UTL_NLA_ARRAY_FLT/DBL of dimension at least
661: -- ( 1 + ( n - 1 )*abs( INCY ) ).
662: -- Before entry, the incremented array Y must contain the n
663: -- element vector y. On exit, Y is overwritten by the updated
664: -- vector y.
685:
686: PROCEDURE blas_symv(uplo IN flag,
687: n IN POSITIVEN,
688: alpha IN scalar_float,
689: a IN UTL_NLA_ARRAY_FLT,
690: lda IN POSITIVEN,
691: x IN UTL_NLA_ARRAY_FLT,
692: incx IN POSITIVEN,
693: beta IN scalar_float,
687: n IN POSITIVEN,
688: alpha IN scalar_float,
689: a IN UTL_NLA_ARRAY_FLT,
690: lda IN POSITIVEN,
691: x IN UTL_NLA_ARRAY_FLT,
692: incx IN POSITIVEN,
693: beta IN scalar_float,
694: y IN OUT UTL_NLA_ARRAY_FLT,
695: incy IN POSITIVEN,
690: lda IN POSITIVEN,
691: x IN UTL_NLA_ARRAY_FLT,
692: incx IN POSITIVEN,
693: beta IN scalar_float,
694: y IN OUT UTL_NLA_ARRAY_FLT,
695: incy IN POSITIVEN,
696: pack IN flag DEFAULT 'C');
697:
698: -- Purpose
725: -- Unchanged on exit.
726: -- ALPHA - SCALAR_FLOAT/DOUBLE .
727: -- On entry, ALPHA specifies the scalar alpha.
728: -- Unchanged on exit.
729: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
730: -- Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
731: -- by n part of the array A must contain the upper triangular
732: -- band part of the symmetric matrix, supplied column by
733: -- column, with the leading diagonal of the matrix in row
746: -- On entry, LDA specifies the first dimension of A as declared
747: -- in the calling (sub) program. LDA must be at least
748: -- ( k + 1 ).
749: -- Unchanged on exit.
750: -- X - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
751: -- ( 1 + ( n - 1 )*abs( INCX ) ).
752: -- Before entry, the incremented array X must contain the
753: -- vector x.
754: -- Unchanged on exit.
758: -- Unchanged on exit.
759: -- BETA - SCALAR_FLOAT/DOUBLE .
760: -- On entry, BETA specifies the scalar beta.
761: -- Unchanged on exit.
762: -- Y - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
763: -- ( 1 + ( n - 1 )*abs( INCY ) ).
764: -- Before entry, the incremented array Y must contain the
765: -- vector y. On exit, Y is overwritten by the updated vector y.
766: -- INCY - INTEGER.
788: PROCEDURE blas_sbmv(uplo IN flag,
789: n IN POSITIVEN,
790: k IN NATURALN,
791: alpha IN scalar_float,
792: a IN UTL_NLA_ARRAY_FLT,
793: lda IN POSITIVEN,
794: x IN UTL_NLA_ARRAY_FLT,
795: incx IN POSITIVEN,
796: beta IN scalar_float,
790: k IN NATURALN,
791: alpha IN scalar_float,
792: a IN UTL_NLA_ARRAY_FLT,
793: lda IN POSITIVEN,
794: x IN UTL_NLA_ARRAY_FLT,
795: incx IN POSITIVEN,
796: beta IN scalar_float,
797: y IN OUT UTL_NLA_ARRAY_FLT,
798: incy IN POSITIVEN,
793: lda IN POSITIVEN,
794: x IN UTL_NLA_ARRAY_FLT,
795: incx IN POSITIVEN,
796: beta IN scalar_float,
797: y IN OUT UTL_NLA_ARRAY_FLT,
798: incy IN POSITIVEN,
799: pack IN flag DEFAULT 'C');
800:
801: -- Purpose
824: -- Unchanged on exit.
825: -- ALPHA - SCALAR_FLOAT/DOUBLE .
826: -- On entry, ALPHA specifies the scalar alpha.
827: -- Unchanged on exit.
828: -- AP - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
829: -- ( ( n*( n + 1 ) )/2 ).
830: -- Before entry with UPLO = 'U' or 'u', the array AP must
831: -- contain the upper triangular part of the symmetric matrix
832: -- packed sequentially, column by column, so that AP( 1 )
837: -- packed sequentially, column by column, so that AP( 1 )
838: -- contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
839: -- and a( 3, 1 ) respectively, and so on.
840: -- Unchanged on exit.
841: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
842: -- ( 1 + ( n - 1 )*abs( INCX ) ).
843: -- Before entry, the incremented array X must contain the n
844: -- element vector x.
845: -- Unchanged on exit.
850: -- BETA - SCALAR_FLOAT/DOUBLE .
851: -- On entry, BETA specifies the scalar beta. When BETA is
852: -- supplied as zero then Y need not be set on input.
853: -- Unchanged on exit.
854: -- Y - UTL_NLA_ARRAY_FLT/DBL of dimension at least
855: -- ( 1 + ( n - 1 )*abs( INCY ) ).
856: -- Before entry, the incremented array Y must contain the n
857: -- element vector y. On exit, Y is overwritten by the updated
858: -- vector y.
878:
879: PROCEDURE blas_spmv(uplo IN flag,
880: n IN POSITIVEN,
881: alpha IN scalar_float,
882: ap IN UTL_NLA_ARRAY_FLT,
883: x IN UTL_NLA_ARRAY_FLT,
884: incx IN POSITIVEN,
885: beta IN scalar_float,
886: y IN OUT UTL_NLA_ARRAY_FLT,
879: PROCEDURE blas_spmv(uplo IN flag,
880: n IN POSITIVEN,
881: alpha IN scalar_float,
882: ap IN UTL_NLA_ARRAY_FLT,
883: x IN UTL_NLA_ARRAY_FLT,
884: incx IN POSITIVEN,
885: beta IN scalar_float,
886: y IN OUT UTL_NLA_ARRAY_FLT,
887: incy IN POSITIVEN,
882: ap IN UTL_NLA_ARRAY_FLT,
883: x IN UTL_NLA_ARRAY_FLT,
884: incx IN POSITIVEN,
885: beta IN scalar_float,
886: y IN OUT UTL_NLA_ARRAY_FLT,
887: incy IN POSITIVEN,
888: pack IN flag DEFAULT 'C');
889:
890: -- Purpose
921: -- N - INTEGER.
922: -- On entry, N specifies the order of the matrix A.
923: -- N must be at least zero.
924: -- Unchanged on exit.
925: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
926: -- Before entry with UPLO = 'U' or 'u', the leading n by n
927: -- upper triangular part of the array A must contain the upper
928: -- triangular matrix and the strictly lower triangular part of
929: -- A is not referenced.
938: -- On entry, LDA specifies the first dimension of A as declared
939: -- in the calling (sub) program. LDA must be at least
940: -- max( 1, n ).
941: -- Unchanged on exit.
942: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
943: -- ( 1 + ( n - 1 )*abs( INCX ) ).
944: -- Before entry, the incremented array X must contain the n
945: -- element vector x. On exit, X is overwritten with the
946: -- tranformed vector x.
966: PROCEDURE blas_trmv(uplo IN flag,
967: trans IN flag,
968: diag IN flag,
969: n IN POSITIVEN,
970: a IN UTL_NLA_ARRAY_FLT,
971: lda IN POSITIVEN,
972: x IN OUT UTL_NLA_ARRAY_FLT,
973: incx IN POSITIVEN,
974: pack IN flag DEFAULT 'C');
968: diag IN flag,
969: n IN POSITIVEN,
970: a IN UTL_NLA_ARRAY_FLT,
971: lda IN POSITIVEN,
972: x IN OUT UTL_NLA_ARRAY_FLT,
973: incx IN POSITIVEN,
974: pack IN flag DEFAULT 'C');
975:
976: -- Purpose
1014: -- On entry with UPLO = 'L' or 'l', K specifies the number of
1015: -- sub-diagonals of the matrix A.
1016: -- K must satisfy 0 .le. K.
1017: -- Unchanged on exit.
1018: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1019: -- Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
1020: -- by n part of the array A must contain the upper triangular
1021: -- band part of the matrix of coefficients, supplied column by
1022: -- column, with the leading diagonal of the matrix in row
1038: -- On entry, LDA specifies the first dimension of A as declared
1039: -- in the calling (sub) program. LDA must be at least
1040: -- ( k + 1 ).
1041: -- Unchanged on exit.
1042: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1043: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1044: -- Before entry, the incremented array X must contain the n
1045: -- element vector x. On exit, X is overwritten with the
1046: -- tranformed vector x.
1068: trans IN flag,
1069: diag IN flag,
1070: n IN POSITIVEN,
1071: k IN NATURALN,
1072: a IN UTL_NLA_ARRAY_FLT,
1073: lda IN POSITIVEN,
1074: x IN OUT UTL_NLA_ARRAY_FLT,
1075: incx IN POSITIVEN,
1076: pack IN flag DEFAULT 'C');
1070: n IN POSITIVEN,
1071: k IN NATURALN,
1072: a IN UTL_NLA_ARRAY_FLT,
1073: lda IN POSITIVEN,
1074: x IN OUT UTL_NLA_ARRAY_FLT,
1075: incx IN POSITIVEN,
1076: pack IN flag DEFAULT 'C');
1077:
1078: -- Purpose
1109: -- N - INTEGER.
1110: -- On entry, N specifies the order of the matrix A.
1111: -- N must be at least zero.
1112: -- Unchanged on exit.
1113: -- AP - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
1114: -- ( ( n*( n + 1 ) )/2 ).
1115: -- Before entry with UPLO = 'U' or 'u', the array AP must
1116: -- contain the upper triangular matrix packed sequentially,
1117: -- column by column, so that AP( 1 ) contains a( 1, 1 ),
1124: -- respectively, and so on.
1125: -- Note that when DIAG = 'U' or 'u', the diagonal elements of
1126: -- A are not referenced, but are assumed to be unity.
1127: -- Unchanged on exit.
1128: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1129: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1130: -- Before entry, the incremented array X must contain the n
1131: -- element vector x. On exit, X is overwritten with the
1132: -- tranformed vector x.
1151: PROCEDURE blas_tpmv(uplo IN flag,
1152: trans IN flag,
1153: diag IN flag,
1154: n IN POSITIVEN,
1155: ap IN UTL_NLA_ARRAY_FLT,
1156: x IN OUT UTL_NLA_ARRAY_FLT,
1157: incx IN POSITIVEN,
1158: pack IN flag DEFAULT 'C');
1159:
1152: trans IN flag,
1153: diag IN flag,
1154: n IN POSITIVEN,
1155: ap IN UTL_NLA_ARRAY_FLT,
1156: x IN OUT UTL_NLA_ARRAY_FLT,
1157: incx IN POSITIVEN,
1158: pack IN flag DEFAULT 'C');
1159:
1160: -- Purpose
1193: -- N - INTEGER.
1194: -- On entry, N specifies the order of the matrix A.
1195: -- N must be at least zero.
1196: -- Unchanged on exit.
1197: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1198: -- Before entry with UPLO = 'U' or 'u', the leading n by n
1199: -- upper triangular part of the array A must contain the upper
1200: -- triangular matrix and the strictly lower triangular part of
1201: -- A is not referenced.
1210: -- On entry, LDA specifies the first dimension of A as declared
1211: -- in the calling (sub) program. LDA must be at least
1212: -- max( 1, n ).
1213: -- Unchanged on exit.
1214: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1215: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1216: -- Before entry, the incremented array X must contain the n
1217: -- element right-hand side vector b. On exit, X is overwritten
1218: -- with the solution vector x.
1238: PROCEDURE blas_trsv(uplo IN flag,
1239: trans IN flag,
1240: diag IN flag,
1241: n IN POSITIVEN,
1242: a IN UTL_NLA_ARRAY_FLT,
1243: lda IN POSITIVEN,
1244: x IN OUT UTL_NLA_ARRAY_FLT,
1245: incx IN POSITIVEN,
1246: pack IN flag DEFAULT 'C');
1240: diag IN flag,
1241: n IN POSITIVEN,
1242: a IN UTL_NLA_ARRAY_FLT,
1243: lda IN POSITIVEN,
1244: x IN OUT UTL_NLA_ARRAY_FLT,
1245: incx IN POSITIVEN,
1246: pack IN flag DEFAULT 'C');
1247:
1248: -- Purpose
1289: -- On entry with UPLO = 'L' or 'l', K specifies the number of
1290: -- sub-diagonals of the matrix A.
1291: -- K must satisfy 0 .le. K.
1292: -- Unchanged on exit.
1293: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1294: -- Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
1295: -- by n part of the array A must contain the upper triangular
1296: -- band part of the matrix of coefficients, supplied column by
1297: -- column, with the leading diagonal of the matrix in row
1313: -- On entry, LDA specifies the first dimension of A as declared
1314: -- in the calling (sub) program. LDA must be at least
1315: -- ( k + 1 ).
1316: -- Unchanged on exit.
1317: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1318: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1319: -- Before entry, the incremented array X must contain the n
1320: -- element right-hand side vector b. On exit, X is overwritten
1321: -- with the solution vector x.
1343: trans IN flag,
1344: diag IN flag,
1345: n IN POSITIVEN,
1346: k IN NATURALN,
1347: a IN UTL_NLA_ARRAY_FLT,
1348: lda IN POSITIVEN,
1349: x IN OUT UTL_NLA_ARRAY_FLT,
1350: incx IN POSITIVEN,
1351: pack IN flag DEFAULT 'C');
1345: n IN POSITIVEN,
1346: k IN NATURALN,
1347: a IN UTL_NLA_ARRAY_FLT,
1348: lda IN POSITIVEN,
1349: x IN OUT UTL_NLA_ARRAY_FLT,
1350: incx IN POSITIVEN,
1351: pack IN flag DEFAULT 'C');
1352:
1353: -- Purpose
1386: -- N - INTEGER.
1387: -- On entry, N specifies the order of the matrix A.
1388: -- N must be at least zero.
1389: -- Unchanged on exit.
1390: -- AP - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
1391: -- ( ( n*( n + 1 ) )/2 ).
1392: -- Before entry with UPLO = 'U' or 'u', the array AP must
1393: -- contain the upper triangular matrix packed sequentially,
1394: -- column by column, so that AP( 1 ) contains a( 1, 1 ),
1401: -- respectively, and so on.
1402: -- Note that when DIAG = 'U' or 'u', the diagonal elements of
1403: -- A are not referenced, but are assumed to be unity.
1404: -- Unchanged on exit.
1405: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1406: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1407: -- Before entry, the incremented array X must contain the n
1408: -- element right-hand side vector b. On exit, X is overwritten
1409: -- with the solution vector x.
1428: PROCEDURE blas_tpsv(uplo IN flag,
1429: trans IN flag,
1430: diag IN flag,
1431: n IN POSITIVEN,
1432: ap IN UTL_NLA_ARRAY_FLT,
1433: x IN OUT UTL_NLA_ARRAY_FLT,
1434: incx IN POSITIVEN,
1435: pack IN flag DEFAULT 'C');
1436:
1429: trans IN flag,
1430: diag IN flag,
1431: n IN POSITIVEN,
1432: ap IN UTL_NLA_ARRAY_FLT,
1433: x IN OUT UTL_NLA_ARRAY_FLT,
1434: incx IN POSITIVEN,
1435: pack IN flag DEFAULT 'C');
1436:
1437: -- Purpose
1455: -- Unchanged on exit.
1456: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1457: -- On entry, ALPHA specifies the scalar alpha.
1458: -- Unchanged on exit.
1459: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1460: -- ( 1 + ( m - 1 )*abs( INCX ) ).
1461: -- Before entry, the incremented array X must contain the m
1462: -- element vector x.
1463: -- Unchanged on exit.
1464: -- INCX - INTEGER.
1465: -- On entry, INCX specifies the increment for the elements of
1466: -- X. INCX must not be zero.
1467: -- Unchanged on exit.
1468: -- Y - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1469: -- ( 1 + ( n - 1 )*abs( INCY ) ).
1470: -- Before entry, the incremented array Y must contain the n
1471: -- element vector y.
1472: -- Unchanged on exit.
1473: -- INCY - INTEGER.
1474: -- On entry, INCY specifies the increment for the elements of
1475: -- Y. INCY must not be zero.
1476: -- Unchanged on exit.
1477: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1478: -- Before entry, the leading m by n part of the array A must
1479: -- contain the matrix of coefficients. On exit, A is
1480: -- overwritten by the updated matrix.
1481: -- LDA - INTEGER.
1501:
1502: PROCEDURE blas_ger(m IN POSITIVEN,
1503: n IN POSITIVEN,
1504: alpha IN scalar_float,
1505: x IN UTL_NLA_ARRAY_FLT,
1506: incx IN POSITIVEN,
1507: y IN UTL_NLA_ARRAY_FLT,
1508: incy IN POSITIVEN,
1509: a IN OUT UTL_NLA_ARRAY_FLT,
1503: n IN POSITIVEN,
1504: alpha IN scalar_float,
1505: x IN UTL_NLA_ARRAY_FLT,
1506: incx IN POSITIVEN,
1507: y IN UTL_NLA_ARRAY_FLT,
1508: incy IN POSITIVEN,
1509: a IN OUT UTL_NLA_ARRAY_FLT,
1510: lda IN POSITIVEN,
1511: pack IN flag DEFAULT 'C');
1505: x IN UTL_NLA_ARRAY_FLT,
1506: incx IN POSITIVEN,
1507: y IN UTL_NLA_ARRAY_FLT,
1508: incy IN POSITIVEN,
1509: a IN OUT UTL_NLA_ARRAY_FLT,
1510: lda IN POSITIVEN,
1511: pack IN flag DEFAULT 'C');
1512:
1513: -- Purpose
1536: -- Unchanged on exit.
1537: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1538: -- On entry, ALPHA specifies the scalar alpha.
1539: -- Unchanged on exit.
1540: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1541: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1542: -- Before entry, the incremented array X must contain the n
1543: -- element vector x.
1544: -- Unchanged on exit.
1545: -- INCX - INTEGER.
1546: -- On entry, INCX specifies the increment for the elements of
1547: -- X. INCX must not be zero.
1548: -- Unchanged on exit.
1549: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1550: -- Before entry with UPLO = 'U' or 'u', the leading n by n
1551: -- upper triangular part of the array A must contain the upper
1552: -- triangular part of the symmetric matrix and the strictly
1553: -- lower triangular part of A is not referenced. On exit, the
1580:
1581: PROCEDURE blas_syr(uplo IN flag,
1582: n IN POSITIVEN,
1583: alpha IN scalar_float,
1584: x IN UTL_NLA_ARRAY_FLT,
1585: incx IN POSITIVEN,
1586: a IN OUT UTL_NLA_ARRAY_FLT,
1587: lda IN POSITIVEN,
1588: pack IN flag DEFAULT 'C');
1582: n IN POSITIVEN,
1583: alpha IN scalar_float,
1584: x IN UTL_NLA_ARRAY_FLT,
1585: incx IN POSITIVEN,
1586: a IN OUT UTL_NLA_ARRAY_FLT,
1587: lda IN POSITIVEN,
1588: pack IN flag DEFAULT 'C');
1589:
1590: -- Purpose
1613: -- Unchanged on exit.
1614: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1615: -- On entry, ALPHA specifies the scalar alpha.
1616: -- Unchanged on exit.
1617: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1618: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1619: -- Before entry, the incremented array X must contain the n
1620: -- element vector x.
1621: -- Unchanged on exit.
1622: -- INCX - INTEGER.
1623: -- On entry, INCX specifies the increment for the elements of
1624: -- X. INCX must not be zero.
1625: -- Unchanged on exit.
1626: -- AP - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
1627: -- ( ( n*( n + 1 ) )/2 ).
1628: -- Before entry with UPLO = 'U' or 'u', the array AP must
1629: -- contain the upper triangular part of the symmetric matrix
1630: -- packed sequentially, column by column, so that AP( 1 )
1654:
1655: PROCEDURE blas_spr(uplo IN flag,
1656: n IN POSITIVEN,
1657: alpha IN scalar_float,
1658: x IN UTL_NLA_ARRAY_FLT,
1659: incx IN POSITIVEN,
1660: ap IN OUT UTL_NLA_ARRAY_FLT,
1661: pack IN flag DEFAULT 'C');
1662:
1656: n IN POSITIVEN,
1657: alpha IN scalar_float,
1658: x IN UTL_NLA_ARRAY_FLT,
1659: incx IN POSITIVEN,
1660: ap IN OUT UTL_NLA_ARRAY_FLT,
1661: pack IN flag DEFAULT 'C');
1662:
1663: -- Purpose
1664: -- =======
1686: -- Unchanged on exit.
1687: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1688: -- On entry, ALPHA specifies the scalar alpha.
1689: -- Unchanged on exit.
1690: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1691: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1692: -- Before entry, the incremented array X must contain the n
1693: -- element vector x.
1694: -- Unchanged on exit.
1695: -- INCX - INTEGER.
1696: -- On entry, INCX specifies the increment for the elements of
1697: -- X. INCX must not be zero.
1698: -- Unchanged on exit.
1699: -- Y - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1700: -- ( 1 + ( n - 1 )*abs( INCY ) ).
1701: -- Before entry, the incremented array Y must contain the n
1702: -- element vector y.
1703: -- Unchanged on exit.
1704: -- INCY - INTEGER.
1705: -- On entry, INCY specifies the increment for the elements of
1706: -- Y. INCY must not be zero.
1707: -- Unchanged on exit.
1708: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, n ).
1709: -- Before entry with UPLO = 'U' or 'u', the leading n by n
1710: -- upper triangular part of the array A must contain the upper
1711: -- triangular part of the symmetric matrix and the strictly
1712: -- lower triangular part of A is not referenced. On exit, the
1741:
1742: PROCEDURE blas_syr2(uplo IN flag,
1743: n IN POSITIVEN,
1744: alpha IN scalar_float,
1745: x IN UTL_NLA_ARRAY_FLT,
1746: incx IN POSITIVEN,
1747: y IN UTL_NLA_ARRAY_FLT,
1748: incy IN POSITIVEN,
1749: a IN OUT UTL_NLA_ARRAY_FLT,
1743: n IN POSITIVEN,
1744: alpha IN scalar_float,
1745: x IN UTL_NLA_ARRAY_FLT,
1746: incx IN POSITIVEN,
1747: y IN UTL_NLA_ARRAY_FLT,
1748: incy IN POSITIVEN,
1749: a IN OUT UTL_NLA_ARRAY_FLT,
1750: lda IN POSITIVEN,
1751: pack IN flag DEFAULT 'C');
1745: x IN UTL_NLA_ARRAY_FLT,
1746: incx IN POSITIVEN,
1747: y IN UTL_NLA_ARRAY_FLT,
1748: incy IN POSITIVEN,
1749: a IN OUT UTL_NLA_ARRAY_FLT,
1750: lda IN POSITIVEN,
1751: pack IN flag DEFAULT 'C');
1752:
1753: -- Purpose
1776: -- Unchanged on exit.
1777: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1778: -- On entry, ALPHA specifies the scalar alpha.
1779: -- Unchanged on exit.
1780: -- X - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1781: -- ( 1 + ( n - 1 )*abs( INCX ) ).
1782: -- Before entry, the incremented array X must contain the n
1783: -- element vector x.
1784: -- Unchanged on exit.
1785: -- INCX - INTEGER.
1786: -- On entry, INCX specifies the increment for the elements of
1787: -- X. INCX must not be zero.
1788: -- Unchanged on exit.
1789: -- Y - UTL_NLA_ARRAY_FLT/DBL of dimension at least
1790: -- ( 1 + ( n - 1 )*abs( INCY ) ).
1791: -- Before entry, the incremented array Y must contain the n
1792: -- element vector y.
1793: -- Unchanged on exit.
1794: -- INCY - INTEGER.
1795: -- On entry, INCY specifies the increment for the elements of
1796: -- Y. INCY must not be zero.
1797: -- Unchanged on exit.
1798: -- AP - UTL_NLA_ARRAY_FLT/DBL of DIMENSION at least
1799: -- ( ( n*( n + 1 ) )/2 ).
1800: -- Before entry with UPLO = 'U' or 'u', the array AP must
1801: -- contain the upper triangular part of the symmetric matrix
1802: -- packed sequentially, column by column, so that AP( 1 )
1828:
1829: PROCEDURE blas_spr2(uplo IN flag,
1830: n IN POSITIVEN,
1831: alpha IN scalar_float,
1832: x IN UTL_NLA_ARRAY_FLT,
1833: incx IN POSITIVEN,
1834: y IN UTL_NLA_ARRAY_FLT,
1835: incy IN POSITIVEN,
1836: ap IN OUT UTL_NLA_ARRAY_FLT,
1830: n IN POSITIVEN,
1831: alpha IN scalar_float,
1832: x IN UTL_NLA_ARRAY_FLT,
1833: incx IN POSITIVEN,
1834: y IN UTL_NLA_ARRAY_FLT,
1835: incy IN POSITIVEN,
1836: ap IN OUT UTL_NLA_ARRAY_FLT,
1837: pack IN flag DEFAULT 'C');
1838:
1832: x IN UTL_NLA_ARRAY_FLT,
1833: incx IN POSITIVEN,
1834: y IN UTL_NLA_ARRAY_FLT,
1835: incy IN POSITIVEN,
1836: ap IN OUT UTL_NLA_ARRAY_FLT,
1837: pack IN flag DEFAULT 'C');
1838:
1839:
1840: -- ---------------------------------------- --
1884: -- Unchanged on exit.
1885: -- ALPHA - SCALAR_FLOAT/DOUBLE .
1886: -- On entry, ALPHA specifies the scalar alpha.
1887: -- Unchanged on exit.
1888: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, ka ), where ka is
1889: -- k when TRANSA = 'N' or 'n', and is m otherwise.
1890: -- Before entry with TRANSA = 'N' or 'n', the leading m by k
1891: -- part of the array A must contain the matrix A, otherwise
1892: -- the leading k by m part of the array A must contain the
1897: -- in the calling (sub) program. When TRANSA = 'N' or 'n' then
1898: -- LDA must be at least max( 1, m ), otherwise LDA must be at
1899: -- least max( 1, k ).
1900: -- Unchanged on exit.
1901: -- B - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDB, kb ), where kb is
1902: -- n when TRANSB = 'N' or 'n', and is k otherwise.
1903: -- Before entry with TRANSB = 'N' or 'n', the leading k by n
1904: -- part of the array B must contain the matrix B, otherwise
1905: -- the leading n by k part of the array B must contain the
1914: -- BETA - SCALAR_FLOAT/DOUBLE .
1915: -- On entry, BETA specifies the scalar beta. When BETA is
1916: -- supplied as zero then C need not be set on input.
1917: -- Unchanged on exit.
1918: -- C - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDC, n ).
1919: -- Before entry, the leading m by n part of the array C must
1920: -- contain the matrix C, except when beta is zero, in which
1921: -- case C need not be set on entry.
1922: -- On exit, the array C is overwritten by the m by n matrix
1950: m IN POSITIVEN,
1951: n IN POSITIVEN,
1952: k IN POSITIVEN,
1953: alpha IN scalar_float,
1954: a IN UTL_NLA_ARRAY_FLT,
1955: lda IN POSITIVEN,
1956: b IN UTL_NLA_ARRAY_FLT,
1957: ldb IN POSITIVEN,
1958: beta IN scalar_float,
1952: k IN POSITIVEN,
1953: alpha IN scalar_float,
1954: a IN UTL_NLA_ARRAY_FLT,
1955: lda IN POSITIVEN,
1956: b IN UTL_NLA_ARRAY_FLT,
1957: ldb IN POSITIVEN,
1958: beta IN scalar_float,
1959: c IN OUT UTL_NLA_ARRAY_FLT,
1960: ldc IN POSITIVEN,
1955: lda IN POSITIVEN,
1956: b IN UTL_NLA_ARRAY_FLT,
1957: ldb IN POSITIVEN,
1958: beta IN scalar_float,
1959: c IN OUT UTL_NLA_ARRAY_FLT,
1960: ldc IN POSITIVEN,
1961: pack IN flag DEFAULT 'C');
1962:
1963:
1999: -- Unchanged on exit.
2000: -- ALPHA - SCALAR_FLOAT/DOUBLE .
2001: -- On entry, ALPHA specifies the scalar alpha.
2002: -- Unchanged on exit.
2003: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, ka ), where ka is
2004: -- m when SIDE = 'L' or 'l' and is n otherwise.
2005: -- Before entry with SIDE = 'L' or 'l', the m by m part of
2006: -- the array A must contain the symmetric matrix, such that
2007: -- when UPLO = 'U' or 'u', the leading m by m upper triangular
2028: -- in the calling (sub) program. When SIDE = 'L' or 'l' then
2029: -- LDA must be at least max( 1, m ), otherwise LDA must be at
2030: -- least max( 1, n ).
2031: -- Unchanged on exit.
2032: -- B - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDB, n ).
2033: -- Before entry, the leading m by n part of the array B must
2034: -- contain the matrix B.
2035: -- Unchanged on exit.
2036: -- LDB - INTEGER.
2041: -- BETA - SCALAR_FLOAT/DOUBLE .
2042: -- On entry, BETA specifies the scalar beta. When BETA is
2043: -- supplied as zero then C need not be set on input.
2044: -- Unchanged on exit.
2045: -- C - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDC, n ).
2046: -- Before entry, the leading m by n part of the array C must
2047: -- contain the matrix C, except when beta is zero, in which
2048: -- case C need not be set on entry.
2049: -- On exit, the array C is overwritten by the m by n updated
2075: uplo IN flag,
2076: m IN POSITIVEN,
2077: n IN POSITIVEN,
2078: alpha IN scalar_float,
2079: a IN UTL_NLA_ARRAY_FLT,
2080: lda IN POSITIVEN,
2081: b IN UTL_NLA_ARRAY_FLT,
2082: ldb IN POSITIVEN,
2083: beta IN scalar_float,
2077: n IN POSITIVEN,
2078: alpha IN scalar_float,
2079: a IN UTL_NLA_ARRAY_FLT,
2080: lda IN POSITIVEN,
2081: b IN UTL_NLA_ARRAY_FLT,
2082: ldb IN POSITIVEN,
2083: beta IN scalar_float,
2084: c IN OUT UTL_NLA_ARRAY_FLT,
2085: ldc IN POSITIVEN,
2080: lda IN POSITIVEN,
2081: b IN UTL_NLA_ARRAY_FLT,
2082: ldb IN POSITIVEN,
2083: beta IN scalar_float,
2084: c IN OUT UTL_NLA_ARRAY_FLT,
2085: ldc IN POSITIVEN,
2086: pack IN flag DEFAULT 'C');
2087:
2088: -- Purpose
2135: -- On entry, ALPHA specifies the scalar alpha. When alpha is
2136: -- zero then A is not referenced and B need not be set before
2137: -- entry.
2138: -- Unchanged on exit.
2139: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, k ), where k is m
2140: -- when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
2141: -- Before entry with UPLO = 'U' or 'u', the leading k by k
2142: -- upper triangular part of the array A must contain the upper
2143: -- triangular matrix and the strictly lower triangular part of
2154: -- in the calling (sub) program. When SIDE = 'L' or 'l' then
2155: -- LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
2156: -- then LDA must be at least max( 1, n ).
2157: -- Unchanged on exit.
2158: -- B - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDB, n ).
2159: -- Before entry, the leading m by n part of the array B must
2160: -- contain the matrix B, and on exit is overwritten by the
2161: -- transformed matrix.
2162: -- LDB - INTEGER.
2187: diag IN flag,
2188: m IN POSITIVEN,
2189: n IN POSITIVEN,
2190: alpha IN scalar_float,
2191: a IN UTL_NLA_ARRAY_FLT,
2192: lda IN POSITIVEN,
2193: b IN OUT UTL_NLA_ARRAY_FLT,
2194: ldb IN POSITIVEN,
2195: pack IN flag DEFAULT 'C');
2189: n IN POSITIVEN,
2190: alpha IN scalar_float,
2191: a IN UTL_NLA_ARRAY_FLT,
2192: lda IN POSITIVEN,
2193: b IN OUT UTL_NLA_ARRAY_FLT,
2194: ldb IN POSITIVEN,
2195: pack IN flag DEFAULT 'C');
2196:
2197: -- Purpose
2245: -- On entry, ALPHA specifies the scalar alpha. When alpha is
2246: -- zero then A is not referenced and B need not be set before
2247: -- entry.
2248: -- Unchanged on exit.
2249: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, k ), where k is m
2250: -- when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
2251: -- Before entry with UPLO = 'U' or 'u', the leading k by k
2252: -- upper triangular part of the array A must contain the upper
2253: -- triangular matrix and the strictly lower triangular part of
2264: -- in the calling (sub) program. When SIDE = 'L' or 'l' then
2265: -- LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
2266: -- then LDA must be at least max( 1, n ).
2267: -- Unchanged on exit.
2268: -- B - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDB, n ).
2269: -- Before entry, the leading m by n part of the array B must
2270: -- contain the right-hand side matrix B, and on exit is
2271: -- overwritten by the solution matrix X.
2272: -- LDB - INTEGER.
2298: diag IN flag,
2299: m IN POSITIVEN,
2300: n IN POSITIVEN,
2301: alpha IN scalar_float,
2302: a IN UTL_NLA_ARRAY_FLT,
2303: lda IN POSITIVEN,
2304: b IN OUT UTL_NLA_ARRAY_FLT,
2305: ldb IN POSITIVEN,
2306: pack IN flag DEFAULT 'C');
2300: n IN POSITIVEN,
2301: alpha IN scalar_float,
2302: a IN UTL_NLA_ARRAY_FLT,
2303: lda IN POSITIVEN,
2304: b IN OUT UTL_NLA_ARRAY_FLT,
2305: ldb IN POSITIVEN,
2306: pack IN flag DEFAULT 'C');
2307:
2308: -- Purpose
2346: -- Unchanged on exit.
2347: -- ALPHA - SCALAR_FLOAT/DOUBLE .
2348: -- On entry, ALPHA specifies the scalar alpha.
2349: -- Unchanged on exit.
2350: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, ka ), where ka is
2351: -- k when TRANS = 'N' or 'n', and is n otherwise.
2352: -- Before entry with TRANS = 'N' or 'n', the leading n by k
2353: -- part of the array A must contain the matrix A, otherwise
2354: -- the leading k by n part of the array A must contain the
2362: -- Unchanged on exit.
2363: -- BETA - SCALAR_FLOAT/DOUBLE .
2364: -- On entry, BETA specifies the scalar beta.
2365: -- Unchanged on exit.
2366: -- C - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDC, n ).
2367: -- Before entry with UPLO = 'U' or 'u', the leading n by n
2368: -- upper triangular part of the array C must contain the upper
2369: -- triangular part of the symmetric matrix and the strictly
2370: -- lower triangular part of C is not referenced. On exit, the
2402: trans IN flag,
2403: n IN POSITIVEN,
2404: k IN POSITIVEN,
2405: alpha IN scalar_float,
2406: a IN UTL_NLA_ARRAY_FLT,
2407: lda IN POSITIVEN,
2408: beta IN scalar_float,
2409: c IN OUT UTL_NLA_ARRAY_FLT,
2410: ldc IN POSITIVEN,
2405: alpha IN scalar_float,
2406: a IN UTL_NLA_ARRAY_FLT,
2407: lda IN POSITIVEN,
2408: beta IN scalar_float,
2409: c IN OUT UTL_NLA_ARRAY_FLT,
2410: ldc IN POSITIVEN,
2411: pack IN flag DEFAULT 'C');
2412:
2413: -- Purpose
2454: -- Unchanged on exit.
2455: -- ALPHA - SCALAR_FLOAT/DOUBLE .
2456: -- On entry, ALPHA specifies the scalar alpha.
2457: -- Unchanged on exit.
2458: -- A - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDA, ka ), where ka is
2459: -- k when TRANS = 'N' or 'n', and is n otherwise.
2460: -- Before entry with TRANS = 'N' or 'n', the leading n by k
2461: -- part of the array A must contain the matrix A, otherwise
2462: -- the leading k by n part of the array A must contain the
2467: -- in the calling (sub) program. When TRANS = 'N' or 'n'
2468: -- then LDA must be at least max( 1, n ), otherwise LDA must
2469: -- be at least max( 1, k ).
2470: -- Unchanged on exit.
2471: -- B - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDB, kb ), where kb is
2472: -- k when TRANS = 'N' or 'n', and is n otherwise.
2473: -- Before entry with TRANS = 'N' or 'n', the leading n by k
2474: -- part of the array B must contain the matrix B, otherwise
2475: -- the leading k by n part of the array B must contain the
2483: -- Unchanged on exit.
2484: -- BETA - SCALAR_FLOAT/DOUBLE .
2485: -- On entry, BETA specifies the scalar beta.
2486: -- Unchanged on exit.
2487: -- C - UTL_NLA_ARRAY_FLT/DBL of DIMENSION ( LDC, n ).
2488: -- Before entry with UPLO = 'U' or 'u', the leading n by n
2489: -- upper triangular part of the array C must contain the upper
2490: -- triangular part of the symmetric matrix and the strictly
2491: -- lower triangular part of C is not referenced. On exit, the
2525: trans IN flag,
2526: n IN POSITIVEN,
2527: k IN POSITIVEN,
2528: alpha IN scalar_float,
2529: a IN UTL_NLA_ARRAY_FLT,
2530: lda IN POSITIVEN,
2531: b IN UTL_NLA_ARRAY_FLT,
2532: ldb IN POSITIVEN,
2533: beta IN scalar_float,
2527: k IN POSITIVEN,
2528: alpha IN scalar_float,
2529: a IN UTL_NLA_ARRAY_FLT,
2530: lda IN POSITIVEN,
2531: b IN UTL_NLA_ARRAY_FLT,
2532: ldb IN POSITIVEN,
2533: beta IN scalar_float,
2534: c IN OUT UTL_NLA_ARRAY_FLT,
2535: ldc IN POSITIVEN,
2530: lda IN POSITIVEN,
2531: b IN UTL_NLA_ARRAY_FLT,
2532: ldb IN POSITIVEN,
2533: beta IN scalar_float,
2534: c IN OUT UTL_NLA_ARRAY_FLT,
2535: ldc IN POSITIVEN,
2536: pack IN flag DEFAULT 'C');
2537:
2538:
2565: -- NRHS (input) INTEGER
2566: -- The number of right hand sides, i.e., the number of columns
2567: -- of the matrix B. NRHS >= 0.
2568: --
2569: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
2570: -- On entry, the N-by-N coefficient matrix A.
2571: -- On exit, the factors L and U from the factorization
2572: -- A = P*L*U; the unit diagonal elements of L are not stored.
2573: --
2577: -- IPIV (output) INTEGER array, dimension (N)
2578: -- The pivot indices that define the permutation matrix P;
2579: -- row i of the matrix was interchanged with row IPIV(i).
2580: --
2581: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
2582: -- On entry, the N-by-NRHS matrix of right hand side matrix B.
2583: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
2584: --
2585: -- LDB (input) INTEGER
2607: pack IN flag DEFAULT 'C');
2608:
2609: PROCEDURE lapack_gesv(n IN POSITIVEN,
2610: nrhs IN POSITIVEN,
2611: a IN OUT UTL_NLA_ARRAY_FLT,
2612: lda IN POSITIVEN,
2613: ipiv IN OUT UTL_NLA_ARRAY_INT,
2614: b IN OUT UTL_NLA_ARRAY_FLT,
2615: ldb IN POSITIVEN,
2610: nrhs IN POSITIVEN,
2611: a IN OUT UTL_NLA_ARRAY_FLT,
2612: lda IN POSITIVEN,
2613: ipiv IN OUT UTL_NLA_ARRAY_INT,
2614: b IN OUT UTL_NLA_ARRAY_FLT,
2615: ldb IN POSITIVEN,
2616: info OUT integer,
2617: pack IN flag DEFAULT 'C');
2618:
2646: -- NRHS (input) INTEGER
2647: -- The number of right hand sides, i.e., the number of columns
2648: -- of the matrix B. NRHS >= 0.
2649: --
2650: -- AB (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDAB,N)
2651: -- On entry, the matrix A in band storage, in rows KL+1 to
2652: -- 2*KL+KU+1; rows 1 to KL of the array need not be set.
2653: -- The j-th column of A is stored in the j-th column of the
2654: -- array AB as follows:
2665: -- IPIV (output) INTEGER array, dimension (N)
2666: -- The pivot indices that define the permutation matrix P;
2667: -- row i of the matrix was interchanged with row IPIV(i).
2668: --
2669: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
2670: -- On entry, the N-by-NRHS right hand side matrix B.
2671: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
2672: --
2673: -- LDB (input) INTEGER
2700: PROCEDURE lapack_gbsv (n IN POSITIVEN,
2701: kl IN NATURALN,
2702: ku IN NATURALN,
2703: nrhs IN POSITIVEN,
2704: ab IN OUT UTL_NLA_ARRAY_FLT,
2705: ldab IN POSITIVEN,
2706: ipiv IN OUT UTL_NLA_ARRAY_INT,
2707: b IN OUT UTL_NLA_ARRAY_FLT,
2708: ldb IN POSITIVEN,
2703: nrhs IN POSITIVEN,
2704: ab IN OUT UTL_NLA_ARRAY_FLT,
2705: ldab IN POSITIVEN,
2706: ipiv IN OUT UTL_NLA_ARRAY_INT,
2707: b IN OUT UTL_NLA_ARRAY_FLT,
2708: ldb IN POSITIVEN,
2709: info OUT integer,
2710: pack IN flag DEFAULT 'C');
2711:
2732: -- NRHS (input) INTEGER
2733: -- The number of right hand sides, i.e., the number of columns
2734: -- of the matrix B. NRHS >= 0.
2735: --
2736: -- DL (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N-1)
2737: -- On entry, DL must contain the (n-1) sub-diagonal elements of
2738: -- A.
2739: --
2740: -- On exit, DL is overwritten by the (n-2) elements of the
2740: -- On exit, DL is overwritten by the (n-2) elements of the
2741: -- second super-diagonal of the upper triangular matrix U from
2742: -- the LU factorization of A, in DL(1), ..., DL(n-2).
2743: --
2744: -- D (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
2745: -- On entry, D must contain the diagonal elements of A.
2746: --
2747: -- On exit, D is overwritten by the n diagonal elements of U.
2748: --
2745: -- On entry, D must contain the diagonal elements of A.
2746: --
2747: -- On exit, D is overwritten by the n diagonal elements of U.
2748: --
2749: -- DU (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N-1)
2750: -- On entry, DU must contain the (n-1) super-diagonal elements
2751: -- of A.
2752: --
2753: -- On exit, DU is overwritten by the (n-1) elements of the first
2752: --
2753: -- On exit, DU is overwritten by the (n-1) elements of the first
2754: -- super-diagonal of U.
2755: --
2756: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
2757: -- On entry, the N by NRHS matrix of right hand side matrix B.
2758: -- On exit, if INFO = 0, the N by NRHS solution matrix X.
2759: --
2760: -- LDB (input) INTEGER
2782: pack IN flag DEFAULT 'C');
2783:
2784: PROCEDURE lapack_gtsv (n IN POSITIVEN,
2785: nrhs IN POSITIVEN,
2786: dl IN OUT UTL_NLA_ARRAY_FLT,
2787: d IN OUT UTL_NLA_ARRAY_FLT,
2788: du IN OUT UTL_NLA_ARRAY_FLT,
2789: b IN OUT UTL_NLA_ARRAY_FLT,
2790: ldb IN POSITIVEN,
2783:
2784: PROCEDURE lapack_gtsv (n IN POSITIVEN,
2785: nrhs IN POSITIVEN,
2786: dl IN OUT UTL_NLA_ARRAY_FLT,
2787: d IN OUT UTL_NLA_ARRAY_FLT,
2788: du IN OUT UTL_NLA_ARRAY_FLT,
2789: b IN OUT UTL_NLA_ARRAY_FLT,
2790: ldb IN POSITIVEN,
2791: info OUT integer,
2784: PROCEDURE lapack_gtsv (n IN POSITIVEN,
2785: nrhs IN POSITIVEN,
2786: dl IN OUT UTL_NLA_ARRAY_FLT,
2787: d IN OUT UTL_NLA_ARRAY_FLT,
2788: du IN OUT UTL_NLA_ARRAY_FLT,
2789: b IN OUT UTL_NLA_ARRAY_FLT,
2790: ldb IN POSITIVEN,
2791: info OUT integer,
2792: pack IN flag DEFAULT 'C');
2785: nrhs IN POSITIVEN,
2786: dl IN OUT UTL_NLA_ARRAY_FLT,
2787: d IN OUT UTL_NLA_ARRAY_FLT,
2788: du IN OUT UTL_NLA_ARRAY_FLT,
2789: b IN OUT UTL_NLA_ARRAY_FLT,
2790: ldb IN POSITIVEN,
2791: info OUT integer,
2792: pack IN flag DEFAULT 'C');
2793:
2821: -- NRHS (input) INTEGER
2822: -- The number of right hand sides, i.e., the number of columns
2823: -- of the matrix B. NRHS >= 0.
2824: --
2825: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
2826: -- On entry, the symmetric matrix A. If UPLO = 'U', the leading
2827: -- N-by-N upper triangular part of A contains the upper
2828: -- triangular part of the matrix A, and the strictly lower
2829: -- triangular part of A is not referenced. If UPLO = 'L', the
2836: --
2837: -- LDA (input) INTEGER
2838: -- The leading dimension of the array A. LDA >= max(1,N).
2839: --
2840: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
2841: -- On entry, the N-by-NRHS right hand side matrix B.
2842: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
2843: --
2844: -- LDB (input) INTEGER
2867:
2868: PROCEDURE lapack_posv (uplo IN flag,
2869: n IN POSITIVEN,
2870: nrhs IN POSITIVEN,
2871: a IN OUT UTL_NLA_ARRAY_FLT,
2872: lda IN POSITIVEN,
2873: b IN OUT UTL_NLA_ARRAY_FLT,
2874: ldb IN POSITIVEN,
2875: info OUT integer,
2869: n IN POSITIVEN,
2870: nrhs IN POSITIVEN,
2871: a IN OUT UTL_NLA_ARRAY_FLT,
2872: lda IN POSITIVEN,
2873: b IN OUT UTL_NLA_ARRAY_FLT,
2874: ldb IN POSITIVEN,
2875: info OUT integer,
2876: pack IN flag DEFAULT 'C');
2877:
2905: -- NRHS (input) INTEGER
2906: -- The number of right hand sides, i.e., the number of columns
2907: -- of the matrix B. NRHS >= 0.
2908: --
2909: -- AP (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N*(N+1)/2)
2910: -- On entry, the upper or lower triangle of the symmetric matrix
2911: -- A, packed columnwise in a linear array. The j-th column of A
2912: -- is stored in the array AP as follows:
2913: -- if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
2917: -- On exit, if INFO = 0, the factor U or L from the Cholesky
2918: -- factorization A = U**T*U or A = L*L**T, in the same storage
2919: -- format as A.
2920: --
2921: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
2922: -- On entry, the N-by-NRHS right hand side matrix B.
2923: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
2924: --
2925: -- LDB (input) INTEGER
2948:
2949: PROCEDURE lapack_ppsv (uplo IN flag,
2950: n IN POSITIVEN,
2951: nrhs IN POSITIVEN,
2952: ap IN OUT UTL_NLA_ARRAY_FLT,
2953: b IN OUT UTL_NLA_ARRAY_FLT,
2954: ldb IN POSITIVEN,
2955: info OUT integer,
2956: pack IN flag DEFAULT 'C');
2949: PROCEDURE lapack_ppsv (uplo IN flag,
2950: n IN POSITIVEN,
2951: nrhs IN POSITIVEN,
2952: ap IN OUT UTL_NLA_ARRAY_FLT,
2953: b IN OUT UTL_NLA_ARRAY_FLT,
2954: ldb IN POSITIVEN,
2955: info OUT integer,
2956: pack IN flag DEFAULT 'C');
2957:
2990: -- NRHS (input) INTEGER
2991: -- The number of right hand sides, i.e., the number of columns
2992: -- of the matrix B. NRHS >= 0.
2993: --
2994: -- AB (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDAB,N)
2995: -- On entry, the upper or lower triangle of the symmetric band
2996: -- matrix A, stored in the first KD+1 rows of the array. The
2997: -- j-th column of A is stored in the j-th column of the array AB
2998: -- as follows:
3006: --
3007: -- LDAB (input) INTEGER
3008: -- The leading dimension of the array AB. LDAB >= KD+1.
3009: --
3010: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
3011: -- On entry, the N-by-NRHS right hand side matrix B.
3012: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
3013: --
3014: -- LDB (input) INTEGER
3039: PROCEDURE lapack_pbsv (uplo IN flag,
3040: n IN POSITIVEN,
3041: kd IN NATURALN,
3042: nrhs IN POSITIVEN,
3043: ab IN OUT UTL_NLA_ARRAY_FLT,
3044: ldab IN POSITIVEN,
3045: b IN OUT UTL_NLA_ARRAY_FLT,
3046: ldb IN POSITIVEN,
3047: info OUT integer,
3041: kd IN NATURALN,
3042: nrhs IN POSITIVEN,
3043: ab IN OUT UTL_NLA_ARRAY_FLT,
3044: ldab IN POSITIVEN,
3045: b IN OUT UTL_NLA_ARRAY_FLT,
3046: ldb IN POSITIVEN,
3047: info OUT integer,
3048: pack IN flag DEFAULT 'C');
3049:
3067: -- NRHS (input) INTEGER
3068: -- The number of right hand sides, i.e., the number of columns
3069: -- of the matrix B. NRHS >= 0.
3070: --
3071: -- D (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3072: -- On entry, the n diagonal elements of the tridiagonal matrix
3073: -- A. On exit, the n diagonal elements of the diagonal matrix
3074: -- D from the factorization A = L*D*L**T.
3075: --
3072: -- On entry, the n diagonal elements of the tridiagonal matrix
3073: -- A. On exit, the n diagonal elements of the diagonal matrix
3074: -- D from the factorization A = L*D*L**T.
3075: --
3076: -- E (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N-1)
3077: -- On entry, the (n-1) subdiagonal elements of the tridiagonal
3078: -- matrix A. On exit, the (n-1) subdiagonal elements of the
3079: -- unit bidiagonal factor L from the L*D*L**T factorization of
3080: -- A. (E can also be regarded as the superdiagonal of the unit
3079: -- unit bidiagonal factor L from the L*D*L**T factorization of
3080: -- A. (E can also be regarded as the superdiagonal of the unit
3081: -- bidiagonal factor U from the U**T*D*U factorization of A.)
3082: --
3083: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
3084: -- On entry, the N-by-NRHS right hand side matrix B.
3085: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
3086: --
3087: -- LDB (input) INTEGER
3109: pack IN flag DEFAULT 'C');
3110:
3111: PROCEDURE lapack_ptsv (n IN POSITIVEN,
3112: nrhs IN POSITIVEN,
3113: d IN OUT UTL_NLA_ARRAY_FLT,
3114: e IN OUT UTL_NLA_ARRAY_FLT,
3115: b IN OUT UTL_NLA_ARRAY_FLT,
3116: ldb IN POSITIVEN,
3117: info OUT integer,
3110:
3111: PROCEDURE lapack_ptsv (n IN POSITIVEN,
3112: nrhs IN POSITIVEN,
3113: d IN OUT UTL_NLA_ARRAY_FLT,
3114: e IN OUT UTL_NLA_ARRAY_FLT,
3115: b IN OUT UTL_NLA_ARRAY_FLT,
3116: ldb IN POSITIVEN,
3117: info OUT integer,
3118: pack IN flag DEFAULT 'C');
3111: PROCEDURE lapack_ptsv (n IN POSITIVEN,
3112: nrhs IN POSITIVEN,
3113: d IN OUT UTL_NLA_ARRAY_FLT,
3114: e IN OUT UTL_NLA_ARRAY_FLT,
3115: b IN OUT UTL_NLA_ARRAY_FLT,
3116: ldb IN POSITIVEN,
3117: info OUT integer,
3118: pack IN flag DEFAULT 'C');
3119:
3148: -- NRHS (input) INTEGER
3149: -- The number of right hand sides, i.e., the number of columns
3150: -- of the matrix B. NRHS >= 0.
3151: --
3152: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
3153: -- On entry, the symmetric matrix A. If UPLO = 'U', the leading
3154: -- N-by-N upper triangular part of A contains the upper
3155: -- triangular part of the matrix A, and the strictly lower
3156: -- triangular part of A is not referenced. If UPLO = 'L', the
3176: -- IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
3177: -- -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
3178: -- diagonal block.
3179: --
3180: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
3181: -- On entry, the N-by-NRHS right hand side matrix B.
3182: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
3183: --
3184: -- LDB (input) INTEGER
3208:
3209: PROCEDURE lapack_sysv (uplo IN flag,
3210: n IN POSITIVEN,
3211: nrhs IN POSITIVEN,
3212: a IN OUT UTL_NLA_ARRAY_FLT,
3213: lda IN POSITIVEN,
3214: ipiv IN OUT UTL_NLA_ARRAY_INT,
3215: b IN OUT UTL_NLA_ARRAY_FLT,
3216: ldb IN POSITIVEN,
3211: nrhs IN POSITIVEN,
3212: a IN OUT UTL_NLA_ARRAY_FLT,
3213: lda IN POSITIVEN,
3214: ipiv IN OUT UTL_NLA_ARRAY_INT,
3215: b IN OUT UTL_NLA_ARRAY_FLT,
3216: ldb IN POSITIVEN,
3217: info OUT integer,
3218: pack IN flag DEFAULT 'C');
3219:
3248: -- NRHS (input) INTEGER
3249: -- The number of right hand sides, i.e., the number of columns
3250: -- of the matrix B. NRHS >= 0.
3251: --
3252: -- AP (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N*(N+1)/2)
3253: -- On entry, the upper or lower triangle of the symmetric matrix
3254: -- A, packed columnwise in a linear array. The j-th column of A
3255: -- is stored in the array AP as follows:
3256: -- if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
3272: -- IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
3273: -- -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
3274: -- diagonal block.
3275: --
3276: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
3277: -- On entry, the N-by-NRHS right hand side matrix B.
3278: -- On exit, if INFO = 0, the N-by-NRHS solution matrix X.
3279: --
3280: -- LDB (input) INTEGER
3304:
3305: PROCEDURE lapack_spsv (uplo IN flag,
3306: n IN POSITIVEN,
3307: nrhs IN POSITIVEN,
3308: ap IN OUT UTL_NLA_ARRAY_FLT,
3309: ipiv IN OUT UTL_NLA_ARRAY_INT,
3310: b IN OUT UTL_NLA_ARRAY_FLT,
3311: ldb IN POSITIVEN,
3312: info OUT integer,
3306: n IN POSITIVEN,
3307: nrhs IN POSITIVEN,
3308: ap IN OUT UTL_NLA_ARRAY_FLT,
3309: ipiv IN OUT UTL_NLA_ARRAY_INT,
3310: b IN OUT UTL_NLA_ARRAY_FLT,
3311: ldb IN POSITIVEN,
3312: info OUT integer,
3313: pack IN flag DEFAULT 'C');
3314:
3363: -- NRHS (input) INTEGER
3364: -- The number of right hand sides, i.e., the number of
3365: -- columns of the matrices B and X. NRHS >=0.
3366: --
3367: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
3368: -- On entry, the M-by-N matrix A.
3369: -- On exit,
3370: -- if M >= N, A is overwritten by details of its QR
3371: -- factorization as returned by SGEQRF;
3374: --
3375: -- LDA (input) INTEGER
3376: -- The leading dimension of the array A. LDA >= max(1,M).
3377: --
3378: -- B (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDB,NRHS)
3379: -- On entry, the matrix B of right hand side vectors, stored
3380: -- columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS
3381: -- if TRANS = 'T'.
3382: -- On exit, B is overwritten by the solution vectors, stored
3420: PROCEDURE lapack_gels(trans IN flag,
3421: m IN POSITIVEN,
3422: n IN POSITIVEN,
3423: nrhs IN POSITIVEN,
3424: a IN OUT UTL_NLA_ARRAY_FLT,
3425: lda IN POSITIVEN,
3426: b IN OUT UTL_NLA_ARRAY_FLT,
3427: ldb IN POSITIVEN,
3428: info OUT integer,
3422: n IN POSITIVEN,
3423: nrhs IN POSITIVEN,
3424: a IN OUT UTL_NLA_ARRAY_FLT,
3425: lda IN POSITIVEN,
3426: b IN OUT UTL_NLA_ARRAY_FLT,
3427: ldb IN POSITIVEN,
3428: info OUT integer,
3429: pack IN flag DEFAULT 'C');
3430:
3450: --
3451: -- N (input) INTEGER
3452: -- The order of the matrix A. N >= 0.
3453: --
3454: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA, N)
3455: -- On entry, the symmetric matrix A. If UPLO = 'U', the
3456: -- leading N-by-N upper triangular part of A contains the
3457: -- upper triangular part of the matrix A. If UPLO = 'L',
3458: -- the leading N-by-N lower triangular part of A contains
3465: --
3466: -- LDA (input) INTEGER
3467: -- The leading dimension of the array A. LDA >= max(1,N).
3468: --
3469: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3470: -- If INFO = 0, the eigenvalues in ascending order.
3471: --
3472: -- INFO (output) INTEGER
3473: -- = 0: successful exit
3492:
3493: PROCEDURE lapack_syev(jobz IN flag,
3494: uplo IN flag,
3495: n IN POSITIVEN,
3496: a IN OUT UTL_NLA_ARRAY_FLT,
3497: lda IN POSITIVEN,
3498: w IN OUT UTL_NLA_ARRAY_FLT,
3499: info OUT integer,
3500: pack IN flag DEFAULT 'C');
3494: uplo IN flag,
3495: n IN POSITIVEN,
3496: a IN OUT UTL_NLA_ARRAY_FLT,
3497: lda IN POSITIVEN,
3498: w IN OUT UTL_NLA_ARRAY_FLT,
3499: info OUT integer,
3500: pack IN flag DEFAULT 'C');
3501:
3502: --
3523: --
3524: -- N (input) INTEGER
3525: -- The order of the matrix A. N >= 0.
3526: --
3527: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA, N)
3528: -- On entry, the symmetric matrix A. If UPLO = 'U', the
3529: -- leading N-by-N upper triangular part of A contains the
3530: -- upper triangular part of the matrix A. If UPLO = 'L',
3531: -- the leading N-by-N lower triangular part of A contains
3538: --
3539: -- LDA (input) INTEGER
3540: -- The leading dimension of the array A. LDA >= max(1,N).
3541: --
3542: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3543: -- If INFO = 0, the eigenvalues in ascending order.
3544: --
3545: -- INFO (output) INTEGER
3546: -- = 0: successful exit
3565:
3566: PROCEDURE lapack_syevd(jobz IN flag,
3567: uplo IN flag,
3568: n IN POSITIVEN,
3569: a IN OUT UTL_NLA_ARRAY_FLT,
3570: lda IN POSITIVEN,
3571: w IN OUT UTL_NLA_ARRAY_FLT,
3572: info OUT integer,
3573: pack IN flag DEFAULT 'C');
3567: uplo IN flag,
3568: n IN POSITIVEN,
3569: a IN OUT UTL_NLA_ARRAY_FLT,
3570: lda IN POSITIVEN,
3571: w IN OUT UTL_NLA_ARRAY_FLT,
3572: info OUT integer,
3573: pack IN flag DEFAULT 'C');
3574:
3575: --
3592: --
3593: -- N (input) INTEGER
3594: -- The order of the matrix A. N >= 0.
3595: --
3596: -- AP (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N*(N+1)/2)
3597: -- On entry, the upper or lower triangle of the symmetric matrix
3598: -- A, packed columnwise in a linear array. The j-th column of A
3599: -- is stored in the array AP as follows:
3600: -- if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
3606: -- the corresponding elements of A, and if UPLO = 'L', the
3607: -- diagonal and first subdiagonal of T overwrite the
3608: -- corresponding elements of A.
3609: --
3610: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3611: -- If INFO = 0, the eigenvalues in ascending order.
3612: --
3613: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3614: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3609: --
3610: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3611: -- If INFO = 0, the eigenvalues in ascending order.
3612: --
3613: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3614: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3615: -- eigenvectors of the matrix A, with the i-th column of Z
3616: -- holding the eigenvector associated with W(i).
3617: -- If JOBZ = 'N', then Z is not referenced.
3644:
3645: PROCEDURE lapack_spev(jobz IN flag,
3646: uplo IN flag,
3647: n IN POSITIVEN,
3648: ap IN OUT UTL_NLA_ARRAY_FLT,
3649: w IN OUT UTL_NLA_ARRAY_FLT,
3650: z IN OUT UTL_NLA_ARRAY_FLT,
3651: ldz IN POSITIVEN,
3652: info OUT integer,
3645: PROCEDURE lapack_spev(jobz IN flag,
3646: uplo IN flag,
3647: n IN POSITIVEN,
3648: ap IN OUT UTL_NLA_ARRAY_FLT,
3649: w IN OUT UTL_NLA_ARRAY_FLT,
3650: z IN OUT UTL_NLA_ARRAY_FLT,
3651: ldz IN POSITIVEN,
3652: info OUT integer,
3653: pack IN flag DEFAULT 'C');
3646: uplo IN flag,
3647: n IN POSITIVEN,
3648: ap IN OUT UTL_NLA_ARRAY_FLT,
3649: w IN OUT UTL_NLA_ARRAY_FLT,
3650: z IN OUT UTL_NLA_ARRAY_FLT,
3651: ldz IN POSITIVEN,
3652: info OUT integer,
3653: pack IN flag DEFAULT 'C');
3654:
3676: --
3677: -- N (input) INTEGER
3678: -- The order of the matrix A. N >= 0.
3679: --
3680: -- AP (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N*(N+1)/2)
3681: -- On entry, the upper or lower triangle of the symmetric matrix
3682: -- A, packed columnwise in a linear array. The j-th column of A
3683: -- is stored in the array AP as follows:
3684: -- if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
3690: -- the corresponding elements of A, and if UPLO = 'L', the
3691: -- diagonal and first subdiagonal of T overwrite the
3692: -- corresponding elements of A.
3693: --
3694: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3695: -- If INFO = 0, the eigenvalues in ascending order.
3696: --
3697: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3698: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3693: --
3694: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3695: -- If INFO = 0, the eigenvalues in ascending order.
3696: --
3697: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3698: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3699: -- eigenvectors of the matrix A, with the i-th column of Z
3700: -- holding the eigenvector associated with W(i).
3701: -- If JOBZ = 'N', then Z is not referenced.
3728:
3729: PROCEDURE lapack_spevd(jobz IN flag,
3730: uplo IN flag,
3731: n IN POSITIVEN,
3732: ap IN OUT UTL_NLA_ARRAY_FLT,
3733: w IN OUT UTL_NLA_ARRAY_FLT,
3734: z IN OUT UTL_NLA_ARRAY_FLT,
3735: ldz IN POSITIVEN,
3736: info OUT integer,
3729: PROCEDURE lapack_spevd(jobz IN flag,
3730: uplo IN flag,
3731: n IN POSITIVEN,
3732: ap IN OUT UTL_NLA_ARRAY_FLT,
3733: w IN OUT UTL_NLA_ARRAY_FLT,
3734: z IN OUT UTL_NLA_ARRAY_FLT,
3735: ldz IN POSITIVEN,
3736: info OUT integer,
3737: pack IN flag DEFAULT 'C');
3730: uplo IN flag,
3731: n IN POSITIVEN,
3732: ap IN OUT UTL_NLA_ARRAY_FLT,
3733: w IN OUT UTL_NLA_ARRAY_FLT,
3734: z IN OUT UTL_NLA_ARRAY_FLT,
3735: ldz IN POSITIVEN,
3736: info OUT integer,
3737: pack IN flag DEFAULT 'C');
3738:
3760: -- KD (input) INTEGER
3761: -- The number of superdiagonals of the matrix A if UPLO = 'U',
3762: -- or the number of subdiagonals if UPLO = 'L'. KD >= 0.
3763: --
3764: -- AB (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDAB, N)
3765: -- On entry, the upper or lower triangle of the symmetric band
3766: -- matrix A, stored in the first KD+1 rows of the array. The
3767: -- j-th column of A is stored in the j-th column of the array AB
3768: -- as follows:
3778: --
3779: -- LDAB (input) INTEGER
3780: -- The leading dimension of the array AB. LDAB >= KD + 1.
3781: --
3782: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3783: -- If INFO = 0, the eigenvalues in ascending order.
3784: --
3785: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3786: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3781: --
3782: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3783: -- If INFO = 0, the eigenvalues in ascending order.
3784: --
3785: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3786: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3787: -- eigenvectors of the matrix A, with the i-th column of Z
3788: -- holding the eigenvector associated with W(i).
3789: -- If JOBZ = 'N', then Z is not referenced.
3819: PROCEDURE lapack_sbev(jobz IN flag,
3820: uplo IN flag,
3821: n IN POSITIVEN,
3822: kd IN NATURALN,
3823: ab IN OUT UTL_NLA_ARRAY_FLT,
3824: ldab IN POSITIVEN,
3825: w IN OUT UTL_NLA_ARRAY_FLT,
3826: z IN OUT UTL_NLA_ARRAY_FLT,
3827: ldz IN POSITIVEN,
3821: n IN POSITIVEN,
3822: kd IN NATURALN,
3823: ab IN OUT UTL_NLA_ARRAY_FLT,
3824: ldab IN POSITIVEN,
3825: w IN OUT UTL_NLA_ARRAY_FLT,
3826: z IN OUT UTL_NLA_ARRAY_FLT,
3827: ldz IN POSITIVEN,
3828: info OUT integer,
3829: pack IN flag DEFAULT 'C');
3822: kd IN NATURALN,
3823: ab IN OUT UTL_NLA_ARRAY_FLT,
3824: ldab IN POSITIVEN,
3825: w IN OUT UTL_NLA_ARRAY_FLT,
3826: z IN OUT UTL_NLA_ARRAY_FLT,
3827: ldz IN POSITIVEN,
3828: info OUT integer,
3829: pack IN flag DEFAULT 'C');
3830:
3856: -- KD (input) INTEGER
3857: -- The number of superdiagonals of the matrix A if UPLO = 'U',
3858: -- or the number of subdiagonals if UPLO = 'L'. KD >= 0.
3859: --
3860: -- AB (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDAB, N)
3861: -- On entry, the upper or lower triangle of the symmetric band
3862: -- matrix A, stored in the first KD+1 rows of the array. The
3863: -- j-th column of A is stored in the j-th column of the array AB
3864: -- as follows:
3874: --
3875: -- LDAB (input) INTEGER
3876: -- The leading dimension of the array AB. LDAB >= KD + 1.
3877: --
3878: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3879: -- If INFO = 0, the eigenvalues in ascending order.
3880: --
3881: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3882: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3877: --
3878: -- W (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3879: -- If INFO = 0, the eigenvalues in ascending order.
3880: --
3881: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3882: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3883: -- eigenvectors of the matrix A, with the i-th column of Z
3884: -- holding the eigenvector associated with W(i).
3885: -- If JOBZ = 'N', then Z is not referenced.
3915: PROCEDURE lapack_sbevd(jobz IN flag,
3916: uplo IN flag,
3917: n IN POSITIVEN,
3918: kd IN NATURALN,
3919: ab IN OUT UTL_NLA_ARRAY_FLT,
3920: ldab IN POSITIVEN,
3921: w IN OUT UTL_NLA_ARRAY_FLT,
3922: z IN OUT UTL_NLA_ARRAY_FLT,
3923: ldz IN POSITIVEN,
3917: n IN POSITIVEN,
3918: kd IN NATURALN,
3919: ab IN OUT UTL_NLA_ARRAY_FLT,
3920: ldab IN POSITIVEN,
3921: w IN OUT UTL_NLA_ARRAY_FLT,
3922: z IN OUT UTL_NLA_ARRAY_FLT,
3923: ldz IN POSITIVEN,
3924: info OUT integer,
3925: pack IN flag DEFAULT 'C');
3918: kd IN NATURALN,
3919: ab IN OUT UTL_NLA_ARRAY_FLT,
3920: ldab IN POSITIVEN,
3921: w IN OUT UTL_NLA_ARRAY_FLT,
3922: z IN OUT UTL_NLA_ARRAY_FLT,
3923: ldz IN POSITIVEN,
3924: info OUT integer,
3925: pack IN flag DEFAULT 'C');
3926:
3940: --
3941: -- N (input) INTEGER
3942: -- The order of the matrix. N >= 0.
3943: --
3944: -- D (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3945: -- On entry, the n diagonal elements of the tridiagonal matrix
3946: -- A.
3947: -- On exit, if INFO = 0, the eigenvalues in ascending order.
3948: --
3945: -- On entry, the n diagonal elements of the tridiagonal matrix
3946: -- A.
3947: -- On exit, if INFO = 0, the eigenvalues in ascending order.
3948: --
3949: -- E (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
3950: -- On entry, the (n-1) subdiagonal elements of the tridiagonal
3951: -- matrix A, stored in elements 1 to N-1 of E; E(N) need not
3952: -- be set, but is used by the routine.
3953: -- On exit, the contents of E are destroyed.
3951: -- matrix A, stored in elements 1 to N-1 of E; E(N) need not
3952: -- be set, but is used by the routine.
3953: -- On exit, the contents of E are destroyed.
3954: --
3955: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
3956: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
3957: -- eigenvectors of the matrix A, with the i-th column of Z
3958: -- holding the eigenvector associated with D(i).
3959: -- If JOBZ = 'N', then Z is not referenced.
3983: pack IN flag DEFAULT 'C');
3984:
3985: PROCEDURE lapack_stev(jobz IN flag,
3986: n IN POSITIVEN,
3987: d IN OUT UTL_NLA_ARRAY_FLT,
3988: e IN OUT UTL_NLA_ARRAY_FLT,
3989: z IN OUT UTL_NLA_ARRAY_FLT,
3990: ldz IN POSITIVEN,
3991: info OUT integer,
3984:
3985: PROCEDURE lapack_stev(jobz IN flag,
3986: n IN POSITIVEN,
3987: d IN OUT UTL_NLA_ARRAY_FLT,
3988: e IN OUT UTL_NLA_ARRAY_FLT,
3989: z IN OUT UTL_NLA_ARRAY_FLT,
3990: ldz IN POSITIVEN,
3991: info OUT integer,
3992: pack IN flag DEFAULT 'C');
3985: PROCEDURE lapack_stev(jobz IN flag,
3986: n IN POSITIVEN,
3987: d IN OUT UTL_NLA_ARRAY_FLT,
3988: e IN OUT UTL_NLA_ARRAY_FLT,
3989: z IN OUT UTL_NLA_ARRAY_FLT,
3990: ldz IN POSITIVEN,
3991: info OUT integer,
3992: pack IN flag DEFAULT 'C');
3993:
4011: --
4012: -- N (input) INTEGER
4013: -- The order of the matrix. N >= 0.
4014: --
4015: -- D (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4016: -- On entry, the n diagonal elements of the tridiagonal matrix
4017: -- A.
4018: -- On exit, if INFO = 0, the eigenvalues in ascending order.
4019: --
4016: -- On entry, the n diagonal elements of the tridiagonal matrix
4017: -- A.
4018: -- On exit, if INFO = 0, the eigenvalues in ascending order.
4019: --
4020: -- E (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4021: -- On entry, the (n-1) subdiagonal elements of the tridiagonal
4022: -- matrix A, stored in elements 1 to N-1 of E; E(N) need not
4023: -- be set, but is used by the routine.
4024: -- On exit, the contents of E are destroyed.
4022: -- matrix A, stored in elements 1 to N-1 of E; E(N) need not
4023: -- be set, but is used by the routine.
4024: -- On exit, the contents of E are destroyed.
4025: --
4026: -- Z (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDZ, N)
4027: -- If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
4028: -- eigenvectors of the matrix A, with the i-th column of Z
4029: -- holding the eigenvector associated with D(i).
4030: -- If JOBZ = 'N', then Z is not referenced.
4054: pack IN flag DEFAULT 'C');
4055:
4056: PROCEDURE lapack_stevd(jobz IN flag,
4057: n IN POSITIVEN,
4058: d IN OUT UTL_NLA_ARRAY_FLT,
4059: e IN OUT UTL_NLA_ARRAY_FLT,
4060: z IN OUT UTL_NLA_ARRAY_FLT,
4061: ldz IN POSITIVEN,
4062: info OUT integer,
4055:
4056: PROCEDURE lapack_stevd(jobz IN flag,
4057: n IN POSITIVEN,
4058: d IN OUT UTL_NLA_ARRAY_FLT,
4059: e IN OUT UTL_NLA_ARRAY_FLT,
4060: z IN OUT UTL_NLA_ARRAY_FLT,
4061: ldz IN POSITIVEN,
4062: info OUT integer,
4063: pack IN flag DEFAULT 'C');
4056: PROCEDURE lapack_stevd(jobz IN flag,
4057: n IN POSITIVEN,
4058: d IN OUT UTL_NLA_ARRAY_FLT,
4059: e IN OUT UTL_NLA_ARRAY_FLT,
4060: z IN OUT UTL_NLA_ARRAY_FLT,
4061: ldz IN POSITIVEN,
4062: info OUT integer,
4063: pack IN flag DEFAULT 'C');
4064:
4089: --
4090: -- N (input) INTEGER
4091: -- The order of the matrix A. N >= 0.
4092: --
4093: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
4094: -- On entry, the N-by-N matrix A.
4095: -- On exit, A has been overwritten by its real Schur form T.
4096: --
4097: -- LDA (input) INTEGER
4096: --
4097: -- LDA (input) INTEGER
4098: -- The leading dimension of the array A. LDA >= max(1,N).
4099: --
4100: -- WR (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4101: -- WI (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4102: -- WR and WI contain the real and imaginary parts,
4103: -- respectively, of the computed eigenvalues in the same order
4104: -- that they appear on the diagonal of the output Schur form T.
4097: -- LDA (input) INTEGER
4098: -- The leading dimension of the array A. LDA >= max(1,N).
4099: --
4100: -- WR (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4101: -- WI (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4102: -- WR and WI contain the real and imaginary parts,
4103: -- respectively, of the computed eigenvalues in the same order
4104: -- that they appear on the diagonal of the output Schur form T.
4105: -- Complex conjugate pairs of eigenvalues will appear
4105: -- Complex conjugate pairs of eigenvalues will appear
4106: -- consecutively with the eigenvalue having the positive
4107: -- imaginary part first.
4108: --
4109: -- VS (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDVS,N)
4110: -- If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
4111: -- vectors.
4112: -- If JOBVS = 'N', VS is not referenced.
4113: --
4142: pack IN flag DEFAULT 'C');
4143:
4144: PROCEDURE lapack_gees(jobvs IN flag,
4145: n IN POSITIVEN,
4146: a IN OUT UTL_NLA_ARRAY_FLT,
4147: lda IN POSITIVEN,
4148: wr IN OUT UTL_NLA_ARRAY_FLT,
4149: wi IN OUT UTL_NLA_ARRAY_FLT,
4150: vs IN OUT UTL_NLA_ARRAY_FLT,
4144: PROCEDURE lapack_gees(jobvs IN flag,
4145: n IN POSITIVEN,
4146: a IN OUT UTL_NLA_ARRAY_FLT,
4147: lda IN POSITIVEN,
4148: wr IN OUT UTL_NLA_ARRAY_FLT,
4149: wi IN OUT UTL_NLA_ARRAY_FLT,
4150: vs IN OUT UTL_NLA_ARRAY_FLT,
4151: ldvs IN POSITIVEN,
4152: info OUT integer,
4145: n IN POSITIVEN,
4146: a IN OUT UTL_NLA_ARRAY_FLT,
4147: lda IN POSITIVEN,
4148: wr IN OUT UTL_NLA_ARRAY_FLT,
4149: wi IN OUT UTL_NLA_ARRAY_FLT,
4150: vs IN OUT UTL_NLA_ARRAY_FLT,
4151: ldvs IN POSITIVEN,
4152: info OUT integer,
4153: pack IN flag DEFAULT 'C');
4146: a IN OUT UTL_NLA_ARRAY_FLT,
4147: lda IN POSITIVEN,
4148: wr IN OUT UTL_NLA_ARRAY_FLT,
4149: wi IN OUT UTL_NLA_ARRAY_FLT,
4150: vs IN OUT UTL_NLA_ARRAY_FLT,
4151: ldvs IN POSITIVEN,
4152: info OUT integer,
4153: pack IN flag DEFAULT 'C');
4154:
4182: --
4183: -- N (input) INTEGER
4184: -- The order of the matrix A. N >= 0.
4185: --
4186: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
4187: -- On entry, the N-by-N matrix A.
4188: -- On exit, A has been overwritten.
4189: --
4190: -- LDA (input) INTEGER
4189: --
4190: -- LDA (input) INTEGER
4191: -- The leading dimension of the array A. LDA >= max(1,N).
4192: --
4193: -- WR (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4194: -- WI (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4195: -- WR and WI contain the real and imaginary parts,
4196: -- respectively, of the computed eigenvalues. Complex
4197: -- conjugate pairs of eigenvalues appear consecutively
4190: -- LDA (input) INTEGER
4191: -- The leading dimension of the array A. LDA >= max(1,N).
4192: --
4193: -- WR (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4194: -- WI (output) UTL_NLA_ARRAY_FLT/DBL, dimension (N)
4195: -- WR and WI contain the real and imaginary parts,
4196: -- respectively, of the computed eigenvalues. Complex
4197: -- conjugate pairs of eigenvalues appear consecutively
4198: -- with the eigenvalue having the positive imaginary part
4197: -- conjugate pairs of eigenvalues appear consecutively
4198: -- with the eigenvalue having the positive imaginary part
4199: -- first.
4200: --
4201: -- VL (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDVL,N)
4202: -- If JOBVL = 'V', the left eigenvectors u(j) are stored one
4203: -- after another in the columns of VL, in the same order
4204: -- as their eigenvalues.
4205: -- If JOBVL = 'N', VL is not referenced.
4212: -- LDVL (input) INTEGER
4213: -- The leading dimension of the array VL. LDVL >= 1; if
4214: -- JOBVL = 'V', LDVL >= N.
4215: --
4216: -- VR (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDVR,N)
4217: -- If JOBVR = 'V', the right eigenvectors v(j) are stored one
4218: -- after another in the columns of VR, in the same order
4219: -- as their eigenvalues.
4220: -- If JOBVR = 'N', VR is not referenced.
4257:
4258: PROCEDURE lapack_geev(jobvl IN flag,
4259: jobvr IN flag,
4260: n IN POSITIVEN,
4261: a IN OUT UTL_NLA_ARRAY_FLT,
4262: lda IN POSITIVEN,
4263: wr IN OUT UTL_NLA_ARRAY_FLT,
4264: wi IN OUT UTL_NLA_ARRAY_FLT,
4265: vl IN OUT UTL_NLA_ARRAY_FLT,
4259: jobvr IN flag,
4260: n IN POSITIVEN,
4261: a IN OUT UTL_NLA_ARRAY_FLT,
4262: lda IN POSITIVEN,
4263: wr IN OUT UTL_NLA_ARRAY_FLT,
4264: wi IN OUT UTL_NLA_ARRAY_FLT,
4265: vl IN OUT UTL_NLA_ARRAY_FLT,
4266: ldvl IN POSITIVEN,
4267: vr IN OUT UTL_NLA_ARRAY_FLT,
4260: n IN POSITIVEN,
4261: a IN OUT UTL_NLA_ARRAY_FLT,
4262: lda IN POSITIVEN,
4263: wr IN OUT UTL_NLA_ARRAY_FLT,
4264: wi IN OUT UTL_NLA_ARRAY_FLT,
4265: vl IN OUT UTL_NLA_ARRAY_FLT,
4266: ldvl IN POSITIVEN,
4267: vr IN OUT UTL_NLA_ARRAY_FLT,
4268: ldvr IN POSITIVEN,
4261: a IN OUT UTL_NLA_ARRAY_FLT,
4262: lda IN POSITIVEN,
4263: wr IN OUT UTL_NLA_ARRAY_FLT,
4264: wi IN OUT UTL_NLA_ARRAY_FLT,
4265: vl IN OUT UTL_NLA_ARRAY_FLT,
4266: ldvl IN POSITIVEN,
4267: vr IN OUT UTL_NLA_ARRAY_FLT,
4268: ldvr IN POSITIVEN,
4269: info OUT INTEGER,
4263: wr IN OUT UTL_NLA_ARRAY_FLT,
4264: wi IN OUT UTL_NLA_ARRAY_FLT,
4265: vl IN OUT UTL_NLA_ARRAY_FLT,
4266: ldvl IN POSITIVEN,
4267: vr IN OUT UTL_NLA_ARRAY_FLT,
4268: ldvr IN POSITIVEN,
4269: info OUT INTEGER,
4270: pack IN flag DEFAULT 'C');
4271:
4321: --
4322: -- N (input) INTEGER
4323: -- The number of columns of the input matrix A. N >= 0.
4324: --
4325: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
4326: -- On entry, the M-by-N matrix A.
4327: -- On exit,
4328: -- if JOBU = 'O', A is overwritten with the first min(m,n)
4329: -- columns of U (the left singular vectors,
4336: --
4337: -- LDA (input) INTEGER
4338: -- The leading dimension of the array A. LDA >= max(1,M).
4339: --
4340: -- S (output) UTL_NLA_ARRAY_FLT/DBL, dimension (min(M,N))
4341: -- The singular values of A, sorted so that S(i) >= S(i+1).
4342: --
4343: -- U (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDU,UCOL)
4344: -- (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
4339: --
4340: -- S (output) UTL_NLA_ARRAY_FLT/DBL, dimension (min(M,N))
4341: -- The singular values of A, sorted so that S(i) >= S(i+1).
4342: --
4343: -- U (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDU,UCOL)
4344: -- (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
4345: -- If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
4346: -- if JOBU = 'S', U contains the first min(m,n) columns of U
4347: -- (the left singular vectors, stored columnwise);
4350: -- LDU (input) INTEGER
4351: -- The leading dimension of the array U. LDU >= 1; if
4352: -- JOBU = 'S' or 'A', LDU >= M.
4353: --
4354: -- VT (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDVT,N)
4355: -- If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
4356: -- V**T;
4357: -- if JOBVT = 'S', VT contains the first min(m,n) rows of
4358: -- V**T (the right singular vectors, stored rowwise);
4392: PROCEDURE lapack_gesvd(jobu IN flag,
4393: jobvt IN flag,
4394: m IN POSITIVEN,
4395: n IN POSITIVEN,
4396: a IN OUT UTL_NLA_ARRAY_FLT,
4397: lda IN POSITIVEN,
4398: s IN OUT UTL_NLA_ARRAY_FLT,
4399: u IN OUT UTL_NLA_ARRAY_FLT,
4400: ldu IN POSITIVEN,
4394: m IN POSITIVEN,
4395: n IN POSITIVEN,
4396: a IN OUT UTL_NLA_ARRAY_FLT,
4397: lda IN POSITIVEN,
4398: s IN OUT UTL_NLA_ARRAY_FLT,
4399: u IN OUT UTL_NLA_ARRAY_FLT,
4400: ldu IN POSITIVEN,
4401: vt IN OUT UTL_NLA_ARRAY_FLT,
4402: ldvt IN POSITIVEN,
4395: n IN POSITIVEN,
4396: a IN OUT UTL_NLA_ARRAY_FLT,
4397: lda IN POSITIVEN,
4398: s IN OUT UTL_NLA_ARRAY_FLT,
4399: u IN OUT UTL_NLA_ARRAY_FLT,
4400: ldu IN POSITIVEN,
4401: vt IN OUT UTL_NLA_ARRAY_FLT,
4402: ldvt IN POSITIVEN,
4403: info OUT integer,
4397: lda IN POSITIVEN,
4398: s IN OUT UTL_NLA_ARRAY_FLT,
4399: u IN OUT UTL_NLA_ARRAY_FLT,
4400: ldu IN POSITIVEN,
4401: vt IN OUT UTL_NLA_ARRAY_FLT,
4402: ldvt IN POSITIVEN,
4403: info OUT integer,
4404: pack IN flag DEFAULT 'C');
4405:
4451: --
4452: -- N (input) INTEGER
4453: -- The number of columns of the input matrix A. N >= 0.
4454: --
4455: -- A (input/output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDA,N)
4456: -- On entry, the M-by-N matrix A.
4457: -- On exit,
4458: -- if JOBZ = 'O', A is overwritten with the first N columns
4459: -- of U (the left singular vectors, stored
4465: --
4466: -- LDA (input) INTEGER
4467: -- The leading dimension of the array A. LDA >= max(1,M).
4468: --
4469: -- S (output) UTL_NLA_ARRAY_FLT/DBL, dimension (min(M,N))
4470: -- The singular values of A, sorted so that S(i) >= S(i+1).
4471: --
4472: -- U (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDU,UCOL)
4473: -- UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
4468: --
4469: -- S (output) UTL_NLA_ARRAY_FLT/DBL, dimension (min(M,N))
4470: -- The singular values of A, sorted so that S(i) >= S(i+1).
4471: --
4472: -- U (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDU,UCOL)
4473: -- UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
4474: -- UCOL = min(M,N) if JOBZ = 'S'.
4475: -- If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
4476: -- orthogonal matrix U;
4481: -- LDU (input) INTEGER
4482: -- The leading dimension of the array U. LDU >= 1; if
4483: -- JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
4484: --
4485: -- VT (output) UTL_NLA_ARRAY_FLT/DBL, dimension (LDVT,N)
4486: -- If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
4487: -- N-by-N orthogonal matrix V**T;
4488: -- if JOBZ = 'S', VT contains the first min(M,N) rows of
4489: -- V**T (the right singular vectors, stored rowwise);
4519:
4520: PROCEDURE lapack_gesdd(jobz IN flag,
4521: m IN POSITIVEN,
4522: n IN POSITIVEN,
4523: a IN OUT UTL_NLA_ARRAY_FLT,
4524: lda IN POSITIVEN,
4525: s IN OUT UTL_NLA_ARRAY_FLT,
4526: u IN OUT UTL_NLA_ARRAY_FLT,
4527: ldu IN POSITIVEN,
4521: m IN POSITIVEN,
4522: n IN POSITIVEN,
4523: a IN OUT UTL_NLA_ARRAY_FLT,
4524: lda IN POSITIVEN,
4525: s IN OUT UTL_NLA_ARRAY_FLT,
4526: u IN OUT UTL_NLA_ARRAY_FLT,
4527: ldu IN POSITIVEN,
4528: vt IN OUT UTL_NLA_ARRAY_FLT,
4529: ldvt IN POSITIVEN,
4522: n IN POSITIVEN,
4523: a IN OUT UTL_NLA_ARRAY_FLT,
4524: lda IN POSITIVEN,
4525: s IN OUT UTL_NLA_ARRAY_FLT,
4526: u IN OUT UTL_NLA_ARRAY_FLT,
4527: ldu IN POSITIVEN,
4528: vt IN OUT UTL_NLA_ARRAY_FLT,
4529: ldvt IN POSITIVEN,
4530: info OUT INTEGER,
4524: lda IN POSITIVEN,
4525: s IN OUT UTL_NLA_ARRAY_FLT,
4526: u IN OUT UTL_NLA_ARRAY_FLT,
4527: ldu IN POSITIVEN,
4528: vt IN OUT UTL_NLA_ARRAY_FLT,
4529: ldvt IN POSITIVEN,
4530: info OUT INTEGER,
4531: pack IN flag DEFAULT 'C');
4532: END UTL_NLA;