NIPY

Merge lp://qastaging/~nipy-developers/nipy/lapack-included into lp://qastaging/~nipy-developers/nipy/obsolete-do-not-use

  1. lapack-included
  2. Merge into obsolete-do-not-use
Proposed by Alexis Roche
Status: Rejected
Rejected by: Matthew Brett
Proposed branch: lp://qastaging/~nipy-developers/nipy/lapack-included
Merge into: lp://qastaging/~nipy-developers/nipy/obsolete-do-not-use
Diff against target: 49385 lines (+49271/-35)
10 files modified
libcstat/lapack_lite/blas_lite.c (+5676/-0)
libcstat/lapack_lite/dlamch.c (+951/-0)
libcstat/lapack_lite/dlapack_lite.c (+41548/-0)
libcstat/lapack_lite/f2c.h (+217/-0)
libcstat/lapack_lite/f2c_lite.c (+519/-0)
libcstat/lapack_lite/remake/README (+31/-0)
libcstat/lapack_lite/remake/make_lite.py (+264/-0)
libcstat/lapack_lite/remake/wrapped_routines.txt (+40/-0)
nipy/neurospin/__init__.py (+2/-1)
nipy/neurospin/setup.py (+23/-34)
To merge this branch: bzr merge lp://qastaging/~nipy-developers/nipy/lapack-included
Reviewer Review Type Date Requested Status
Matthew Brett Disapprove
Review via email: mp+14762@code.qastaging.launchpad.net
To post a comment you must log in.
Revision history for this message
Alexis Roche (alexis-roche) wrote :

This branch includes a "lapack lite" distribution so that nipy can build on systems where lapack is not installed. More specifically, if the setup doesn't find lapack on the system, then it builds the necessary blas/lapack routines (as translated in C from the original fortran code using f2c). A similar approach is implemented in numpy, however this implementation is completely independent.

It currently triggers run-time errors on Windows with python 2.6 due to a known issue that has necessitated a fair amount of hacks in numpy:

http://cournape.wordpress.com/2008/09/02/how-to-embed-a-manifest-into-a-dll-with-mingw-tools-only/

http://svn.scipy.org/svn/numpy/trunk/numpy/random/setup.py

I feel that it would be a waste of time to develop code to work around this specific problem, given that most windows users will generally prefer to use binary installers anyway. It seems to work fine on linux, and should therefore be of some help.

Revision history for this message
Matthew Brett (matthew-brett) wrote :

Thanks for doing this.

Just a question - can you think of any way of dealing with this by an automated pull-and-patch from the numpy sources? Is there anything of the fixes here that we should contribute back to numpy, to make it easier to maintain?

I see you've made the dependency checks not raise an error, but this means that anyone running the tests and without the dependencies, is likely to hit lots of errors. I suggest we take that back to the list, and remove it from this patch, because it's solving a different problem.

For future portability and to reduce some odd effects, all classes should be explicitly new-style;

class FortranRoutine: -> class FortranRoutine(object):

review: Needs Information
lp://qastaging/~nipy-developers/nipy/lapack-included updated
1801. By Alexis Roche

Revert main setup.py to original version (hard dependency check)

Revision history for this message
Alexis Roche (alexis-roche) wrote :

Hi,

> Just a question - can you think of any way of dealing with this by an automated pull-and-patch from the numpy sources?  Is there anything of the fixes here that we should contribute back to numpy, to make it easier to maintain?

The mechanism I implemented is mainly a copy-paste from the numpy
approach, so I am afraid there is not much to contribute back at the
moment. This is described here:

http://bazaar.launchpad.net/~nipy-developers/nipy/lapack-included/annotate/head%3A/libcstat/lapack_lite/remake/README

Of course, the ideal situation would be to have lapack_lite exposed by
numpy, and I am willing to contribute any effort in that direction if
I can help. From the nipy side, we will have to make sure that all the
routines we need are included in that library.

Note that we have the very same problem with the randomkit library (a
copy of which is currently sleeping in our repo).

> I see you've made the dependency checks not raise an error, but this means that anyone running the tests and without the dependencies, is likely to hit lots of errors.  I suggest we take that back to the list, and remove it from this patch, because it's solving a different problem.
>

Yeah, I agree, I just reverted it (it was my initial intention, but forgot).

This brings us back to the ease-of-installation issue raised by Satra
last week. I am using this custom setup.py to avoid installing pynifti
on my windows system, which is currently a non-trivial task with
python 2.6 (last time I checked, there was no binary installer).

Cheers,

Alexis

Revision history for this message
Matthew Brett (matthew-brett) wrote :

Alexis - I believe this branch is superseded by the later neurospin trunk merge? OK to 'supersede' this branch?

Revision history for this message
Alexis Roche (alexis-roche) wrote :

OK.

Happy new year BTW.

Cheers,

Alexis

On Wed, Jan 13, 2010 at 2:06 PM, Matthew Brett <email address hidden> wrote:
> Alexis - I believe this branch is superseded by the later neurospin trunk merge?  OK to 'supersede' this branch?
> --
> https://code.launchpad.net/~nipy-developers/nipy/lapack-included/+merge/14762
> You proposed lp:~nipy-developers/nipy/lapack-included for merging.
>

--
Alexis Roche, PhD
Researcher, CEA, Neurospin, Paris, France
Academic Guest, ETHZ, Computer Vision Lab, Zurich, Switzerland
http://alexis.roche.googlepages.com

Revision history for this message
Matthew Brett (matthew-brett) wrote :

Thanks - likewise...

review: Disapprove
Revision history for this message
Alexis Roche (alexis-roche) wrote :

Hi,

I&#39;d like to add you to my professional network on LinkedIn.

- Alexis

Accept: http://www.linkedin.com/blink?simpleRedirect=3wOdP4SdjATc3wVejAMcP4OejkZh4BKrSBQonhFtCVF9ClpqD9fujsSfnBBiShBsC5EsOpQsSlRpRZBt6BSrCAZqSkConhzbmlQqnpKqiRQsSlRpORIrmkZpSVFqSdxsDgCpnhFtCV9pSlipn9Mfm4CdPkJdPxRrT9Gc6AJtmpBuj4NbjRBfP9SbSkLrmZzbCVFp6lHrCBIbDtTtOYLeDdMt7hE&msgID=I7984211713_1&markAsRead=

You received an invitation to connect. LinkedIn will use your email address to make suggestions to our members in features like People You May Know. Unsubscribe here: http://www.linkedin.com/blink?simpleRedirect=1QpmV5cylAon1EoSVRomN5cylBp6Zzc3gBczoTd352cylMrjRIqm5JpipEqSZLon1Mr71ysn1GoPgZp6Bx9z4Sc30OfmhF9z4JfmhFrioTdiQTe7lLsCEMqiRRpClVcj4JfmhFpipQsSlRpRZBt6BSrCAZqSkCkjoPp4l7q5p6sCR6kk4ZrClHrRhAqmQCsSVRfngCdPkJdPxRrT9Gc6AJtmpBuj4NbjRBfP9SbSkLrmZzbCVFp6lHrCBIbDtTtOYLeDdMt7hE&amp;msgID=I7984211713_1&amp;markAsRead= Learn why we included this at the following link: http://www.linkedin.com/blink?simpleRedirect=e3wTd3RAimlIoSBQsC4Ct7dBtmtvpnhFtCVFfmJB9CNOlmlzqnpOpldOpmRLt7dRoPRx9zsRbjsUtmZOqz1FbnlCpnANciQZpjYOtyZBbSRLoOVKqmhBqSVFr2VTtTsLbPFMt7hE&msgID=I7984211713_1&markAsRead=
&copy; 2014, LinkedIn Corporation. 2029 Stierlin Ct. Mountain View, CA 94043, USA

Unmerged revisions

1801. By Alexis Roche

Revert main setup.py to original version (hard dependency check)

Preview Diff

[H/L] Next/Prev Comment, [J/K] Next/Prev File, [N/P] Next/Prev Hunk
1=== added directory 'libcstat/lapack_lite'
2=== added file 'libcstat/lapack_lite/blas_lite.c'
3--- libcstat/lapack_lite/blas_lite.c 1970-01-01 00:00:00 +0000
4+++ libcstat/lapack_lite/blas_lite.c 2009-11-14 08:49:09 +0000
5@@ -0,0 +1,5676 @@
6+/*
7+NOTE: This is generated code. Look in Misc/lapack_lite for information on
8+ remaking this file.
9+*/
10+#include "f2c.h"
11+
12+#ifdef HAVE_CONFIG
13+#include "config.h"
14+#else
15+extern doublereal dlamch_(char *);
16+#define EPSILON dlamch_("Epsilon")
17+#define SAFEMINIMUM dlamch_("Safe minimum")
18+#define PRECISION dlamch_("Precision")
19+#define BASE dlamch_("Base")
20+#endif
21+
22+extern doublereal dlapy2_(doublereal *x, doublereal *y);
23+
24+
25+
26+/* Table of constant values */
27+
28+static doublereal c_b90 = 1.;
29+static integer c__1 = 1;
30+
31+doublereal dasum_(integer *n, doublereal *dx, integer *incx)
32+{
33+ /* System generated locals */
34+ integer i__1, i__2;
35+ doublereal ret_val, d__1, d__2, d__3, d__4, d__5, d__6;
36+
37+ /* Local variables */
38+ static integer i__, m;
39+ static doublereal dtemp;
40+ static integer nincx, mp1;
41+
42+
43+/*
44+ Purpose
45+ =======
46+
47+ takes the sum of the absolute values.
48+ jack dongarra, linpack, 3/11/78.
49+ modified 3/93 to return if incx .le. 0.
50+ modified 12/3/93, array(1) declarations changed to array(*)
51+*/
52+
53+
54+ /* Parameter adjustments */
55+ --dx;
56+
57+ /* Function Body */
58+ ret_val = 0.;
59+ dtemp = 0.;
60+ if (*n <= 0 || *incx <= 0) {
61+ return ret_val;
62+ }
63+ if (*incx == 1) {
64+ goto L20;
65+ }
66+
67+/* code for increment not equal to 1 */
68+
69+ nincx = *n * *incx;
70+ i__1 = nincx;
71+ i__2 = *incx;
72+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
73+ dtemp += (d__1 = dx[i__], abs(d__1));
74+/* L10: */
75+ }
76+ ret_val = dtemp;
77+ return ret_val;
78+
79+/*
80+ code for increment equal to 1
81+
82+
83+ clean-up loop
84+*/
85+
86+L20:
87+ m = *n % 6;
88+ if (m == 0) {
89+ goto L40;
90+ }
91+ i__2 = m;
92+ for (i__ = 1; i__ <= i__2; ++i__) {
93+ dtemp += (d__1 = dx[i__], abs(d__1));
94+/* L30: */
95+ }
96+ if (*n < 6) {
97+ goto L60;
98+ }
99+L40:
100+ mp1 = m + 1;
101+ i__2 = *n;
102+ for (i__ = mp1; i__ <= i__2; i__ += 6) {
103+ dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1],
104+ abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = dx[i__
105+ + 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) + (d__6 =
106+ dx[i__ + 5], abs(d__6));
107+/* L50: */
108+ }
109+L60:
110+ ret_val = dtemp;
111+ return ret_val;
112+} /* dasum_ */
113+
114+/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx,
115+ integer *incx, doublereal *dy, integer *incy)
116+{
117+ /* System generated locals */
118+ integer i__1;
119+
120+ /* Local variables */
121+ static integer i__, m, ix, iy, mp1;
122+
123+
124+/*
125+ Purpose
126+ =======
127+
128+ constant times a vector plus a vector.
129+ uses unrolled loops for increments equal to one.
130+ jack dongarra, linpack, 3/11/78.
131+ modified 12/3/93, array(1) declarations changed to array(*)
132+*/
133+
134+
135+ /* Parameter adjustments */
136+ --dy;
137+ --dx;
138+
139+ /* Function Body */
140+ if (*n <= 0) {
141+ return 0;
142+ }
143+ if (*da == 0.) {
144+ return 0;
145+ }
146+ if (*incx == 1 && *incy == 1) {
147+ goto L20;
148+ }
149+
150+/*
151+ code for unequal increments or equal increments
152+ not equal to 1
153+*/
154+
155+ ix = 1;
156+ iy = 1;
157+ if (*incx < 0) {
158+ ix = (-(*n) + 1) * *incx + 1;
159+ }
160+ if (*incy < 0) {
161+ iy = (-(*n) + 1) * *incy + 1;
162+ }
163+ i__1 = *n;
164+ for (i__ = 1; i__ <= i__1; ++i__) {
165+ dy[iy] += *da * dx[ix];
166+ ix += *incx;
167+ iy += *incy;
168+/* L10: */
169+ }
170+ return 0;
171+
172+/*
173+ code for both increments equal to 1
174+
175+
176+ clean-up loop
177+*/
178+
179+L20:
180+ m = *n % 4;
181+ if (m == 0) {
182+ goto L40;
183+ }
184+ i__1 = m;
185+ for (i__ = 1; i__ <= i__1; ++i__) {
186+ dy[i__] += *da * dx[i__];
187+/* L30: */
188+ }
189+ if (*n < 4) {
190+ return 0;
191+ }
192+L40:
193+ mp1 = m + 1;
194+ i__1 = *n;
195+ for (i__ = mp1; i__ <= i__1; i__ += 4) {
196+ dy[i__] += *da * dx[i__];
197+ dy[i__ + 1] += *da * dx[i__ + 1];
198+ dy[i__ + 2] += *da * dx[i__ + 2];
199+ dy[i__ + 3] += *da * dx[i__ + 3];
200+/* L50: */
201+ }
202+ return 0;
203+} /* daxpy_ */
204+
205+doublereal dcabs1_(doublecomplex *z__)
206+{
207+ /* System generated locals */
208+ doublereal ret_val, d__1, d__2;
209+
210+ /* Builtin functions */
211+ double d_imag(doublecomplex *);
212+
213+/*
214+ Purpose
215+ =======
216+
217+ DCABS1 computes absolute value of a double complex number
218+*/
219+
220+
221+ ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_imag(z__), abs(d__2));
222+ return ret_val;
223+} /* dcabs1_ */
224+
225+/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx,
226+ doublereal *dy, integer *incy)
227+{
228+ /* System generated locals */
229+ integer i__1;
230+
231+ /* Local variables */
232+ static integer i__, m, ix, iy, mp1;
233+
234+
235+/*
236+ Purpose
237+ =======
238+
239+ copies a vector, x, to a vector, y.
240+ uses unrolled loops for increments equal to one.
241+ jack dongarra, linpack, 3/11/78.
242+ modified 12/3/93, array(1) declarations changed to array(*)
243+*/
244+
245+
246+ /* Parameter adjustments */
247+ --dy;
248+ --dx;
249+
250+ /* Function Body */
251+ if (*n <= 0) {
252+ return 0;
253+ }
254+ if (*incx == 1 && *incy == 1) {
255+ goto L20;
256+ }
257+
258+/*
259+ code for unequal increments or equal increments
260+ not equal to 1
261+*/
262+
263+ ix = 1;
264+ iy = 1;
265+ if (*incx < 0) {
266+ ix = (-(*n) + 1) * *incx + 1;
267+ }
268+ if (*incy < 0) {
269+ iy = (-(*n) + 1) * *incy + 1;
270+ }
271+ i__1 = *n;
272+ for (i__ = 1; i__ <= i__1; ++i__) {
273+ dy[iy] = dx[ix];
274+ ix += *incx;
275+ iy += *incy;
276+/* L10: */
277+ }
278+ return 0;
279+
280+/*
281+ code for both increments equal to 1
282+
283+
284+ clean-up loop
285+*/
286+
287+L20:
288+ m = *n % 7;
289+ if (m == 0) {
290+ goto L40;
291+ }
292+ i__1 = m;
293+ for (i__ = 1; i__ <= i__1; ++i__) {
294+ dy[i__] = dx[i__];
295+/* L30: */
296+ }
297+ if (*n < 7) {
298+ return 0;
299+ }
300+L40:
301+ mp1 = m + 1;
302+ i__1 = *n;
303+ for (i__ = mp1; i__ <= i__1; i__ += 7) {
304+ dy[i__] = dx[i__];
305+ dy[i__ + 1] = dx[i__ + 1];
306+ dy[i__ + 2] = dx[i__ + 2];
307+ dy[i__ + 3] = dx[i__ + 3];
308+ dy[i__ + 4] = dx[i__ + 4];
309+ dy[i__ + 5] = dx[i__ + 5];
310+ dy[i__ + 6] = dx[i__ + 6];
311+/* L50: */
312+ }
313+ return 0;
314+} /* dcopy_ */
315+
316+doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy,
317+ integer *incy)
318+{
319+ /* System generated locals */
320+ integer i__1;
321+ doublereal ret_val;
322+
323+ /* Local variables */
324+ static integer i__, m;
325+ static doublereal dtemp;
326+ static integer ix, iy, mp1;
327+
328+
329+/*
330+ Purpose
331+ =======
332+
333+ forms the dot product of two vectors.
334+ uses unrolled loops for increments equal to one.
335+ jack dongarra, linpack, 3/11/78.
336+ modified 12/3/93, array(1) declarations changed to array(*)
337+*/
338+
339+
340+ /* Parameter adjustments */
341+ --dy;
342+ --dx;
343+
344+ /* Function Body */
345+ ret_val = 0.;
346+ dtemp = 0.;
347+ if (*n <= 0) {
348+ return ret_val;
349+ }
350+ if (*incx == 1 && *incy == 1) {
351+ goto L20;
352+ }
353+
354+/*
355+ code for unequal increments or equal increments
356+ not equal to 1
357+*/
358+
359+ ix = 1;
360+ iy = 1;
361+ if (*incx < 0) {
362+ ix = (-(*n) + 1) * *incx + 1;
363+ }
364+ if (*incy < 0) {
365+ iy = (-(*n) + 1) * *incy + 1;
366+ }
367+ i__1 = *n;
368+ for (i__ = 1; i__ <= i__1; ++i__) {
369+ dtemp += dx[ix] * dy[iy];
370+ ix += *incx;
371+ iy += *incy;
372+/* L10: */
373+ }
374+ ret_val = dtemp;
375+ return ret_val;
376+
377+/*
378+ code for both increments equal to 1
379+
380+
381+ clean-up loop
382+*/
383+
384+L20:
385+ m = *n % 5;
386+ if (m == 0) {
387+ goto L40;
388+ }
389+ i__1 = m;
390+ for (i__ = 1; i__ <= i__1; ++i__) {
391+ dtemp += dx[i__] * dy[i__];
392+/* L30: */
393+ }
394+ if (*n < 5) {
395+ goto L60;
396+ }
397+L40:
398+ mp1 = m + 1;
399+ i__1 = *n;
400+ for (i__ = mp1; i__ <= i__1; i__ += 5) {
401+ dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[
402+ i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ +
403+ 4] * dy[i__ + 4];
404+/* L50: */
405+ }
406+L60:
407+ ret_val = dtemp;
408+ return ret_val;
409+} /* ddot_ */
410+
411+/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer *
412+ n, integer *k, doublereal *alpha, doublereal *a, integer *lda,
413+ doublereal *b, integer *ldb, doublereal *beta, doublereal *c__,
414+ integer *ldc)
415+{
416+ /* System generated locals */
417+ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
418+ i__3;
419+
420+ /* Local variables */
421+ static integer info;
422+ static logical nota, notb;
423+ static doublereal temp;
424+ static integer i__, j, l, ncola;
425+ extern logical lsame_(char *, char *);
426+ static integer nrowa, nrowb;
427+ extern /* Subroutine */ int xerbla_(char *, integer *);
428+
429+
430+/*
431+ Purpose
432+ =======
433+
434+ DGEMM performs one of the matrix-matrix operations
435+
436+ C := alpha*op( A )*op( B ) + beta*C,
437+
438+ where op( X ) is one of
439+
440+ op( X ) = X or op( X ) = X',
441+
442+ alpha and beta are scalars, and A, B and C are matrices, with op( A )
443+ an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
444+
445+ Arguments
446+ ==========
447+
448+ TRANSA - CHARACTER*1.
449+ On entry, TRANSA specifies the form of op( A ) to be used in
450+ the matrix multiplication as follows:
451+
452+ TRANSA = 'N' or 'n', op( A ) = A.
453+
454+ TRANSA = 'T' or 't', op( A ) = A'.
455+
456+ TRANSA = 'C' or 'c', op( A ) = A'.
457+
458+ Unchanged on exit.
459+
460+ TRANSB - CHARACTER*1.
461+ On entry, TRANSB specifies the form of op( B ) to be used in
462+ the matrix multiplication as follows:
463+
464+ TRANSB = 'N' or 'n', op( B ) = B.
465+
466+ TRANSB = 'T' or 't', op( B ) = B'.
467+
468+ TRANSB = 'C' or 'c', op( B ) = B'.
469+
470+ Unchanged on exit.
471+
472+ M - INTEGER.
473+ On entry, M specifies the number of rows of the matrix
474+ op( A ) and of the matrix C. M must be at least zero.
475+ Unchanged on exit.
476+
477+ N - INTEGER.
478+ On entry, N specifies the number of columns of the matrix
479+ op( B ) and the number of columns of the matrix C. N must be
480+ at least zero.
481+ Unchanged on exit.
482+
483+ K - INTEGER.
484+ On entry, K specifies the number of columns of the matrix
485+ op( A ) and the number of rows of the matrix op( B ). K must
486+ be at least zero.
487+ Unchanged on exit.
488+
489+ ALPHA - DOUBLE PRECISION.
490+ On entry, ALPHA specifies the scalar alpha.
491+ Unchanged on exit.
492+
493+ A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
494+ k when TRANSA = 'N' or 'n', and is m otherwise.
495+ Before entry with TRANSA = 'N' or 'n', the leading m by k
496+ part of the array A must contain the matrix A, otherwise
497+ the leading k by m part of the array A must contain the
498+ matrix A.
499+ Unchanged on exit.
500+
501+ LDA - INTEGER.
502+ On entry, LDA specifies the first dimension of A as declared
503+ in the calling (sub) program. When TRANSA = 'N' or 'n' then
504+ LDA must be at least max( 1, m ), otherwise LDA must be at
505+ least max( 1, k ).
506+ Unchanged on exit.
507+
508+ B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
509+ n when TRANSB = 'N' or 'n', and is k otherwise.
510+ Before entry with TRANSB = 'N' or 'n', the leading k by n
511+ part of the array B must contain the matrix B, otherwise
512+ the leading n by k part of the array B must contain the
513+ matrix B.
514+ Unchanged on exit.
515+
516+ LDB - INTEGER.
517+ On entry, LDB specifies the first dimension of B as declared
518+ in the calling (sub) program. When TRANSB = 'N' or 'n' then
519+ LDB must be at least max( 1, k ), otherwise LDB must be at
520+ least max( 1, n ).
521+ Unchanged on exit.
522+
523+ BETA - DOUBLE PRECISION.
524+ On entry, BETA specifies the scalar beta. When BETA is
525+ supplied as zero then C need not be set on input.
526+ Unchanged on exit.
527+
528+ C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
529+ Before entry, the leading m by n part of the array C must
530+ contain the matrix C, except when beta is zero, in which
531+ case C need not be set on entry.
532+ On exit, the array C is overwritten by the m by n matrix
533+ ( alpha*op( A )*op( B ) + beta*C ).
534+
535+ LDC - INTEGER.
536+ On entry, LDC specifies the first dimension of C as declared
537+ in the calling (sub) program. LDC must be at least
538+ max( 1, m ).
539+ Unchanged on exit.
540+
541+
542+ Level 3 Blas routine.
543+
544+ -- Written on 8-February-1989.
545+ Jack Dongarra, Argonne National Laboratory.
546+ Iain Duff, AERE Harwell.
547+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
548+ Sven Hammarling, Numerical Algorithms Group Ltd.
549+
550+
551+ Set NOTA and NOTB as true if A and B respectively are not
552+ transposed and set NROWA, NCOLA and NROWB as the number of rows
553+ and columns of A and the number of rows of B respectively.
554+*/
555+
556+ /* Parameter adjustments */
557+ a_dim1 = *lda;
558+ a_offset = 1 + a_dim1 * 1;
559+ a -= a_offset;
560+ b_dim1 = *ldb;
561+ b_offset = 1 + b_dim1 * 1;
562+ b -= b_offset;
563+ c_dim1 = *ldc;
564+ c_offset = 1 + c_dim1 * 1;
565+ c__ -= c_offset;
566+
567+ /* Function Body */
568+ nota = lsame_(transa, "N");
569+ notb = lsame_(transb, "N");
570+ if (nota) {
571+ nrowa = *m;
572+ ncola = *k;
573+ } else {
574+ nrowa = *k;
575+ ncola = *m;
576+ }
577+ if (notb) {
578+ nrowb = *k;
579+ } else {
580+ nrowb = *n;
581+ }
582+
583+/* Test the input parameters. */
584+
585+ info = 0;
586+ if (! nota && ! lsame_(transa, "C") && ! lsame_(
587+ transa, "T")) {
588+ info = 1;
589+ } else if (! notb && ! lsame_(transb, "C") && !
590+ lsame_(transb, "T")) {
591+ info = 2;
592+ } else if (*m < 0) {
593+ info = 3;
594+ } else if (*n < 0) {
595+ info = 4;
596+ } else if (*k < 0) {
597+ info = 5;
598+ } else if (*lda < max(1,nrowa)) {
599+ info = 8;
600+ } else if (*ldb < max(1,nrowb)) {
601+ info = 10;
602+ } else if (*ldc < max(1,*m)) {
603+ info = 13;
604+ }
605+ if (info != 0) {
606+ xerbla_("DGEMM ", &info);
607+ return 0;
608+ }
609+
610+/* Quick return if possible. */
611+
612+ if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
613+ return 0;
614+ }
615+
616+/* And if alpha.eq.zero. */
617+
618+ if (*alpha == 0.) {
619+ if (*beta == 0.) {
620+ i__1 = *n;
621+ for (j = 1; j <= i__1; ++j) {
622+ i__2 = *m;
623+ for (i__ = 1; i__ <= i__2; ++i__) {
624+ c__[i__ + j * c_dim1] = 0.;
625+/* L10: */
626+ }
627+/* L20: */
628+ }
629+ } else {
630+ i__1 = *n;
631+ for (j = 1; j <= i__1; ++j) {
632+ i__2 = *m;
633+ for (i__ = 1; i__ <= i__2; ++i__) {
634+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
635+/* L30: */
636+ }
637+/* L40: */
638+ }
639+ }
640+ return 0;
641+ }
642+
643+/* Start the operations. */
644+
645+ if (notb) {
646+ if (nota) {
647+
648+/* Form C := alpha*A*B + beta*C. */
649+
650+ i__1 = *n;
651+ for (j = 1; j <= i__1; ++j) {
652+ if (*beta == 0.) {
653+ i__2 = *m;
654+ for (i__ = 1; i__ <= i__2; ++i__) {
655+ c__[i__ + j * c_dim1] = 0.;
656+/* L50: */
657+ }
658+ } else if (*beta != 1.) {
659+ i__2 = *m;
660+ for (i__ = 1; i__ <= i__2; ++i__) {
661+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
662+/* L60: */
663+ }
664+ }
665+ i__2 = *k;
666+ for (l = 1; l <= i__2; ++l) {
667+ if (b[l + j * b_dim1] != 0.) {
668+ temp = *alpha * b[l + j * b_dim1];
669+ i__3 = *m;
670+ for (i__ = 1; i__ <= i__3; ++i__) {
671+ c__[i__ + j * c_dim1] += temp * a[i__ + l *
672+ a_dim1];
673+/* L70: */
674+ }
675+ }
676+/* L80: */
677+ }
678+/* L90: */
679+ }
680+ } else {
681+
682+/* Form C := alpha*A'*B + beta*C */
683+
684+ i__1 = *n;
685+ for (j = 1; j <= i__1; ++j) {
686+ i__2 = *m;
687+ for (i__ = 1; i__ <= i__2; ++i__) {
688+ temp = 0.;
689+ i__3 = *k;
690+ for (l = 1; l <= i__3; ++l) {
691+ temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
692+/* L100: */
693+ }
694+ if (*beta == 0.) {
695+ c__[i__ + j * c_dim1] = *alpha * temp;
696+ } else {
697+ c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
698+ i__ + j * c_dim1];
699+ }
700+/* L110: */
701+ }
702+/* L120: */
703+ }
704+ }
705+ } else {
706+ if (nota) {
707+
708+/* Form C := alpha*A*B' + beta*C */
709+
710+ i__1 = *n;
711+ for (j = 1; j <= i__1; ++j) {
712+ if (*beta == 0.) {
713+ i__2 = *m;
714+ for (i__ = 1; i__ <= i__2; ++i__) {
715+ c__[i__ + j * c_dim1] = 0.;
716+/* L130: */
717+ }
718+ } else if (*beta != 1.) {
719+ i__2 = *m;
720+ for (i__ = 1; i__ <= i__2; ++i__) {
721+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
722+/* L140: */
723+ }
724+ }
725+ i__2 = *k;
726+ for (l = 1; l <= i__2; ++l) {
727+ if (b[j + l * b_dim1] != 0.) {
728+ temp = *alpha * b[j + l * b_dim1];
729+ i__3 = *m;
730+ for (i__ = 1; i__ <= i__3; ++i__) {
731+ c__[i__ + j * c_dim1] += temp * a[i__ + l *
732+ a_dim1];
733+/* L150: */
734+ }
735+ }
736+/* L160: */
737+ }
738+/* L170: */
739+ }
740+ } else {
741+
742+/* Form C := alpha*A'*B' + beta*C */
743+
744+ i__1 = *n;
745+ for (j = 1; j <= i__1; ++j) {
746+ i__2 = *m;
747+ for (i__ = 1; i__ <= i__2; ++i__) {
748+ temp = 0.;
749+ i__3 = *k;
750+ for (l = 1; l <= i__3; ++l) {
751+ temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
752+/* L180: */
753+ }
754+ if (*beta == 0.) {
755+ c__[i__ + j * c_dim1] = *alpha * temp;
756+ } else {
757+ c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
758+ i__ + j * c_dim1];
759+ }
760+/* L190: */
761+ }
762+/* L200: */
763+ }
764+ }
765+ }
766+
767+ return 0;
768+
769+/* End of DGEMM . */
770+
771+} /* dgemm_ */
772+
773+/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal *
774+ alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
775+ doublereal *beta, doublereal *y, integer *incy)
776+{
777+ /* System generated locals */
778+ integer a_dim1, a_offset, i__1, i__2;
779+
780+ /* Local variables */
781+ static integer info;
782+ static doublereal temp;
783+ static integer lenx, leny, i__, j;
784+ extern logical lsame_(char *, char *);
785+ static integer ix, iy, jx, jy, kx, ky;
786+ extern /* Subroutine */ int xerbla_(char *, integer *);
787+
788+
789+/*
790+ Purpose
791+ =======
792+
793+ DGEMV performs one of the matrix-vector operations
794+
795+ y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
796+
797+ where alpha and beta are scalars, x and y are vectors and A is an
798+ m by n matrix.
799+
800+ Arguments
801+ ==========
802+
803+ TRANS - CHARACTER*1.
804+ On entry, TRANS specifies the operation to be performed as
805+ follows:
806+
807+ TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
808+
809+ TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
810+
811+ TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
812+
813+ Unchanged on exit.
814+
815+ M - INTEGER.
816+ On entry, M specifies the number of rows of the matrix A.
817+ M must be at least zero.
818+ Unchanged on exit.
819+
820+ N - INTEGER.
821+ On entry, N specifies the number of columns of the matrix A.
822+ N must be at least zero.
823+ Unchanged on exit.
824+
825+ ALPHA - DOUBLE PRECISION.
826+ On entry, ALPHA specifies the scalar alpha.
827+ Unchanged on exit.
828+
829+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
830+ Before entry, the leading m by n part of the array A must
831+ contain the matrix of coefficients.
832+ Unchanged on exit.
833+
834+ LDA - INTEGER.
835+ On entry, LDA specifies the first dimension of A as declared
836+ in the calling (sub) program. LDA must be at least
837+ max( 1, m ).
838+ Unchanged on exit.
839+
840+ X - DOUBLE PRECISION array of DIMENSION at least
841+ ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
842+ and at least
843+ ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
844+ Before entry, the incremented array X must contain the
845+ vector x.
846+ Unchanged on exit.
847+
848+ INCX - INTEGER.
849+ On entry, INCX specifies the increment for the elements of
850+ X. INCX must not be zero.
851+ Unchanged on exit.
852+
853+ BETA - DOUBLE PRECISION.
854+ On entry, BETA specifies the scalar beta. When BETA is
855+ supplied as zero then Y need not be set on input.
856+ Unchanged on exit.
857+
858+ Y - DOUBLE PRECISION array of DIMENSION at least
859+ ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
860+ and at least
861+ ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
862+ Before entry with BETA non-zero, the incremented array Y
863+ must contain the vector y. On exit, Y is overwritten by the
864+ updated vector y.
865+
866+ INCY - INTEGER.
867+ On entry, INCY specifies the increment for the elements of
868+ Y. INCY must not be zero.
869+ Unchanged on exit.
870+
871+
872+ Level 2 Blas routine.
873+
874+ -- Written on 22-October-1986.
875+ Jack Dongarra, Argonne National Lab.
876+ Jeremy Du Croz, Nag Central Office.
877+ Sven Hammarling, Nag Central Office.
878+ Richard Hanson, Sandia National Labs.
879+
880+
881+ Test the input parameters.
882+*/
883+
884+ /* Parameter adjustments */
885+ a_dim1 = *lda;
886+ a_offset = 1 + a_dim1 * 1;
887+ a -= a_offset;
888+ --x;
889+ --y;
890+
891+ /* Function Body */
892+ info = 0;
893+ if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
894+ ) {
895+ info = 1;
896+ } else if (*m < 0) {
897+ info = 2;
898+ } else if (*n < 0) {
899+ info = 3;
900+ } else if (*lda < max(1,*m)) {
901+ info = 6;
902+ } else if (*incx == 0) {
903+ info = 8;
904+ } else if (*incy == 0) {
905+ info = 11;
906+ }
907+ if (info != 0) {
908+ xerbla_("DGEMV ", &info);
909+ return 0;
910+ }
911+
912+/* Quick return if possible. */
913+
914+ if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
915+ return 0;
916+ }
917+
918+/*
919+ Set LENX and LENY, the lengths of the vectors x and y, and set
920+ up the start points in X and Y.
921+*/
922+
923+ if (lsame_(trans, "N")) {
924+ lenx = *n;
925+ leny = *m;
926+ } else {
927+ lenx = *m;
928+ leny = *n;
929+ }
930+ if (*incx > 0) {
931+ kx = 1;
932+ } else {
933+ kx = 1 - (lenx - 1) * *incx;
934+ }
935+ if (*incy > 0) {
936+ ky = 1;
937+ } else {
938+ ky = 1 - (leny - 1) * *incy;
939+ }
940+
941+/*
942+ Start the operations. In this version the elements of A are
943+ accessed sequentially with one pass through A.
944+
945+ First form y := beta*y.
946+*/
947+
948+ if (*beta != 1.) {
949+ if (*incy == 1) {
950+ if (*beta == 0.) {
951+ i__1 = leny;
952+ for (i__ = 1; i__ <= i__1; ++i__) {
953+ y[i__] = 0.;
954+/* L10: */
955+ }
956+ } else {
957+ i__1 = leny;
958+ for (i__ = 1; i__ <= i__1; ++i__) {
959+ y[i__] = *beta * y[i__];
960+/* L20: */
961+ }
962+ }
963+ } else {
964+ iy = ky;
965+ if (*beta == 0.) {
966+ i__1 = leny;
967+ for (i__ = 1; i__ <= i__1; ++i__) {
968+ y[iy] = 0.;
969+ iy += *incy;
970+/* L30: */
971+ }
972+ } else {
973+ i__1 = leny;
974+ for (i__ = 1; i__ <= i__1; ++i__) {
975+ y[iy] = *beta * y[iy];
976+ iy += *incy;
977+/* L40: */
978+ }
979+ }
980+ }
981+ }
982+ if (*alpha == 0.) {
983+ return 0;
984+ }
985+ if (lsame_(trans, "N")) {
986+
987+/* Form y := alpha*A*x + y. */
988+
989+ jx = kx;
990+ if (*incy == 1) {
991+ i__1 = *n;
992+ for (j = 1; j <= i__1; ++j) {
993+ if (x[jx] != 0.) {
994+ temp = *alpha * x[jx];
995+ i__2 = *m;
996+ for (i__ = 1; i__ <= i__2; ++i__) {
997+ y[i__] += temp * a[i__ + j * a_dim1];
998+/* L50: */
999+ }
1000+ }
1001+ jx += *incx;
1002+/* L60: */
1003+ }
1004+ } else {
1005+ i__1 = *n;
1006+ for (j = 1; j <= i__1; ++j) {
1007+ if (x[jx] != 0.) {
1008+ temp = *alpha * x[jx];
1009+ iy = ky;
1010+ i__2 = *m;
1011+ for (i__ = 1; i__ <= i__2; ++i__) {
1012+ y[iy] += temp * a[i__ + j * a_dim1];
1013+ iy += *incy;
1014+/* L70: */
1015+ }
1016+ }
1017+ jx += *incx;
1018+/* L80: */
1019+ }
1020+ }
1021+ } else {
1022+
1023+/* Form y := alpha*A'*x + y. */
1024+
1025+ jy = ky;
1026+ if (*incx == 1) {
1027+ i__1 = *n;
1028+ for (j = 1; j <= i__1; ++j) {
1029+ temp = 0.;
1030+ i__2 = *m;
1031+ for (i__ = 1; i__ <= i__2; ++i__) {
1032+ temp += a[i__ + j * a_dim1] * x[i__];
1033+/* L90: */
1034+ }
1035+ y[jy] += *alpha * temp;
1036+ jy += *incy;
1037+/* L100: */
1038+ }
1039+ } else {
1040+ i__1 = *n;
1041+ for (j = 1; j <= i__1; ++j) {
1042+ temp = 0.;
1043+ ix = kx;
1044+ i__2 = *m;
1045+ for (i__ = 1; i__ <= i__2; ++i__) {
1046+ temp += a[i__ + j * a_dim1] * x[ix];
1047+ ix += *incx;
1048+/* L110: */
1049+ }
1050+ y[jy] += *alpha * temp;
1051+ jy += *incy;
1052+/* L120: */
1053+ }
1054+ }
1055+ }
1056+
1057+ return 0;
1058+
1059+/* End of DGEMV . */
1060+
1061+} /* dgemv_ */
1062+
1063+/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha,
1064+ doublereal *x, integer *incx, doublereal *y, integer *incy,
1065+ doublereal *a, integer *lda)
1066+{
1067+ /* System generated locals */
1068+ integer a_dim1, a_offset, i__1, i__2;
1069+
1070+ /* Local variables */
1071+ static integer info;
1072+ static doublereal temp;
1073+ static integer i__, j, ix, jy, kx;
1074+ extern /* Subroutine */ int xerbla_(char *, integer *);
1075+
1076+
1077+/*
1078+ Purpose
1079+ =======
1080+
1081+ DGER performs the rank 1 operation
1082+
1083+ A := alpha*x*y' + A,
1084+
1085+ where alpha is a scalar, x is an m element vector, y is an n element
1086+ vector and A is an m by n matrix.
1087+
1088+ Arguments
1089+ ==========
1090+
1091+ M - INTEGER.
1092+ On entry, M specifies the number of rows of the matrix A.
1093+ M must be at least zero.
1094+ Unchanged on exit.
1095+
1096+ N - INTEGER.
1097+ On entry, N specifies the number of columns of the matrix A.
1098+ N must be at least zero.
1099+ Unchanged on exit.
1100+
1101+ ALPHA - DOUBLE PRECISION.
1102+ On entry, ALPHA specifies the scalar alpha.
1103+ Unchanged on exit.
1104+
1105+ X - DOUBLE PRECISION array of dimension at least
1106+ ( 1 + ( m - 1 )*abs( INCX ) ).
1107+ Before entry, the incremented array X must contain the m
1108+ element vector x.
1109+ Unchanged on exit.
1110+
1111+ INCX - INTEGER.
1112+ On entry, INCX specifies the increment for the elements of
1113+ X. INCX must not be zero.
1114+ Unchanged on exit.
1115+
1116+ Y - DOUBLE PRECISION array of dimension at least
1117+ ( 1 + ( n - 1 )*abs( INCY ) ).
1118+ Before entry, the incremented array Y must contain the n
1119+ element vector y.
1120+ Unchanged on exit.
1121+
1122+ INCY - INTEGER.
1123+ On entry, INCY specifies the increment for the elements of
1124+ Y. INCY must not be zero.
1125+ Unchanged on exit.
1126+
1127+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
1128+ Before entry, the leading m by n part of the array A must
1129+ contain the matrix of coefficients. On exit, A is
1130+ overwritten by the updated matrix.
1131+
1132+ LDA - INTEGER.
1133+ On entry, LDA specifies the first dimension of A as declared
1134+ in the calling (sub) program. LDA must be at least
1135+ max( 1, m ).
1136+ Unchanged on exit.
1137+
1138+
1139+ Level 2 Blas routine.
1140+
1141+ -- Written on 22-October-1986.
1142+ Jack Dongarra, Argonne National Lab.
1143+ Jeremy Du Croz, Nag Central Office.
1144+ Sven Hammarling, Nag Central Office.
1145+ Richard Hanson, Sandia National Labs.
1146+
1147+
1148+ Test the input parameters.
1149+*/
1150+
1151+ /* Parameter adjustments */
1152+ --x;
1153+ --y;
1154+ a_dim1 = *lda;
1155+ a_offset = 1 + a_dim1 * 1;
1156+ a -= a_offset;
1157+
1158+ /* Function Body */
1159+ info = 0;
1160+ if (*m < 0) {
1161+ info = 1;
1162+ } else if (*n < 0) {
1163+ info = 2;
1164+ } else if (*incx == 0) {
1165+ info = 5;
1166+ } else if (*incy == 0) {
1167+ info = 7;
1168+ } else if (*lda < max(1,*m)) {
1169+ info = 9;
1170+ }
1171+ if (info != 0) {
1172+ xerbla_("DGER ", &info);
1173+ return 0;
1174+ }
1175+
1176+/* Quick return if possible. */
1177+
1178+ if (*m == 0 || *n == 0 || *alpha == 0.) {
1179+ return 0;
1180+ }
1181+
1182+/*
1183+ Start the operations. In this version the elements of A are
1184+ accessed sequentially with one pass through A.
1185+*/
1186+
1187+ if (*incy > 0) {
1188+ jy = 1;
1189+ } else {
1190+ jy = 1 - (*n - 1) * *incy;
1191+ }
1192+ if (*incx == 1) {
1193+ i__1 = *n;
1194+ for (j = 1; j <= i__1; ++j) {
1195+ if (y[jy] != 0.) {
1196+ temp = *alpha * y[jy];
1197+ i__2 = *m;
1198+ for (i__ = 1; i__ <= i__2; ++i__) {
1199+ a[i__ + j * a_dim1] += x[i__] * temp;
1200+/* L10: */
1201+ }
1202+ }
1203+ jy += *incy;
1204+/* L20: */
1205+ }
1206+ } else {
1207+ if (*incx > 0) {
1208+ kx = 1;
1209+ } else {
1210+ kx = 1 - (*m - 1) * *incx;
1211+ }
1212+ i__1 = *n;
1213+ for (j = 1; j <= i__1; ++j) {
1214+ if (y[jy] != 0.) {
1215+ temp = *alpha * y[jy];
1216+ ix = kx;
1217+ i__2 = *m;
1218+ for (i__ = 1; i__ <= i__2; ++i__) {
1219+ a[i__ + j * a_dim1] += x[ix] * temp;
1220+ ix += *incx;
1221+/* L30: */
1222+ }
1223+ }
1224+ jy += *incy;
1225+/* L40: */
1226+ }
1227+ }
1228+
1229+ return 0;
1230+
1231+/* End of DGER . */
1232+
1233+} /* dger_ */
1234+
1235+doublereal dnrm2_(integer *n, doublereal *x, integer *incx)
1236+{
1237+ /* System generated locals */
1238+ integer i__1, i__2;
1239+ doublereal ret_val, d__1;
1240+
1241+ /* Builtin functions */
1242+ double sqrt(doublereal);
1243+
1244+ /* Local variables */
1245+ static doublereal norm, scale, absxi;
1246+ static integer ix;
1247+ static doublereal ssq;
1248+
1249+
1250+/*
1251+ Purpose
1252+ =======
1253+
1254+ DNRM2 returns the euclidean norm of a vector via the function
1255+ name, so that
1256+
1257+ DNRM2 := sqrt( x'*x )
1258+
1259+
1260+ -- This version written on 25-October-1982.
1261+ Modified on 14-October-1993 to inline the call to DLASSQ.
1262+ Sven Hammarling, Nag Ltd.
1263+*/
1264+
1265+
1266+ /* Parameter adjustments */
1267+ --x;
1268+
1269+ /* Function Body */
1270+ if (*n < 1 || *incx < 1) {
1271+ norm = 0.;
1272+ } else if (*n == 1) {
1273+ norm = abs(x[1]);
1274+ } else {
1275+ scale = 0.;
1276+ ssq = 1.;
1277+/*
1278+ The following loop is equivalent to this call to the LAPACK
1279+ auxiliary routine:
1280+ CALL DLASSQ( N, X, INCX, SCALE, SSQ )
1281+*/
1282+
1283+ i__1 = (*n - 1) * *incx + 1;
1284+ i__2 = *incx;
1285+ for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
1286+ if (x[ix] != 0.) {
1287+ absxi = (d__1 = x[ix], abs(d__1));
1288+ if (scale < absxi) {
1289+/* Computing 2nd power */
1290+ d__1 = scale / absxi;
1291+ ssq = ssq * (d__1 * d__1) + 1.;
1292+ scale = absxi;
1293+ } else {
1294+/* Computing 2nd power */
1295+ d__1 = absxi / scale;
1296+ ssq += d__1 * d__1;
1297+ }
1298+ }
1299+/* L10: */
1300+ }
1301+ norm = scale * sqrt(ssq);
1302+ }
1303+
1304+ ret_val = norm;
1305+ return ret_val;
1306+
1307+/* End of DNRM2. */
1308+
1309+} /* dnrm2_ */
1310+
1311+/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx,
1312+ doublereal *dy, integer *incy, doublereal *c__, doublereal *s)
1313+{
1314+ /* System generated locals */
1315+ integer i__1;
1316+
1317+ /* Local variables */
1318+ static integer i__;
1319+ static doublereal dtemp;
1320+ static integer ix, iy;
1321+
1322+
1323+/*
1324+ Purpose
1325+ =======
1326+
1327+ applies a plane rotation.
1328+ jack dongarra, linpack, 3/11/78.
1329+ modified 12/3/93, array(1) declarations changed to array(*)
1330+*/
1331+
1332+
1333+ /* Parameter adjustments */
1334+ --dy;
1335+ --dx;
1336+
1337+ /* Function Body */
1338+ if (*n <= 0) {
1339+ return 0;
1340+ }
1341+ if (*incx == 1 && *incy == 1) {
1342+ goto L20;
1343+ }
1344+
1345+/*
1346+ code for unequal increments or equal increments not equal
1347+ to 1
1348+*/
1349+
1350+ ix = 1;
1351+ iy = 1;
1352+ if (*incx < 0) {
1353+ ix = (-(*n) + 1) * *incx + 1;
1354+ }
1355+ if (*incy < 0) {
1356+ iy = (-(*n) + 1) * *incy + 1;
1357+ }
1358+ i__1 = *n;
1359+ for (i__ = 1; i__ <= i__1; ++i__) {
1360+ dtemp = *c__ * dx[ix] + *s * dy[iy];
1361+ dy[iy] = *c__ * dy[iy] - *s * dx[ix];
1362+ dx[ix] = dtemp;
1363+ ix += *incx;
1364+ iy += *incy;
1365+/* L10: */
1366+ }
1367+ return 0;
1368+
1369+/* code for both increments equal to 1 */
1370+
1371+L20:
1372+ i__1 = *n;
1373+ for (i__ = 1; i__ <= i__1; ++i__) {
1374+ dtemp = *c__ * dx[i__] + *s * dy[i__];
1375+ dy[i__] = *c__ * dy[i__] - *s * dx[i__];
1376+ dx[i__] = dtemp;
1377+/* L30: */
1378+ }
1379+ return 0;
1380+} /* drot_ */
1381+
1382+/* Subroutine */ int drotg_(doublereal *da, doublereal *db, doublereal *c__,
1383+ doublereal *s)
1384+{
1385+ /* System generated locals */
1386+ doublereal d__1, d__2;
1387+
1388+ /* Builtin functions */
1389+ double sqrt(doublereal), d_sign(doublereal *, doublereal *);
1390+
1391+ /* Local variables */
1392+ static doublereal r__, scale, z__, roe;
1393+
1394+
1395+/*
1396+ Purpose
1397+ =======
1398+
1399+ construct givens plane rotation.
1400+ jack dongarra, linpack, 3/11/78.
1401+*/
1402+
1403+
1404+ roe = *db;
1405+ if (abs(*da) > abs(*db)) {
1406+ roe = *da;
1407+ }
1408+ scale = abs(*da) + abs(*db);
1409+ if (scale != 0.) {
1410+ goto L10;
1411+ }
1412+ *c__ = 1.;
1413+ *s = 0.;
1414+ r__ = 0.;
1415+ z__ = 0.;
1416+ goto L20;
1417+L10:
1418+/* Computing 2nd power */
1419+ d__1 = *da / scale;
1420+/* Computing 2nd power */
1421+ d__2 = *db / scale;
1422+ r__ = scale * sqrt(d__1 * d__1 + d__2 * d__2);
1423+ r__ = d_sign(&c_b90, &roe) * r__;
1424+ *c__ = *da / r__;
1425+ *s = *db / r__;
1426+ z__ = 1.;
1427+ if (abs(*da) > abs(*db)) {
1428+ z__ = *s;
1429+ }
1430+ if (abs(*db) >= abs(*da) && *c__ != 0.) {
1431+ z__ = 1. / *c__;
1432+ }
1433+L20:
1434+ *da = r__;
1435+ *db = z__;
1436+ return 0;
1437+} /* drotg_ */
1438+
1439+/* Subroutine */ int drotm_(integer *n, doublereal *dx, integer *incx,
1440+ doublereal *dy, integer *incy, doublereal *dparam)
1441+{
1442+ /* Initialized data */
1443+
1444+ static doublereal zero = 0.;
1445+ static doublereal two = 2.;
1446+
1447+ /* System generated locals */
1448+ integer i__1, i__2;
1449+
1450+ /* Local variables */
1451+ static integer i__;
1452+ static doublereal dflag, w, z__;
1453+ static integer kx, ky, nsteps;
1454+ static doublereal dh11, dh12, dh21, dh22;
1455+
1456+
1457+/*
1458+ Purpose
1459+ =======
1460+
1461+ APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
1462+
1463+ (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
1464+ (DY**T)
1465+
1466+ DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
1467+ LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY.
1468+ WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
1469+
1470+ DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0
1471+
1472+ (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0)
1473+ H=( ) ( ) ( ) ( )
1474+ (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
1475+ SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.
1476+
1477+ Arguments
1478+ =========
1479+
1480+ N (input) INTEGER
1481+ number of elements in input vector(s)
1482+
1483+ DX (input/output) DOUBLE PRECISION array, dimension N
1484+ double precision vector with 5 elements
1485+
1486+ INCX (input) INTEGER
1487+ storage spacing between elements of DX
1488+
1489+ DY (input/output) DOUBLE PRECISION array, dimension N
1490+ double precision vector with N elements
1491+
1492+ INCY (input) INTEGER
1493+ storage spacing between elements of DY
1494+
1495+ DPARAM (input/output) DOUBLE PRECISION array, dimension 5
1496+ DPARAM(1)=DFLAG
1497+ DPARAM(2)=DH11
1498+ DPARAM(3)=DH21
1499+ DPARAM(4)=DH12
1500+ DPARAM(5)=DH22
1501+
1502+ =====================================================================
1503+*/
1504+
1505+ /* Parameter adjustments */
1506+ --dparam;
1507+ --dy;
1508+ --dx;
1509+
1510+ /* Function Body */
1511+
1512+ dflag = dparam[1];
1513+ if (*n <= 0 || dflag + two == zero) {
1514+ goto L140;
1515+ }
1516+ if (! (*incx == *incy && *incx > 0)) {
1517+ goto L70;
1518+ }
1519+
1520+ nsteps = *n * *incx;
1521+ if (dflag < 0.) {
1522+ goto L50;
1523+ } else if (dflag == 0) {
1524+ goto L10;
1525+ } else {
1526+ goto L30;
1527+ }
1528+L10:
1529+ dh12 = dparam[4];
1530+ dh21 = dparam[3];
1531+ i__1 = nsteps;
1532+ i__2 = *incx;
1533+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
1534+ w = dx[i__];
1535+ z__ = dy[i__];
1536+ dx[i__] = w + z__ * dh12;
1537+ dy[i__] = w * dh21 + z__;
1538+/* L20: */
1539+ }
1540+ goto L140;
1541+L30:
1542+ dh11 = dparam[2];
1543+ dh22 = dparam[5];
1544+ i__2 = nsteps;
1545+ i__1 = *incx;
1546+ for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
1547+ w = dx[i__];
1548+ z__ = dy[i__];
1549+ dx[i__] = w * dh11 + z__;
1550+ dy[i__] = -w + dh22 * z__;
1551+/* L40: */
1552+ }
1553+ goto L140;
1554+L50:
1555+ dh11 = dparam[2];
1556+ dh12 = dparam[4];
1557+ dh21 = dparam[3];
1558+ dh22 = dparam[5];
1559+ i__1 = nsteps;
1560+ i__2 = *incx;
1561+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
1562+ w = dx[i__];
1563+ z__ = dy[i__];
1564+ dx[i__] = w * dh11 + z__ * dh12;
1565+ dy[i__] = w * dh21 + z__ * dh22;
1566+/* L60: */
1567+ }
1568+ goto L140;
1569+L70:
1570+ kx = 1;
1571+ ky = 1;
1572+ if (*incx < 0) {
1573+ kx = (1 - *n) * *incx + 1;
1574+ }
1575+ if (*incy < 0) {
1576+ ky = (1 - *n) * *incy + 1;
1577+ }
1578+
1579+ if (dflag < 0.) {
1580+ goto L120;
1581+ } else if (dflag == 0) {
1582+ goto L80;
1583+ } else {
1584+ goto L100;
1585+ }
1586+L80:
1587+ dh12 = dparam[4];
1588+ dh21 = dparam[3];
1589+ i__2 = *n;
1590+ for (i__ = 1; i__ <= i__2; ++i__) {
1591+ w = dx[kx];
1592+ z__ = dy[ky];
1593+ dx[kx] = w + z__ * dh12;
1594+ dy[ky] = w * dh21 + z__;
1595+ kx += *incx;
1596+ ky += *incy;
1597+/* L90: */
1598+ }
1599+ goto L140;
1600+L100:
1601+ dh11 = dparam[2];
1602+ dh22 = dparam[5];
1603+ i__2 = *n;
1604+ for (i__ = 1; i__ <= i__2; ++i__) {
1605+ w = dx[kx];
1606+ z__ = dy[ky];
1607+ dx[kx] = w * dh11 + z__;
1608+ dy[ky] = -w + dh22 * z__;
1609+ kx += *incx;
1610+ ky += *incy;
1611+/* L110: */
1612+ }
1613+ goto L140;
1614+L120:
1615+ dh11 = dparam[2];
1616+ dh12 = dparam[4];
1617+ dh21 = dparam[3];
1618+ dh22 = dparam[5];
1619+ i__2 = *n;
1620+ for (i__ = 1; i__ <= i__2; ++i__) {
1621+ w = dx[kx];
1622+ z__ = dy[ky];
1623+ dx[kx] = w * dh11 + z__ * dh12;
1624+ dy[ky] = w * dh21 + z__ * dh22;
1625+ kx += *incx;
1626+ ky += *incy;
1627+/* L130: */
1628+ }
1629+L140:
1630+ return 0;
1631+} /* drotm_ */
1632+
1633+/* Subroutine */ int drotmg_(doublereal *dd1, doublereal *dd2, doublereal *
1634+ dx1, doublereal *dy1, doublereal *dparam)
1635+{
1636+ /* Initialized data */
1637+
1638+ static doublereal zero = 0.;
1639+ static doublereal one = 1.;
1640+ static doublereal two = 2.;
1641+ static doublereal gam = 4096.;
1642+ static doublereal gamsq = 16777216.;
1643+ static doublereal rgamsq = 5.9604645e-8;
1644+
1645+ /* Format strings */
1646+ static char fmt_120[] = "";
1647+ static char fmt_150[] = "";
1648+ static char fmt_180[] = "";
1649+ static char fmt_210[] = "";
1650+
1651+ /* System generated locals */
1652+ doublereal d__1;
1653+
1654+ /* Local variables */
1655+ static doublereal dflag, dtemp, du, dp1, dp2, dq1, dq2, dh11, dh12, dh21,
1656+ dh22;
1657+ static integer igo;
1658+
1659+ /* Assigned format variables */
1660+ static char *igo_fmt;
1661+
1662+
1663+/*
1664+ Purpose
1665+ =======
1666+
1667+ CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
1668+ THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*
1669+ DY2)**T.
1670+ WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
1671+
1672+ DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0
1673+
1674+ (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0)
1675+ H=( ) ( ) ( ) ( )
1676+ (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
1677+ LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
1678+ RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
1679+ VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)
1680+
1681+ THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
1682+ INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
1683+ OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
1684+
1685+
1686+ Arguments
1687+ =========
1688+
1689+ DD1 (input/output) DOUBLE PRECISION
1690+
1691+ DD2 (input/output) DOUBLE PRECISION
1692+
1693+ DX1 (input/output) DOUBLE PRECISION
1694+
1695+ DY1 (input) DOUBLE PRECISION
1696+
1697+ DPARAM (input/output) DOUBLE PRECISION array, dimension 5
1698+ DPARAM(1)=DFLAG
1699+ DPARAM(2)=DH11
1700+ DPARAM(3)=DH21
1701+ DPARAM(4)=DH12
1702+ DPARAM(5)=DH22
1703+
1704+ =====================================================================
1705+*/
1706+
1707+
1708+ /* Parameter adjustments */
1709+ --dparam;
1710+
1711+ /* Function Body */
1712+ if (! (*dd1 < zero)) {
1713+ goto L10;
1714+ }
1715+/* GO ZERO-H-D-AND-DX1.. */
1716+ goto L60;
1717+L10:
1718+/* CASE-DD1-NONNEGATIVE */
1719+ dp2 = *dd2 * *dy1;
1720+ if (! (dp2 == zero)) {
1721+ goto L20;
1722+ }
1723+ dflag = -two;
1724+ goto L260;
1725+/* REGULAR-CASE.. */
1726+L20:
1727+ dp1 = *dd1 * *dx1;
1728+ dq2 = dp2 * *dy1;
1729+ dq1 = dp1 * *dx1;
1730+
1731+ if (! (abs(dq1) > abs(dq2))) {
1732+ goto L40;
1733+ }
1734+ dh21 = -(*dy1) / *dx1;
1735+ dh12 = dp2 / dp1;
1736+
1737+ du = one - dh12 * dh21;
1738+
1739+ if (! (du <= zero)) {
1740+ goto L30;
1741+ }
1742+/* GO ZERO-H-D-AND-DX1.. */
1743+ goto L60;
1744+L30:
1745+ dflag = zero;
1746+ *dd1 /= du;
1747+ *dd2 /= du;
1748+ *dx1 *= du;
1749+/* GO SCALE-CHECK.. */
1750+ goto L100;
1751+L40:
1752+ if (! (dq2 < zero)) {
1753+ goto L50;
1754+ }
1755+/* GO ZERO-H-D-AND-DX1.. */
1756+ goto L60;
1757+L50:
1758+ dflag = one;
1759+ dh11 = dp1 / dp2;
1760+ dh22 = *dx1 / *dy1;
1761+ du = one + dh11 * dh22;
1762+ dtemp = *dd2 / du;
1763+ *dd2 = *dd1 / du;
1764+ *dd1 = dtemp;
1765+ *dx1 = *dy1 * du;
1766+/* GO SCALE-CHECK */
1767+ goto L100;
1768+/* PROCEDURE..ZERO-H-D-AND-DX1.. */
1769+L60:
1770+ dflag = -one;
1771+ dh11 = zero;
1772+ dh12 = zero;
1773+ dh21 = zero;
1774+ dh22 = zero;
1775+
1776+ *dd1 = zero;
1777+ *dd2 = zero;
1778+ *dx1 = zero;
1779+/* RETURN.. */
1780+ goto L220;
1781+/* PROCEDURE..FIX-H.. */
1782+L70:
1783+ if (! (dflag >= zero)) {
1784+ goto L90;
1785+ }
1786+
1787+ if (! (dflag == zero)) {
1788+ goto L80;
1789+ }
1790+ dh11 = one;
1791+ dh22 = one;
1792+ dflag = -one;
1793+ goto L90;
1794+L80:
1795+ dh21 = -one;
1796+ dh12 = one;
1797+ dflag = -one;
1798+L90:
1799+ switch (igo) {
1800+ case 0: goto L120;
1801+ case 1: goto L150;
1802+ case 2: goto L180;
1803+ case 3: goto L210;
1804+ }
1805+/* PROCEDURE..SCALE-CHECK */
1806+L100:
1807+L110:
1808+ if (! (*dd1 <= rgamsq)) {
1809+ goto L130;
1810+ }
1811+ if (*dd1 == zero) {
1812+ goto L160;
1813+ }
1814+ igo = 0;
1815+ igo_fmt = fmt_120;
1816+/* FIX-H.. */
1817+ goto L70;
1818+L120:
1819+/* Computing 2nd power */
1820+ d__1 = gam;
1821+ *dd1 *= d__1 * d__1;
1822+ *dx1 /= gam;
1823+ dh11 /= gam;
1824+ dh12 /= gam;
1825+ goto L110;
1826+L130:
1827+L140:
1828+ if (! (*dd1 >= gamsq)) {
1829+ goto L160;
1830+ }
1831+ igo = 1;
1832+ igo_fmt = fmt_150;
1833+/* FIX-H.. */
1834+ goto L70;
1835+L150:
1836+/* Computing 2nd power */
1837+ d__1 = gam;
1838+ *dd1 /= d__1 * d__1;
1839+ *dx1 *= gam;
1840+ dh11 *= gam;
1841+ dh12 *= gam;
1842+ goto L140;
1843+L160:
1844+L170:
1845+ if (! (abs(*dd2) <= rgamsq)) {
1846+ goto L190;
1847+ }
1848+ if (*dd2 == zero) {
1849+ goto L220;
1850+ }
1851+ igo = 2;
1852+ igo_fmt = fmt_180;
1853+/* FIX-H.. */
1854+ goto L70;
1855+L180:
1856+/* Computing 2nd power */
1857+ d__1 = gam;
1858+ *dd2 *= d__1 * d__1;
1859+ dh21 /= gam;
1860+ dh22 /= gam;
1861+ goto L170;
1862+L190:
1863+L200:
1864+ if (! (abs(*dd2) >= gamsq)) {
1865+ goto L220;
1866+ }
1867+ igo = 3;
1868+ igo_fmt = fmt_210;
1869+/* FIX-H.. */
1870+ goto L70;
1871+L210:
1872+/* Computing 2nd power */
1873+ d__1 = gam;
1874+ *dd2 /= d__1 * d__1;
1875+ dh21 *= gam;
1876+ dh22 *= gam;
1877+ goto L200;
1878+L220:
1879+ if (dflag < 0.) {
1880+ goto L250;
1881+ } else if (dflag == 0) {
1882+ goto L230;
1883+ } else {
1884+ goto L240;
1885+ }
1886+L230:
1887+ dparam[3] = dh21;
1888+ dparam[4] = dh12;
1889+ goto L260;
1890+L240:
1891+ dparam[2] = dh11;
1892+ dparam[5] = dh22;
1893+ goto L260;
1894+L250:
1895+ dparam[2] = dh11;
1896+ dparam[3] = dh21;
1897+ dparam[4] = dh12;
1898+ dparam[5] = dh22;
1899+L260:
1900+ dparam[1] = dflag;
1901+ return 0;
1902+} /* drotmg_ */
1903+
1904+/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx,
1905+ integer *incx)
1906+{
1907+ /* System generated locals */
1908+ integer i__1, i__2;
1909+
1910+ /* Local variables */
1911+ static integer i__, m, nincx, mp1;
1912+
1913+
1914+/*
1915+ Purpose
1916+ =======
1917+ *
1918+ scales a vector by a constant.
1919+ uses unrolled loops for increment equal to one.
1920+ jack dongarra, linpack, 3/11/78.
1921+ modified 3/93 to return if incx .le. 0.
1922+ modified 12/3/93, array(1) declarations changed to array(*)
1923+*/
1924+
1925+
1926+ /* Parameter adjustments */
1927+ --dx;
1928+
1929+ /* Function Body */
1930+ if (*n <= 0 || *incx <= 0) {
1931+ return 0;
1932+ }
1933+ if (*incx == 1) {
1934+ goto L20;
1935+ }
1936+
1937+/* code for increment not equal to 1 */
1938+
1939+ nincx = *n * *incx;
1940+ i__1 = nincx;
1941+ i__2 = *incx;
1942+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
1943+ dx[i__] = *da * dx[i__];
1944+/* L10: */
1945+ }
1946+ return 0;
1947+
1948+/*
1949+ code for increment equal to 1
1950+
1951+
1952+ clean-up loop
1953+*/
1954+
1955+L20:
1956+ m = *n % 5;
1957+ if (m == 0) {
1958+ goto L40;
1959+ }
1960+ i__2 = m;
1961+ for (i__ = 1; i__ <= i__2; ++i__) {
1962+ dx[i__] = *da * dx[i__];
1963+/* L30: */
1964+ }
1965+ if (*n < 5) {
1966+ return 0;
1967+ }
1968+L40:
1969+ mp1 = m + 1;
1970+ i__2 = *n;
1971+ for (i__ = mp1; i__ <= i__2; i__ += 5) {
1972+ dx[i__] = *da * dx[i__];
1973+ dx[i__ + 1] = *da * dx[i__ + 1];
1974+ dx[i__ + 2] = *da * dx[i__ + 2];
1975+ dx[i__ + 3] = *da * dx[i__ + 3];
1976+ dx[i__ + 4] = *da * dx[i__ + 4];
1977+/* L50: */
1978+ }
1979+ return 0;
1980+} /* dscal_ */
1981+
1982+/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx,
1983+ doublereal *dy, integer *incy)
1984+{
1985+ /* System generated locals */
1986+ integer i__1;
1987+
1988+ /* Local variables */
1989+ static integer i__, m;
1990+ static doublereal dtemp;
1991+ static integer ix, iy, mp1;
1992+
1993+
1994+/*
1995+ Purpose
1996+ =======
1997+
1998+ interchanges two vectors.
1999+ uses unrolled loops for increments equal one.
2000+ jack dongarra, linpack, 3/11/78.
2001+ modified 12/3/93, array(1) declarations changed to array(*)
2002+*/
2003+
2004+
2005+ /* Parameter adjustments */
2006+ --dy;
2007+ --dx;
2008+
2009+ /* Function Body */
2010+ if (*n <= 0) {
2011+ return 0;
2012+ }
2013+ if (*incx == 1 && *incy == 1) {
2014+ goto L20;
2015+ }
2016+
2017+/*
2018+ code for unequal increments or equal increments not equal
2019+ to 1
2020+*/
2021+
2022+ ix = 1;
2023+ iy = 1;
2024+ if (*incx < 0) {
2025+ ix = (-(*n) + 1) * *incx + 1;
2026+ }
2027+ if (*incy < 0) {
2028+ iy = (-(*n) + 1) * *incy + 1;
2029+ }
2030+ i__1 = *n;
2031+ for (i__ = 1; i__ <= i__1; ++i__) {
2032+ dtemp = dx[ix];
2033+ dx[ix] = dy[iy];
2034+ dy[iy] = dtemp;
2035+ ix += *incx;
2036+ iy += *incy;
2037+/* L10: */
2038+ }
2039+ return 0;
2040+
2041+/*
2042+ code for both increments equal to 1
2043+
2044+
2045+ clean-up loop
2046+*/
2047+
2048+L20:
2049+ m = *n % 3;
2050+ if (m == 0) {
2051+ goto L40;
2052+ }
2053+ i__1 = m;
2054+ for (i__ = 1; i__ <= i__1; ++i__) {
2055+ dtemp = dx[i__];
2056+ dx[i__] = dy[i__];
2057+ dy[i__] = dtemp;
2058+/* L30: */
2059+ }
2060+ if (*n < 3) {
2061+ return 0;
2062+ }
2063+L40:
2064+ mp1 = m + 1;
2065+ i__1 = *n;
2066+ for (i__ = mp1; i__ <= i__1; i__ += 3) {
2067+ dtemp = dx[i__];
2068+ dx[i__] = dy[i__];
2069+ dy[i__] = dtemp;
2070+ dtemp = dx[i__ + 1];
2071+ dx[i__ + 1] = dy[i__ + 1];
2072+ dy[i__ + 1] = dtemp;
2073+ dtemp = dx[i__ + 2];
2074+ dx[i__ + 2] = dy[i__ + 2];
2075+ dy[i__ + 2] = dtemp;
2076+/* L50: */
2077+ }
2078+ return 0;
2079+} /* dswap_ */
2080+
2081+/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n,
2082+ doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
2083+ integer *ldb, doublereal *beta, doublereal *c__, integer *ldc)
2084+{
2085+ /* System generated locals */
2086+ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
2087+ i__3;
2088+
2089+ /* Local variables */
2090+ static integer info;
2091+ static doublereal temp1, temp2;
2092+ static integer i__, j, k;
2093+ extern logical lsame_(char *, char *);
2094+ static integer nrowa;
2095+ static logical upper;
2096+ extern /* Subroutine */ int xerbla_(char *, integer *);
2097+
2098+
2099+/*
2100+ Purpose
2101+ =======
2102+
2103+ DSYMM performs one of the matrix-matrix operations
2104+
2105+ C := alpha*A*B + beta*C,
2106+
2107+ or
2108+
2109+ C := alpha*B*A + beta*C,
2110+
2111+ where alpha and beta are scalars, A is a symmetric matrix and B and
2112+ C are m by n matrices.
2113+
2114+ Arguments
2115+ ==========
2116+
2117+ SIDE - CHARACTER*1.
2118+ On entry, SIDE specifies whether the symmetric matrix A
2119+ appears on the left or right in the operation as follows:
2120+
2121+ SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
2122+
2123+ SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
2124+
2125+ Unchanged on exit.
2126+
2127+ UPLO - CHARACTER*1.
2128+ On entry, UPLO specifies whether the upper or lower
2129+ triangular part of the symmetric matrix A is to be
2130+ referenced as follows:
2131+
2132+ UPLO = 'U' or 'u' Only the upper triangular part of the
2133+ symmetric matrix is to be referenced.
2134+
2135+ UPLO = 'L' or 'l' Only the lower triangular part of the
2136+ symmetric matrix is to be referenced.
2137+
2138+ Unchanged on exit.
2139+
2140+ M - INTEGER.
2141+ On entry, M specifies the number of rows of the matrix C.
2142+ M must be at least zero.
2143+ Unchanged on exit.
2144+
2145+ N - INTEGER.
2146+ On entry, N specifies the number of columns of the matrix C.
2147+ N must be at least zero.
2148+ Unchanged on exit.
2149+
2150+ ALPHA - DOUBLE PRECISION.
2151+ On entry, ALPHA specifies the scalar alpha.
2152+ Unchanged on exit.
2153+
2154+ A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
2155+ m when SIDE = 'L' or 'l' and is n otherwise.
2156+ Before entry with SIDE = 'L' or 'l', the m by m part of
2157+ the array A must contain the symmetric matrix, such that
2158+ when UPLO = 'U' or 'u', the leading m by m upper triangular
2159+ part of the array A must contain the upper triangular part
2160+ of the symmetric matrix and the strictly lower triangular
2161+ part of A is not referenced, and when UPLO = 'L' or 'l',
2162+ the leading m by m lower triangular part of the array A
2163+ must contain the lower triangular part of the symmetric
2164+ matrix and the strictly upper triangular part of A is not
2165+ referenced.
2166+ Before entry with SIDE = 'R' or 'r', the n by n part of
2167+ the array A must contain the symmetric matrix, such that
2168+ when UPLO = 'U' or 'u', the leading n by n upper triangular
2169+ part of the array A must contain the upper triangular part
2170+ of the symmetric matrix and the strictly lower triangular
2171+ part of A is not referenced, and when UPLO = 'L' or 'l',
2172+ the leading n by n lower triangular part of the array A
2173+ must contain the lower triangular part of the symmetric
2174+ matrix and the strictly upper triangular part of A is not
2175+ referenced.
2176+ Unchanged on exit.
2177+
2178+ LDA - INTEGER.
2179+ On entry, LDA specifies the first dimension of A as declared
2180+ in the calling (sub) program. When SIDE = 'L' or 'l' then
2181+ LDA must be at least max( 1, m ), otherwise LDA must be at
2182+ least max( 1, n ).
2183+ Unchanged on exit.
2184+
2185+ B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
2186+ Before entry, the leading m by n part of the array B must
2187+ contain the matrix B.
2188+ Unchanged on exit.
2189+
2190+ LDB - INTEGER.
2191+ On entry, LDB specifies the first dimension of B as declared
2192+ in the calling (sub) program. LDB must be at least
2193+ max( 1, m ).
2194+ Unchanged on exit.
2195+
2196+ BETA - DOUBLE PRECISION.
2197+ On entry, BETA specifies the scalar beta. When BETA is
2198+ supplied as zero then C need not be set on input.
2199+ Unchanged on exit.
2200+
2201+ C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
2202+ Before entry, the leading m by n part of the array C must
2203+ contain the matrix C, except when beta is zero, in which
2204+ case C need not be set on entry.
2205+ On exit, the array C is overwritten by the m by n updated
2206+ matrix.
2207+
2208+ LDC - INTEGER.
2209+ On entry, LDC specifies the first dimension of C as declared
2210+ in the calling (sub) program. LDC must be at least
2211+ max( 1, m ).
2212+ Unchanged on exit.
2213+
2214+
2215+ Level 3 Blas routine.
2216+
2217+ -- Written on 8-February-1989.
2218+ Jack Dongarra, Argonne National Laboratory.
2219+ Iain Duff, AERE Harwell.
2220+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
2221+ Sven Hammarling, Numerical Algorithms Group Ltd.
2222+
2223+
2224+ Set NROWA as the number of rows of A.
2225+*/
2226+
2227+ /* Parameter adjustments */
2228+ a_dim1 = *lda;
2229+ a_offset = 1 + a_dim1 * 1;
2230+ a -= a_offset;
2231+ b_dim1 = *ldb;
2232+ b_offset = 1 + b_dim1 * 1;
2233+ b -= b_offset;
2234+ c_dim1 = *ldc;
2235+ c_offset = 1 + c_dim1 * 1;
2236+ c__ -= c_offset;
2237+
2238+ /* Function Body */
2239+ if (lsame_(side, "L")) {
2240+ nrowa = *m;
2241+ } else {
2242+ nrowa = *n;
2243+ }
2244+ upper = lsame_(uplo, "U");
2245+
2246+/* Test the input parameters. */
2247+
2248+ info = 0;
2249+ if (! lsame_(side, "L") && ! lsame_(side, "R")) {
2250+ info = 1;
2251+ } else if (! upper && ! lsame_(uplo, "L")) {
2252+ info = 2;
2253+ } else if (*m < 0) {
2254+ info = 3;
2255+ } else if (*n < 0) {
2256+ info = 4;
2257+ } else if (*lda < max(1,nrowa)) {
2258+ info = 7;
2259+ } else if (*ldb < max(1,*m)) {
2260+ info = 9;
2261+ } else if (*ldc < max(1,*m)) {
2262+ info = 12;
2263+ }
2264+ if (info != 0) {
2265+ xerbla_("DSYMM ", &info);
2266+ return 0;
2267+ }
2268+
2269+/* Quick return if possible. */
2270+
2271+ if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
2272+ return 0;
2273+ }
2274+
2275+/* And when alpha.eq.zero. */
2276+
2277+ if (*alpha == 0.) {
2278+ if (*beta == 0.) {
2279+ i__1 = *n;
2280+ for (j = 1; j <= i__1; ++j) {
2281+ i__2 = *m;
2282+ for (i__ = 1; i__ <= i__2; ++i__) {
2283+ c__[i__ + j * c_dim1] = 0.;
2284+/* L10: */
2285+ }
2286+/* L20: */
2287+ }
2288+ } else {
2289+ i__1 = *n;
2290+ for (j = 1; j <= i__1; ++j) {
2291+ i__2 = *m;
2292+ for (i__ = 1; i__ <= i__2; ++i__) {
2293+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
2294+/* L30: */
2295+ }
2296+/* L40: */
2297+ }
2298+ }
2299+ return 0;
2300+ }
2301+
2302+/* Start the operations. */
2303+
2304+ if (lsame_(side, "L")) {
2305+
2306+/* Form C := alpha*A*B + beta*C. */
2307+
2308+ if (upper) {
2309+ i__1 = *n;
2310+ for (j = 1; j <= i__1; ++j) {
2311+ i__2 = *m;
2312+ for (i__ = 1; i__ <= i__2; ++i__) {
2313+ temp1 = *alpha * b[i__ + j * b_dim1];
2314+ temp2 = 0.;
2315+ i__3 = i__ - 1;
2316+ for (k = 1; k <= i__3; ++k) {
2317+ c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
2318+ temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
2319+/* L50: */
2320+ }
2321+ if (*beta == 0.) {
2322+ c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
2323+ + *alpha * temp2;
2324+ } else {
2325+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
2326+ + temp1 * a[i__ + i__ * a_dim1] + *alpha *
2327+ temp2;
2328+ }
2329+/* L60: */
2330+ }
2331+/* L70: */
2332+ }
2333+ } else {
2334+ i__1 = *n;
2335+ for (j = 1; j <= i__1; ++j) {
2336+ for (i__ = *m; i__ >= 1; --i__) {
2337+ temp1 = *alpha * b[i__ + j * b_dim1];
2338+ temp2 = 0.;
2339+ i__2 = *m;
2340+ for (k = i__ + 1; k <= i__2; ++k) {
2341+ c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
2342+ temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
2343+/* L80: */
2344+ }
2345+ if (*beta == 0.) {
2346+ c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
2347+ + *alpha * temp2;
2348+ } else {
2349+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
2350+ + temp1 * a[i__ + i__ * a_dim1] + *alpha *
2351+ temp2;
2352+ }
2353+/* L90: */
2354+ }
2355+/* L100: */
2356+ }
2357+ }
2358+ } else {
2359+
2360+/* Form C := alpha*B*A + beta*C. */
2361+
2362+ i__1 = *n;
2363+ for (j = 1; j <= i__1; ++j) {
2364+ temp1 = *alpha * a[j + j * a_dim1];
2365+ if (*beta == 0.) {
2366+ i__2 = *m;
2367+ for (i__ = 1; i__ <= i__2; ++i__) {
2368+ c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1];
2369+/* L110: */
2370+ }
2371+ } else {
2372+ i__2 = *m;
2373+ for (i__ = 1; i__ <= i__2; ++i__) {
2374+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] +
2375+ temp1 * b[i__ + j * b_dim1];
2376+/* L120: */
2377+ }
2378+ }
2379+ i__2 = j - 1;
2380+ for (k = 1; k <= i__2; ++k) {
2381+ if (upper) {
2382+ temp1 = *alpha * a[k + j * a_dim1];
2383+ } else {
2384+ temp1 = *alpha * a[j + k * a_dim1];
2385+ }
2386+ i__3 = *m;
2387+ for (i__ = 1; i__ <= i__3; ++i__) {
2388+ c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
2389+/* L130: */
2390+ }
2391+/* L140: */
2392+ }
2393+ i__2 = *n;
2394+ for (k = j + 1; k <= i__2; ++k) {
2395+ if (upper) {
2396+ temp1 = *alpha * a[j + k * a_dim1];
2397+ } else {
2398+ temp1 = *alpha * a[k + j * a_dim1];
2399+ }
2400+ i__3 = *m;
2401+ for (i__ = 1; i__ <= i__3; ++i__) {
2402+ c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
2403+/* L150: */
2404+ }
2405+/* L160: */
2406+ }
2407+/* L170: */
2408+ }
2409+ }
2410+
2411+ return 0;
2412+
2413+/* End of DSYMM . */
2414+
2415+} /* dsymm_ */
2416+
2417+/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha,
2418+ doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal
2419+ *beta, doublereal *y, integer *incy)
2420+{
2421+ /* System generated locals */
2422+ integer a_dim1, a_offset, i__1, i__2;
2423+
2424+ /* Local variables */
2425+ static integer info;
2426+ static doublereal temp1, temp2;
2427+ static integer i__, j;
2428+ extern logical lsame_(char *, char *);
2429+ static integer ix, iy, jx, jy, kx, ky;
2430+ extern /* Subroutine */ int xerbla_(char *, integer *);
2431+
2432+
2433+/*
2434+ Purpose
2435+ =======
2436+
2437+ DSYMV performs the matrix-vector operation
2438+
2439+ y := alpha*A*x + beta*y,
2440+
2441+ where alpha and beta are scalars, x and y are n element vectors and
2442+ A is an n by n symmetric matrix.
2443+
2444+ Arguments
2445+ ==========
2446+
2447+ UPLO - CHARACTER*1.
2448+ On entry, UPLO specifies whether the upper or lower
2449+ triangular part of the array A is to be referenced as
2450+ follows:
2451+
2452+ UPLO = 'U' or 'u' Only the upper triangular part of A
2453+ is to be referenced.
2454+
2455+ UPLO = 'L' or 'l' Only the lower triangular part of A
2456+ is to be referenced.
2457+
2458+ Unchanged on exit.
2459+
2460+ N - INTEGER.
2461+ On entry, N specifies the order of the matrix A.
2462+ N must be at least zero.
2463+ Unchanged on exit.
2464+
2465+ ALPHA - DOUBLE PRECISION.
2466+ On entry, ALPHA specifies the scalar alpha.
2467+ Unchanged on exit.
2468+
2469+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
2470+ Before entry with UPLO = 'U' or 'u', the leading n by n
2471+ upper triangular part of the array A must contain the upper
2472+ triangular part of the symmetric matrix and the strictly
2473+ lower triangular part of A is not referenced.
2474+ Before entry with UPLO = 'L' or 'l', the leading n by n
2475+ lower triangular part of the array A must contain the lower
2476+ triangular part of the symmetric matrix and the strictly
2477+ upper triangular part of A is not referenced.
2478+ Unchanged on exit.
2479+
2480+ LDA - INTEGER.
2481+ On entry, LDA specifies the first dimension of A as declared
2482+ in the calling (sub) program. LDA must be at least
2483+ max( 1, n ).
2484+ Unchanged on exit.
2485+
2486+ X - DOUBLE PRECISION array of dimension at least
2487+ ( 1 + ( n - 1 )*abs( INCX ) ).
2488+ Before entry, the incremented array X must contain the n
2489+ element vector x.
2490+ Unchanged on exit.
2491+
2492+ INCX - INTEGER.
2493+ On entry, INCX specifies the increment for the elements of
2494+ X. INCX must not be zero.
2495+ Unchanged on exit.
2496+
2497+ BETA - DOUBLE PRECISION.
2498+ On entry, BETA specifies the scalar beta. When BETA is
2499+ supplied as zero then Y need not be set on input.
2500+ Unchanged on exit.
2501+
2502+ Y - DOUBLE PRECISION array of dimension at least
2503+ ( 1 + ( n - 1 )*abs( INCY ) ).
2504+ Before entry, the incremented array Y must contain the n
2505+ element vector y. On exit, Y is overwritten by the updated
2506+ vector y.
2507+
2508+ INCY - INTEGER.
2509+ On entry, INCY specifies the increment for the elements of
2510+ Y. INCY must not be zero.
2511+ Unchanged on exit.
2512+
2513+
2514+ Level 2 Blas routine.
2515+
2516+ -- Written on 22-October-1986.
2517+ Jack Dongarra, Argonne National Lab.
2518+ Jeremy Du Croz, Nag Central Office.
2519+ Sven Hammarling, Nag Central Office.
2520+ Richard Hanson, Sandia National Labs.
2521+
2522+
2523+ Test the input parameters.
2524+*/
2525+
2526+ /* Parameter adjustments */
2527+ a_dim1 = *lda;
2528+ a_offset = 1 + a_dim1 * 1;
2529+ a -= a_offset;
2530+ --x;
2531+ --y;
2532+
2533+ /* Function Body */
2534+ info = 0;
2535+ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
2536+ info = 1;
2537+ } else if (*n < 0) {
2538+ info = 2;
2539+ } else if (*lda < max(1,*n)) {
2540+ info = 5;
2541+ } else if (*incx == 0) {
2542+ info = 7;
2543+ } else if (*incy == 0) {
2544+ info = 10;
2545+ }
2546+ if (info != 0) {
2547+ xerbla_("DSYMV ", &info);
2548+ return 0;
2549+ }
2550+
2551+/* Quick return if possible. */
2552+
2553+ if (*n == 0 || *alpha == 0. && *beta == 1.) {
2554+ return 0;
2555+ }
2556+
2557+/* Set up the start points in X and Y. */
2558+
2559+ if (*incx > 0) {
2560+ kx = 1;
2561+ } else {
2562+ kx = 1 - (*n - 1) * *incx;
2563+ }
2564+ if (*incy > 0) {
2565+ ky = 1;
2566+ } else {
2567+ ky = 1 - (*n - 1) * *incy;
2568+ }
2569+
2570+/*
2571+ Start the operations. In this version the elements of A are
2572+ accessed sequentially with one pass through the triangular part
2573+ of A.
2574+
2575+ First form y := beta*y.
2576+*/
2577+
2578+ if (*beta != 1.) {
2579+ if (*incy == 1) {
2580+ if (*beta == 0.) {
2581+ i__1 = *n;
2582+ for (i__ = 1; i__ <= i__1; ++i__) {
2583+ y[i__] = 0.;
2584+/* L10: */
2585+ }
2586+ } else {
2587+ i__1 = *n;
2588+ for (i__ = 1; i__ <= i__1; ++i__) {
2589+ y[i__] = *beta * y[i__];
2590+/* L20: */
2591+ }
2592+ }
2593+ } else {
2594+ iy = ky;
2595+ if (*beta == 0.) {
2596+ i__1 = *n;
2597+ for (i__ = 1; i__ <= i__1; ++i__) {
2598+ y[iy] = 0.;
2599+ iy += *incy;
2600+/* L30: */
2601+ }
2602+ } else {
2603+ i__1 = *n;
2604+ for (i__ = 1; i__ <= i__1; ++i__) {
2605+ y[iy] = *beta * y[iy];
2606+ iy += *incy;
2607+/* L40: */
2608+ }
2609+ }
2610+ }
2611+ }
2612+ if (*alpha == 0.) {
2613+ return 0;
2614+ }
2615+ if (lsame_(uplo, "U")) {
2616+
2617+/* Form y when A is stored in upper triangle. */
2618+
2619+ if (*incx == 1 && *incy == 1) {
2620+ i__1 = *n;
2621+ for (j = 1; j <= i__1; ++j) {
2622+ temp1 = *alpha * x[j];
2623+ temp2 = 0.;
2624+ i__2 = j - 1;
2625+ for (i__ = 1; i__ <= i__2; ++i__) {
2626+ y[i__] += temp1 * a[i__ + j * a_dim1];
2627+ temp2 += a[i__ + j * a_dim1] * x[i__];
2628+/* L50: */
2629+ }
2630+ y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
2631+/* L60: */
2632+ }
2633+ } else {
2634+ jx = kx;
2635+ jy = ky;
2636+ i__1 = *n;
2637+ for (j = 1; j <= i__1; ++j) {
2638+ temp1 = *alpha * x[jx];
2639+ temp2 = 0.;
2640+ ix = kx;
2641+ iy = ky;
2642+ i__2 = j - 1;
2643+ for (i__ = 1; i__ <= i__2; ++i__) {
2644+ y[iy] += temp1 * a[i__ + j * a_dim1];
2645+ temp2 += a[i__ + j * a_dim1] * x[ix];
2646+ ix += *incx;
2647+ iy += *incy;
2648+/* L70: */
2649+ }
2650+ y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
2651+ jx += *incx;
2652+ jy += *incy;
2653+/* L80: */
2654+ }
2655+ }
2656+ } else {
2657+
2658+/* Form y when A is stored in lower triangle. */
2659+
2660+ if (*incx == 1 && *incy == 1) {
2661+ i__1 = *n;
2662+ for (j = 1; j <= i__1; ++j) {
2663+ temp1 = *alpha * x[j];
2664+ temp2 = 0.;
2665+ y[j] += temp1 * a[j + j * a_dim1];
2666+ i__2 = *n;
2667+ for (i__ = j + 1; i__ <= i__2; ++i__) {
2668+ y[i__] += temp1 * a[i__ + j * a_dim1];
2669+ temp2 += a[i__ + j * a_dim1] * x[i__];
2670+/* L90: */
2671+ }
2672+ y[j] += *alpha * temp2;
2673+/* L100: */
2674+ }
2675+ } else {
2676+ jx = kx;
2677+ jy = ky;
2678+ i__1 = *n;
2679+ for (j = 1; j <= i__1; ++j) {
2680+ temp1 = *alpha * x[jx];
2681+ temp2 = 0.;
2682+ y[jy] += temp1 * a[j + j * a_dim1];
2683+ ix = jx;
2684+ iy = jy;
2685+ i__2 = *n;
2686+ for (i__ = j + 1; i__ <= i__2; ++i__) {
2687+ ix += *incx;
2688+ iy += *incy;
2689+ y[iy] += temp1 * a[i__ + j * a_dim1];
2690+ temp2 += a[i__ + j * a_dim1] * x[ix];
2691+/* L110: */
2692+ }
2693+ y[jy] += *alpha * temp2;
2694+ jx += *incx;
2695+ jy += *incy;
2696+/* L120: */
2697+ }
2698+ }
2699+ }
2700+
2701+ return 0;
2702+
2703+/* End of DSYMV . */
2704+
2705+} /* dsymv_ */
2706+
2707+/* Subroutine */ int dsyr_(char *uplo, integer *n, doublereal *alpha,
2708+ doublereal *x, integer *incx, doublereal *a, integer *lda)
2709+{
2710+ /* System generated locals */
2711+ integer a_dim1, a_offset, i__1, i__2;
2712+
2713+ /* Local variables */
2714+ static integer info;
2715+ static doublereal temp;
2716+ static integer i__, j;
2717+ extern logical lsame_(char *, char *);
2718+ static integer ix, jx, kx;
2719+ extern /* Subroutine */ int xerbla_(char *, integer *);
2720+
2721+
2722+/*
2723+ Purpose
2724+ =======
2725+
2726+ DSYR performs the symmetric rank 1 operation
2727+
2728+ A := alpha*x*x' + A,
2729+
2730+ where alpha is a real scalar, x is an n element vector and A is an
2731+ n by n symmetric matrix.
2732+
2733+ Arguments
2734+ ==========
2735+
2736+ UPLO - CHARACTER*1.
2737+ On entry, UPLO specifies whether the upper or lower
2738+ triangular part of the array A is to be referenced as
2739+ follows:
2740+
2741+ UPLO = 'U' or 'u' Only the upper triangular part of A
2742+ is to be referenced.
2743+
2744+ UPLO = 'L' or 'l' Only the lower triangular part of A
2745+ is to be referenced.
2746+
2747+ Unchanged on exit.
2748+
2749+ N - INTEGER.
2750+ On entry, N specifies the order of the matrix A.
2751+ N must be at least zero.
2752+ Unchanged on exit.
2753+
2754+ ALPHA - DOUBLE PRECISION.
2755+ On entry, ALPHA specifies the scalar alpha.
2756+ Unchanged on exit.
2757+
2758+ X - DOUBLE PRECISION array of dimension at least
2759+ ( 1 + ( n - 1 )*abs( INCX ) ).
2760+ Before entry, the incremented array X must contain the n
2761+ element vector x.
2762+ Unchanged on exit.
2763+
2764+ INCX - INTEGER.
2765+ On entry, INCX specifies the increment for the elements of
2766+ X. INCX must not be zero.
2767+ Unchanged on exit.
2768+
2769+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
2770+ Before entry with UPLO = 'U' or 'u', the leading n by n
2771+ upper triangular part of the array A must contain the upper
2772+ triangular part of the symmetric matrix and the strictly
2773+ lower triangular part of A is not referenced. On exit, the
2774+ upper triangular part of the array A is overwritten by the
2775+ upper triangular part of the updated matrix.
2776+ Before entry with UPLO = 'L' or 'l', the leading n by n
2777+ lower triangular part of the array A must contain the lower
2778+ triangular part of the symmetric matrix and the strictly
2779+ upper triangular part of A is not referenced. On exit, the
2780+ lower triangular part of the array A is overwritten by the
2781+ lower triangular part of the updated matrix.
2782+
2783+ LDA - INTEGER.
2784+ On entry, LDA specifies the first dimension of A as declared
2785+ in the calling (sub) program. LDA must be at least
2786+ max( 1, n ).
2787+ Unchanged on exit.
2788+
2789+
2790+ Level 2 Blas routine.
2791+
2792+ -- Written on 22-October-1986.
2793+ Jack Dongarra, Argonne National Lab.
2794+ Jeremy Du Croz, Nag Central Office.
2795+ Sven Hammarling, Nag Central Office.
2796+ Richard Hanson, Sandia National Labs.
2797+
2798+
2799+ Test the input parameters.
2800+*/
2801+
2802+ /* Parameter adjustments */
2803+ --x;
2804+ a_dim1 = *lda;
2805+ a_offset = 1 + a_dim1 * 1;
2806+ a -= a_offset;
2807+
2808+ /* Function Body */
2809+ info = 0;
2810+ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
2811+ info = 1;
2812+ } else if (*n < 0) {
2813+ info = 2;
2814+ } else if (*incx == 0) {
2815+ info = 5;
2816+ } else if (*lda < max(1,*n)) {
2817+ info = 7;
2818+ }
2819+ if (info != 0) {
2820+ xerbla_("DSYR ", &info);
2821+ return 0;
2822+ }
2823+
2824+/* Quick return if possible. */
2825+
2826+ if (*n == 0 || *alpha == 0.) {
2827+ return 0;
2828+ }
2829+
2830+/* Set the start point in X if the increment is not unity. */
2831+
2832+ if (*incx <= 0) {
2833+ kx = 1 - (*n - 1) * *incx;
2834+ } else if (*incx != 1) {
2835+ kx = 1;
2836+ }
2837+
2838+/*
2839+ Start the operations. In this version the elements of A are
2840+ accessed sequentially with one pass through the triangular part
2841+ of A.
2842+*/
2843+
2844+ if (lsame_(uplo, "U")) {
2845+
2846+/* Form A when A is stored in upper triangle. */
2847+
2848+ if (*incx == 1) {
2849+ i__1 = *n;
2850+ for (j = 1; j <= i__1; ++j) {
2851+ if (x[j] != 0.) {
2852+ temp = *alpha * x[j];
2853+ i__2 = j;
2854+ for (i__ = 1; i__ <= i__2; ++i__) {
2855+ a[i__ + j * a_dim1] += x[i__] * temp;
2856+/* L10: */
2857+ }
2858+ }
2859+/* L20: */
2860+ }
2861+ } else {
2862+ jx = kx;
2863+ i__1 = *n;
2864+ for (j = 1; j <= i__1; ++j) {
2865+ if (x[jx] != 0.) {
2866+ temp = *alpha * x[jx];
2867+ ix = kx;
2868+ i__2 = j;
2869+ for (i__ = 1; i__ <= i__2; ++i__) {
2870+ a[i__ + j * a_dim1] += x[ix] * temp;
2871+ ix += *incx;
2872+/* L30: */
2873+ }
2874+ }
2875+ jx += *incx;
2876+/* L40: */
2877+ }
2878+ }
2879+ } else {
2880+
2881+/* Form A when A is stored in lower triangle. */
2882+
2883+ if (*incx == 1) {
2884+ i__1 = *n;
2885+ for (j = 1; j <= i__1; ++j) {
2886+ if (x[j] != 0.) {
2887+ temp = *alpha * x[j];
2888+ i__2 = *n;
2889+ for (i__ = j; i__ <= i__2; ++i__) {
2890+ a[i__ + j * a_dim1] += x[i__] * temp;
2891+/* L50: */
2892+ }
2893+ }
2894+/* L60: */
2895+ }
2896+ } else {
2897+ jx = kx;
2898+ i__1 = *n;
2899+ for (j = 1; j <= i__1; ++j) {
2900+ if (x[jx] != 0.) {
2901+ temp = *alpha * x[jx];
2902+ ix = jx;
2903+ i__2 = *n;
2904+ for (i__ = j; i__ <= i__2; ++i__) {
2905+ a[i__ + j * a_dim1] += x[ix] * temp;
2906+ ix += *incx;
2907+/* L70: */
2908+ }
2909+ }
2910+ jx += *incx;
2911+/* L80: */
2912+ }
2913+ }
2914+ }
2915+
2916+ return 0;
2917+
2918+/* End of DSYR . */
2919+
2920+} /* dsyr_ */
2921+
2922+/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha,
2923+ doublereal *x, integer *incx, doublereal *y, integer *incy,
2924+ doublereal *a, integer *lda)
2925+{
2926+ /* System generated locals */
2927+ integer a_dim1, a_offset, i__1, i__2;
2928+
2929+ /* Local variables */
2930+ static integer info;
2931+ static doublereal temp1, temp2;
2932+ static integer i__, j;
2933+ extern logical lsame_(char *, char *);
2934+ static integer ix, iy, jx, jy, kx, ky;
2935+ extern /* Subroutine */ int xerbla_(char *, integer *);
2936+
2937+
2938+/*
2939+ Purpose
2940+ =======
2941+
2942+ DSYR2 performs the symmetric rank 2 operation
2943+
2944+ A := alpha*x*y' + alpha*y*x' + A,
2945+
2946+ where alpha is a scalar, x and y are n element vectors and A is an n
2947+ by n symmetric matrix.
2948+
2949+ Arguments
2950+ ==========
2951+
2952+ UPLO - CHARACTER*1.
2953+ On entry, UPLO specifies whether the upper or lower
2954+ triangular part of the array A is to be referenced as
2955+ follows:
2956+
2957+ UPLO = 'U' or 'u' Only the upper triangular part of A
2958+ is to be referenced.
2959+
2960+ UPLO = 'L' or 'l' Only the lower triangular part of A
2961+ is to be referenced.
2962+
2963+ Unchanged on exit.
2964+
2965+ N - INTEGER.
2966+ On entry, N specifies the order of the matrix A.
2967+ N must be at least zero.
2968+ Unchanged on exit.
2969+
2970+ ALPHA - DOUBLE PRECISION.
2971+ On entry, ALPHA specifies the scalar alpha.
2972+ Unchanged on exit.
2973+
2974+ X - DOUBLE PRECISION array of dimension at least
2975+ ( 1 + ( n - 1 )*abs( INCX ) ).
2976+ Before entry, the incremented array X must contain the n
2977+ element vector x.
2978+ Unchanged on exit.
2979+
2980+ INCX - INTEGER.
2981+ On entry, INCX specifies the increment for the elements of
2982+ X. INCX must not be zero.
2983+ Unchanged on exit.
2984+
2985+ Y - DOUBLE PRECISION array of dimension at least
2986+ ( 1 + ( n - 1 )*abs( INCY ) ).
2987+ Before entry, the incremented array Y must contain the n
2988+ element vector y.
2989+ Unchanged on exit.
2990+
2991+ INCY - INTEGER.
2992+ On entry, INCY specifies the increment for the elements of
2993+ Y. INCY must not be zero.
2994+ Unchanged on exit.
2995+
2996+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
2997+ Before entry with UPLO = 'U' or 'u', the leading n by n
2998+ upper triangular part of the array A must contain the upper
2999+ triangular part of the symmetric matrix and the strictly
3000+ lower triangular part of A is not referenced. On exit, the
3001+ upper triangular part of the array A is overwritten by the
3002+ upper triangular part of the updated matrix.
3003+ Before entry with UPLO = 'L' or 'l', the leading n by n
3004+ lower triangular part of the array A must contain the lower
3005+ triangular part of the symmetric matrix and the strictly
3006+ upper triangular part of A is not referenced. On exit, the
3007+ lower triangular part of the array A is overwritten by the
3008+ lower triangular part of the updated matrix.
3009+
3010+ LDA - INTEGER.
3011+ On entry, LDA specifies the first dimension of A as declared
3012+ in the calling (sub) program. LDA must be at least
3013+ max( 1, n ).
3014+ Unchanged on exit.
3015+
3016+
3017+ Level 2 Blas routine.
3018+
3019+ -- Written on 22-October-1986.
3020+ Jack Dongarra, Argonne National Lab.
3021+ Jeremy Du Croz, Nag Central Office.
3022+ Sven Hammarling, Nag Central Office.
3023+ Richard Hanson, Sandia National Labs.
3024+
3025+
3026+ Test the input parameters.
3027+*/
3028+
3029+ /* Parameter adjustments */
3030+ --x;
3031+ --y;
3032+ a_dim1 = *lda;
3033+ a_offset = 1 + a_dim1 * 1;
3034+ a -= a_offset;
3035+
3036+ /* Function Body */
3037+ info = 0;
3038+ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
3039+ info = 1;
3040+ } else if (*n < 0) {
3041+ info = 2;
3042+ } else if (*incx == 0) {
3043+ info = 5;
3044+ } else if (*incy == 0) {
3045+ info = 7;
3046+ } else if (*lda < max(1,*n)) {
3047+ info = 9;
3048+ }
3049+ if (info != 0) {
3050+ xerbla_("DSYR2 ", &info);
3051+ return 0;
3052+ }
3053+
3054+/* Quick return if possible. */
3055+
3056+ if (*n == 0 || *alpha == 0.) {
3057+ return 0;
3058+ }
3059+
3060+/*
3061+ Set up the start points in X and Y if the increments are not both
3062+ unity.
3063+*/
3064+
3065+ if (*incx != 1 || *incy != 1) {
3066+ if (*incx > 0) {
3067+ kx = 1;
3068+ } else {
3069+ kx = 1 - (*n - 1) * *incx;
3070+ }
3071+ if (*incy > 0) {
3072+ ky = 1;
3073+ } else {
3074+ ky = 1 - (*n - 1) * *incy;
3075+ }
3076+ jx = kx;
3077+ jy = ky;
3078+ }
3079+
3080+/*
3081+ Start the operations. In this version the elements of A are
3082+ accessed sequentially with one pass through the triangular part
3083+ of A.
3084+*/
3085+
3086+ if (lsame_(uplo, "U")) {
3087+
3088+/* Form A when A is stored in the upper triangle. */
3089+
3090+ if (*incx == 1 && *incy == 1) {
3091+ i__1 = *n;
3092+ for (j = 1; j <= i__1; ++j) {
3093+ if (x[j] != 0. || y[j] != 0.) {
3094+ temp1 = *alpha * y[j];
3095+ temp2 = *alpha * x[j];
3096+ i__2 = j;
3097+ for (i__ = 1; i__ <= i__2; ++i__) {
3098+ a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
3099+ temp1 + y[i__] * temp2;
3100+/* L10: */
3101+ }
3102+ }
3103+/* L20: */
3104+ }
3105+ } else {
3106+ i__1 = *n;
3107+ for (j = 1; j <= i__1; ++j) {
3108+ if (x[jx] != 0. || y[jy] != 0.) {
3109+ temp1 = *alpha * y[jy];
3110+ temp2 = *alpha * x[jx];
3111+ ix = kx;
3112+ iy = ky;
3113+ i__2 = j;
3114+ for (i__ = 1; i__ <= i__2; ++i__) {
3115+ a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
3116+ temp1 + y[iy] * temp2;
3117+ ix += *incx;
3118+ iy += *incy;
3119+/* L30: */
3120+ }
3121+ }
3122+ jx += *incx;
3123+ jy += *incy;
3124+/* L40: */
3125+ }
3126+ }
3127+ } else {
3128+
3129+/* Form A when A is stored in the lower triangle. */
3130+
3131+ if (*incx == 1 && *incy == 1) {
3132+ i__1 = *n;
3133+ for (j = 1; j <= i__1; ++j) {
3134+ if (x[j] != 0. || y[j] != 0.) {
3135+ temp1 = *alpha * y[j];
3136+ temp2 = *alpha * x[j];
3137+ i__2 = *n;
3138+ for (i__ = j; i__ <= i__2; ++i__) {
3139+ a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
3140+ temp1 + y[i__] * temp2;
3141+/* L50: */
3142+ }
3143+ }
3144+/* L60: */
3145+ }
3146+ } else {
3147+ i__1 = *n;
3148+ for (j = 1; j <= i__1; ++j) {
3149+ if (x[jx] != 0. || y[jy] != 0.) {
3150+ temp1 = *alpha * y[jy];
3151+ temp2 = *alpha * x[jx];
3152+ ix = jx;
3153+ iy = jy;
3154+ i__2 = *n;
3155+ for (i__ = j; i__ <= i__2; ++i__) {
3156+ a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
3157+ temp1 + y[iy] * temp2;
3158+ ix += *incx;
3159+ iy += *incy;
3160+/* L70: */
3161+ }
3162+ }
3163+ jx += *incx;
3164+ jy += *incy;
3165+/* L80: */
3166+ }
3167+ }
3168+ }
3169+
3170+ return 0;
3171+
3172+/* End of DSYR2 . */
3173+
3174+} /* dsyr2_ */
3175+
3176+/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k,
3177+ doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
3178+ integer *ldb, doublereal *beta, doublereal *c__, integer *ldc)
3179+{
3180+ /* System generated locals */
3181+ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
3182+ i__3;
3183+
3184+ /* Local variables */
3185+ static integer info;
3186+ static doublereal temp1, temp2;
3187+ static integer i__, j, l;
3188+ extern logical lsame_(char *, char *);
3189+ static integer nrowa;
3190+ static logical upper;
3191+ extern /* Subroutine */ int xerbla_(char *, integer *);
3192+
3193+
3194+/*
3195+ Purpose
3196+ =======
3197+
3198+ DSYR2K performs one of the symmetric rank 2k operations
3199+
3200+ C := alpha*A*B' + alpha*B*A' + beta*C,
3201+
3202+ or
3203+
3204+ C := alpha*A'*B + alpha*B'*A + beta*C,
3205+
3206+ where alpha and beta are scalars, C is an n by n symmetric matrix
3207+ and A and B are n by k matrices in the first case and k by n
3208+ matrices in the second case.
3209+
3210+ Arguments
3211+ ==========
3212+
3213+ UPLO - CHARACTER*1.
3214+ On entry, UPLO specifies whether the upper or lower
3215+ triangular part of the array C is to be referenced as
3216+ follows:
3217+
3218+ UPLO = 'U' or 'u' Only the upper triangular part of C
3219+ is to be referenced.
3220+
3221+ UPLO = 'L' or 'l' Only the lower triangular part of C
3222+ is to be referenced.
3223+
3224+ Unchanged on exit.
3225+
3226+ TRANS - CHARACTER*1.
3227+ On entry, TRANS specifies the operation to be performed as
3228+ follows:
3229+
3230+ TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
3231+ beta*C.
3232+
3233+ TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
3234+ beta*C.
3235+
3236+ TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
3237+ beta*C.
3238+
3239+ Unchanged on exit.
3240+
3241+ N - INTEGER.
3242+ On entry, N specifies the order of the matrix C. N must be
3243+ at least zero.
3244+ Unchanged on exit.
3245+
3246+ K - INTEGER.
3247+ On entry with TRANS = 'N' or 'n', K specifies the number
3248+ of columns of the matrices A and B, and on entry with
3249+ TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
3250+ of rows of the matrices A and B. K must be at least zero.
3251+ Unchanged on exit.
3252+
3253+ ALPHA - DOUBLE PRECISION.
3254+ On entry, ALPHA specifies the scalar alpha.
3255+ Unchanged on exit.
3256+
3257+ A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
3258+ k when TRANS = 'N' or 'n', and is n otherwise.
3259+ Before entry with TRANS = 'N' or 'n', the leading n by k
3260+ part of the array A must contain the matrix A, otherwise
3261+ the leading k by n part of the array A must contain the
3262+ matrix A.
3263+ Unchanged on exit.
3264+
3265+ LDA - INTEGER.
3266+ On entry, LDA specifies the first dimension of A as declared
3267+ in the calling (sub) program. When TRANS = 'N' or 'n'
3268+ then LDA must be at least max( 1, n ), otherwise LDA must
3269+ be at least max( 1, k ).
3270+ Unchanged on exit.
3271+
3272+ B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
3273+ k when TRANS = 'N' or 'n', and is n otherwise.
3274+ Before entry with TRANS = 'N' or 'n', the leading n by k
3275+ part of the array B must contain the matrix B, otherwise
3276+ the leading k by n part of the array B must contain the
3277+ matrix B.
3278+ Unchanged on exit.
3279+
3280+ LDB - INTEGER.
3281+ On entry, LDB specifies the first dimension of B as declared
3282+ in the calling (sub) program. When TRANS = 'N' or 'n'
3283+ then LDB must be at least max( 1, n ), otherwise LDB must
3284+ be at least max( 1, k ).
3285+ Unchanged on exit.
3286+
3287+ BETA - DOUBLE PRECISION.
3288+ On entry, BETA specifies the scalar beta.
3289+ Unchanged on exit.
3290+
3291+ C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
3292+ Before entry with UPLO = 'U' or 'u', the leading n by n
3293+ upper triangular part of the array C must contain the upper
3294+ triangular part of the symmetric matrix and the strictly
3295+ lower triangular part of C is not referenced. On exit, the
3296+ upper triangular part of the array C is overwritten by the
3297+ upper triangular part of the updated matrix.
3298+ Before entry with UPLO = 'L' or 'l', the leading n by n
3299+ lower triangular part of the array C must contain the lower
3300+ triangular part of the symmetric matrix and the strictly
3301+ upper triangular part of C is not referenced. On exit, the
3302+ lower triangular part of the array C is overwritten by the
3303+ lower triangular part of the updated matrix.
3304+
3305+ LDC - INTEGER.
3306+ On entry, LDC specifies the first dimension of C as declared
3307+ in the calling (sub) program. LDC must be at least
3308+ max( 1, n ).
3309+ Unchanged on exit.
3310+
3311+
3312+ Level 3 Blas routine.
3313+
3314+
3315+ -- Written on 8-February-1989.
3316+ Jack Dongarra, Argonne National Laboratory.
3317+ Iain Duff, AERE Harwell.
3318+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
3319+ Sven Hammarling, Numerical Algorithms Group Ltd.
3320+
3321+
3322+ Test the input parameters.
3323+*/
3324+
3325+ /* Parameter adjustments */
3326+ a_dim1 = *lda;
3327+ a_offset = 1 + a_dim1 * 1;
3328+ a -= a_offset;
3329+ b_dim1 = *ldb;
3330+ b_offset = 1 + b_dim1 * 1;
3331+ b -= b_offset;
3332+ c_dim1 = *ldc;
3333+ c_offset = 1 + c_dim1 * 1;
3334+ c__ -= c_offset;
3335+
3336+ /* Function Body */
3337+ if (lsame_(trans, "N")) {
3338+ nrowa = *n;
3339+ } else {
3340+ nrowa = *k;
3341+ }
3342+ upper = lsame_(uplo, "U");
3343+
3344+ info = 0;
3345+ if (! upper && ! lsame_(uplo, "L")) {
3346+ info = 1;
3347+ } else if (! lsame_(trans, "N") && ! lsame_(trans,
3348+ "T") && ! lsame_(trans, "C")) {
3349+ info = 2;
3350+ } else if (*n < 0) {
3351+ info = 3;
3352+ } else if (*k < 0) {
3353+ info = 4;
3354+ } else if (*lda < max(1,nrowa)) {
3355+ info = 7;
3356+ } else if (*ldb < max(1,nrowa)) {
3357+ info = 9;
3358+ } else if (*ldc < max(1,*n)) {
3359+ info = 12;
3360+ }
3361+ if (info != 0) {
3362+ xerbla_("DSYR2K", &info);
3363+ return 0;
3364+ }
3365+
3366+/* Quick return if possible. */
3367+
3368+ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
3369+ return 0;
3370+ }
3371+
3372+/* And when alpha.eq.zero. */
3373+
3374+ if (*alpha == 0.) {
3375+ if (upper) {
3376+ if (*beta == 0.) {
3377+ i__1 = *n;
3378+ for (j = 1; j <= i__1; ++j) {
3379+ i__2 = j;
3380+ for (i__ = 1; i__ <= i__2; ++i__) {
3381+ c__[i__ + j * c_dim1] = 0.;
3382+/* L10: */
3383+ }
3384+/* L20: */
3385+ }
3386+ } else {
3387+ i__1 = *n;
3388+ for (j = 1; j <= i__1; ++j) {
3389+ i__2 = j;
3390+ for (i__ = 1; i__ <= i__2; ++i__) {
3391+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3392+/* L30: */
3393+ }
3394+/* L40: */
3395+ }
3396+ }
3397+ } else {
3398+ if (*beta == 0.) {
3399+ i__1 = *n;
3400+ for (j = 1; j <= i__1; ++j) {
3401+ i__2 = *n;
3402+ for (i__ = j; i__ <= i__2; ++i__) {
3403+ c__[i__ + j * c_dim1] = 0.;
3404+/* L50: */
3405+ }
3406+/* L60: */
3407+ }
3408+ } else {
3409+ i__1 = *n;
3410+ for (j = 1; j <= i__1; ++j) {
3411+ i__2 = *n;
3412+ for (i__ = j; i__ <= i__2; ++i__) {
3413+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3414+/* L70: */
3415+ }
3416+/* L80: */
3417+ }
3418+ }
3419+ }
3420+ return 0;
3421+ }
3422+
3423+/* Start the operations. */
3424+
3425+ if (lsame_(trans, "N")) {
3426+
3427+/* Form C := alpha*A*B' + alpha*B*A' + C. */
3428+
3429+ if (upper) {
3430+ i__1 = *n;
3431+ for (j = 1; j <= i__1; ++j) {
3432+ if (*beta == 0.) {
3433+ i__2 = j;
3434+ for (i__ = 1; i__ <= i__2; ++i__) {
3435+ c__[i__ + j * c_dim1] = 0.;
3436+/* L90: */
3437+ }
3438+ } else if (*beta != 1.) {
3439+ i__2 = j;
3440+ for (i__ = 1; i__ <= i__2; ++i__) {
3441+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3442+/* L100: */
3443+ }
3444+ }
3445+ i__2 = *k;
3446+ for (l = 1; l <= i__2; ++l) {
3447+ if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) {
3448+ temp1 = *alpha * b[j + l * b_dim1];
3449+ temp2 = *alpha * a[j + l * a_dim1];
3450+ i__3 = j;
3451+ for (i__ = 1; i__ <= i__3; ++i__) {
3452+ c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
3453+ i__ + l * a_dim1] * temp1 + b[i__ + l *
3454+ b_dim1] * temp2;
3455+/* L110: */
3456+ }
3457+ }
3458+/* L120: */
3459+ }
3460+/* L130: */
3461+ }
3462+ } else {
3463+ i__1 = *n;
3464+ for (j = 1; j <= i__1; ++j) {
3465+ if (*beta == 0.) {
3466+ i__2 = *n;
3467+ for (i__ = j; i__ <= i__2; ++i__) {
3468+ c__[i__ + j * c_dim1] = 0.;
3469+/* L140: */
3470+ }
3471+ } else if (*beta != 1.) {
3472+ i__2 = *n;
3473+ for (i__ = j; i__ <= i__2; ++i__) {
3474+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3475+/* L150: */
3476+ }
3477+ }
3478+ i__2 = *k;
3479+ for (l = 1; l <= i__2; ++l) {
3480+ if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) {
3481+ temp1 = *alpha * b[j + l * b_dim1];
3482+ temp2 = *alpha * a[j + l * a_dim1];
3483+ i__3 = *n;
3484+ for (i__ = j; i__ <= i__3; ++i__) {
3485+ c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
3486+ i__ + l * a_dim1] * temp1 + b[i__ + l *
3487+ b_dim1] * temp2;
3488+/* L160: */
3489+ }
3490+ }
3491+/* L170: */
3492+ }
3493+/* L180: */
3494+ }
3495+ }
3496+ } else {
3497+
3498+/* Form C := alpha*A'*B + alpha*B'*A + C. */
3499+
3500+ if (upper) {
3501+ i__1 = *n;
3502+ for (j = 1; j <= i__1; ++j) {
3503+ i__2 = j;
3504+ for (i__ = 1; i__ <= i__2; ++i__) {
3505+ temp1 = 0.;
3506+ temp2 = 0.;
3507+ i__3 = *k;
3508+ for (l = 1; l <= i__3; ++l) {
3509+ temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
3510+ temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
3511+/* L190: */
3512+ }
3513+ if (*beta == 0.) {
3514+ c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
3515+ temp2;
3516+ } else {
3517+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
3518+ + *alpha * temp1 + *alpha * temp2;
3519+ }
3520+/* L200: */
3521+ }
3522+/* L210: */
3523+ }
3524+ } else {
3525+ i__1 = *n;
3526+ for (j = 1; j <= i__1; ++j) {
3527+ i__2 = *n;
3528+ for (i__ = j; i__ <= i__2; ++i__) {
3529+ temp1 = 0.;
3530+ temp2 = 0.;
3531+ i__3 = *k;
3532+ for (l = 1; l <= i__3; ++l) {
3533+ temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
3534+ temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
3535+/* L220: */
3536+ }
3537+ if (*beta == 0.) {
3538+ c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
3539+ temp2;
3540+ } else {
3541+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
3542+ + *alpha * temp1 + *alpha * temp2;
3543+ }
3544+/* L230: */
3545+ }
3546+/* L240: */
3547+ }
3548+ }
3549+ }
3550+
3551+ return 0;
3552+
3553+/* End of DSYR2K. */
3554+
3555+} /* dsyr2k_ */
3556+
3557+/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k,
3558+ doublereal *alpha, doublereal *a, integer *lda, doublereal *beta,
3559+ doublereal *c__, integer *ldc)
3560+{
3561+ /* System generated locals */
3562+ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
3563+
3564+ /* Local variables */
3565+ static integer info;
3566+ static doublereal temp;
3567+ static integer i__, j, l;
3568+ extern logical lsame_(char *, char *);
3569+ static integer nrowa;
3570+ static logical upper;
3571+ extern /* Subroutine */ int xerbla_(char *, integer *);
3572+
3573+
3574+/*
3575+ Purpose
3576+ =======
3577+
3578+ DSYRK performs one of the symmetric rank k operations
3579+
3580+ C := alpha*A*A' + beta*C,
3581+
3582+ or
3583+
3584+ C := alpha*A'*A + beta*C,
3585+
3586+ where alpha and beta are scalars, C is an n by n symmetric matrix
3587+ and A is an n by k matrix in the first case and a k by n matrix
3588+ in the second case.
3589+
3590+ Arguments
3591+ ==========
3592+
3593+ UPLO - CHARACTER*1.
3594+ On entry, UPLO specifies whether the upper or lower
3595+ triangular part of the array C is to be referenced as
3596+ follows:
3597+
3598+ UPLO = 'U' or 'u' Only the upper triangular part of C
3599+ is to be referenced.
3600+
3601+ UPLO = 'L' or 'l' Only the lower triangular part of C
3602+ is to be referenced.
3603+
3604+ Unchanged on exit.
3605+
3606+ TRANS - CHARACTER*1.
3607+ On entry, TRANS specifies the operation to be performed as
3608+ follows:
3609+
3610+ TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
3611+
3612+ TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
3613+
3614+ TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
3615+
3616+ Unchanged on exit.
3617+
3618+ N - INTEGER.
3619+ On entry, N specifies the order of the matrix C. N must be
3620+ at least zero.
3621+ Unchanged on exit.
3622+
3623+ K - INTEGER.
3624+ On entry with TRANS = 'N' or 'n', K specifies the number
3625+ of columns of the matrix A, and on entry with
3626+ TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
3627+ of rows of the matrix A. K must be at least zero.
3628+ Unchanged on exit.
3629+
3630+ ALPHA - DOUBLE PRECISION.
3631+ On entry, ALPHA specifies the scalar alpha.
3632+ Unchanged on exit.
3633+
3634+ A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
3635+ k when TRANS = 'N' or 'n', and is n otherwise.
3636+ Before entry with TRANS = 'N' or 'n', the leading n by k
3637+ part of the array A must contain the matrix A, otherwise
3638+ the leading k by n part of the array A must contain the
3639+ matrix A.
3640+ Unchanged on exit.
3641+
3642+ LDA - INTEGER.
3643+ On entry, LDA specifies the first dimension of A as declared
3644+ in the calling (sub) program. When TRANS = 'N' or 'n'
3645+ then LDA must be at least max( 1, n ), otherwise LDA must
3646+ be at least max( 1, k ).
3647+ Unchanged on exit.
3648+
3649+ BETA - DOUBLE PRECISION.
3650+ On entry, BETA specifies the scalar beta.
3651+ Unchanged on exit.
3652+
3653+ C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
3654+ Before entry with UPLO = 'U' or 'u', the leading n by n
3655+ upper triangular part of the array C must contain the upper
3656+ triangular part of the symmetric matrix and the strictly
3657+ lower triangular part of C is not referenced. On exit, the
3658+ upper triangular part of the array C is overwritten by the
3659+ upper triangular part of the updated matrix.
3660+ Before entry with UPLO = 'L' or 'l', the leading n by n
3661+ lower triangular part of the array C must contain the lower
3662+ triangular part of the symmetric matrix and the strictly
3663+ upper triangular part of C is not referenced. On exit, the
3664+ lower triangular part of the array C is overwritten by the
3665+ lower triangular part of the updated matrix.
3666+
3667+ LDC - INTEGER.
3668+ On entry, LDC specifies the first dimension of C as declared
3669+ in the calling (sub) program. LDC must be at least
3670+ max( 1, n ).
3671+ Unchanged on exit.
3672+
3673+
3674+ Level 3 Blas routine.
3675+
3676+ -- Written on 8-February-1989.
3677+ Jack Dongarra, Argonne National Laboratory.
3678+ Iain Duff, AERE Harwell.
3679+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
3680+ Sven Hammarling, Numerical Algorithms Group Ltd.
3681+
3682+
3683+ Test the input parameters.
3684+*/
3685+
3686+ /* Parameter adjustments */
3687+ a_dim1 = *lda;
3688+ a_offset = 1 + a_dim1 * 1;
3689+ a -= a_offset;
3690+ c_dim1 = *ldc;
3691+ c_offset = 1 + c_dim1 * 1;
3692+ c__ -= c_offset;
3693+
3694+ /* Function Body */
3695+ if (lsame_(trans, "N")) {
3696+ nrowa = *n;
3697+ } else {
3698+ nrowa = *k;
3699+ }
3700+ upper = lsame_(uplo, "U");
3701+
3702+ info = 0;
3703+ if (! upper && ! lsame_(uplo, "L")) {
3704+ info = 1;
3705+ } else if (! lsame_(trans, "N") && ! lsame_(trans,
3706+ "T") && ! lsame_(trans, "C")) {
3707+ info = 2;
3708+ } else if (*n < 0) {
3709+ info = 3;
3710+ } else if (*k < 0) {
3711+ info = 4;
3712+ } else if (*lda < max(1,nrowa)) {
3713+ info = 7;
3714+ } else if (*ldc < max(1,*n)) {
3715+ info = 10;
3716+ }
3717+ if (info != 0) {
3718+ xerbla_("DSYRK ", &info);
3719+ return 0;
3720+ }
3721+
3722+/* Quick return if possible. */
3723+
3724+ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
3725+ return 0;
3726+ }
3727+
3728+/* And when alpha.eq.zero. */
3729+
3730+ if (*alpha == 0.) {
3731+ if (upper) {
3732+ if (*beta == 0.) {
3733+ i__1 = *n;
3734+ for (j = 1; j <= i__1; ++j) {
3735+ i__2 = j;
3736+ for (i__ = 1; i__ <= i__2; ++i__) {
3737+ c__[i__ + j * c_dim1] = 0.;
3738+/* L10: */
3739+ }
3740+/* L20: */
3741+ }
3742+ } else {
3743+ i__1 = *n;
3744+ for (j = 1; j <= i__1; ++j) {
3745+ i__2 = j;
3746+ for (i__ = 1; i__ <= i__2; ++i__) {
3747+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3748+/* L30: */
3749+ }
3750+/* L40: */
3751+ }
3752+ }
3753+ } else {
3754+ if (*beta == 0.) {
3755+ i__1 = *n;
3756+ for (j = 1; j <= i__1; ++j) {
3757+ i__2 = *n;
3758+ for (i__ = j; i__ <= i__2; ++i__) {
3759+ c__[i__ + j * c_dim1] = 0.;
3760+/* L50: */
3761+ }
3762+/* L60: */
3763+ }
3764+ } else {
3765+ i__1 = *n;
3766+ for (j = 1; j <= i__1; ++j) {
3767+ i__2 = *n;
3768+ for (i__ = j; i__ <= i__2; ++i__) {
3769+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3770+/* L70: */
3771+ }
3772+/* L80: */
3773+ }
3774+ }
3775+ }
3776+ return 0;
3777+ }
3778+
3779+/* Start the operations. */
3780+
3781+ if (lsame_(trans, "N")) {
3782+
3783+/* Form C := alpha*A*A' + beta*C. */
3784+
3785+ if (upper) {
3786+ i__1 = *n;
3787+ for (j = 1; j <= i__1; ++j) {
3788+ if (*beta == 0.) {
3789+ i__2 = j;
3790+ for (i__ = 1; i__ <= i__2; ++i__) {
3791+ c__[i__ + j * c_dim1] = 0.;
3792+/* L90: */
3793+ }
3794+ } else if (*beta != 1.) {
3795+ i__2 = j;
3796+ for (i__ = 1; i__ <= i__2; ++i__) {
3797+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3798+/* L100: */
3799+ }
3800+ }
3801+ i__2 = *k;
3802+ for (l = 1; l <= i__2; ++l) {
3803+ if (a[j + l * a_dim1] != 0.) {
3804+ temp = *alpha * a[j + l * a_dim1];
3805+ i__3 = j;
3806+ for (i__ = 1; i__ <= i__3; ++i__) {
3807+ c__[i__ + j * c_dim1] += temp * a[i__ + l *
3808+ a_dim1];
3809+/* L110: */
3810+ }
3811+ }
3812+/* L120: */
3813+ }
3814+/* L130: */
3815+ }
3816+ } else {
3817+ i__1 = *n;
3818+ for (j = 1; j <= i__1; ++j) {
3819+ if (*beta == 0.) {
3820+ i__2 = *n;
3821+ for (i__ = j; i__ <= i__2; ++i__) {
3822+ c__[i__ + j * c_dim1] = 0.;
3823+/* L140: */
3824+ }
3825+ } else if (*beta != 1.) {
3826+ i__2 = *n;
3827+ for (i__ = j; i__ <= i__2; ++i__) {
3828+ c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
3829+/* L150: */
3830+ }
3831+ }
3832+ i__2 = *k;
3833+ for (l = 1; l <= i__2; ++l) {
3834+ if (a[j + l * a_dim1] != 0.) {
3835+ temp = *alpha * a[j + l * a_dim1];
3836+ i__3 = *n;
3837+ for (i__ = j; i__ <= i__3; ++i__) {
3838+ c__[i__ + j * c_dim1] += temp * a[i__ + l *
3839+ a_dim1];
3840+/* L160: */
3841+ }
3842+ }
3843+/* L170: */
3844+ }
3845+/* L180: */
3846+ }
3847+ }
3848+ } else {
3849+
3850+/* Form C := alpha*A'*A + beta*C. */
3851+
3852+ if (upper) {
3853+ i__1 = *n;
3854+ for (j = 1; j <= i__1; ++j) {
3855+ i__2 = j;
3856+ for (i__ = 1; i__ <= i__2; ++i__) {
3857+ temp = 0.;
3858+ i__3 = *k;
3859+ for (l = 1; l <= i__3; ++l) {
3860+ temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
3861+/* L190: */
3862+ }
3863+ if (*beta == 0.) {
3864+ c__[i__ + j * c_dim1] = *alpha * temp;
3865+ } else {
3866+ c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
3867+ i__ + j * c_dim1];
3868+ }
3869+/* L200: */
3870+ }
3871+/* L210: */
3872+ }
3873+ } else {
3874+ i__1 = *n;
3875+ for (j = 1; j <= i__1; ++j) {
3876+ i__2 = *n;
3877+ for (i__ = j; i__ <= i__2; ++i__) {
3878+ temp = 0.;
3879+ i__3 = *k;
3880+ for (l = 1; l <= i__3; ++l) {
3881+ temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
3882+/* L220: */
3883+ }
3884+ if (*beta == 0.) {
3885+ c__[i__ + j * c_dim1] = *alpha * temp;
3886+ } else {
3887+ c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
3888+ i__ + j * c_dim1];
3889+ }
3890+/* L230: */
3891+ }
3892+/* L240: */
3893+ }
3894+ }
3895+ }
3896+
3897+ return 0;
3898+
3899+/* End of DSYRK . */
3900+
3901+} /* dsyrk_ */
3902+
3903+/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag,
3904+ integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
3905+ lda, doublereal *b, integer *ldb)
3906+{
3907+ /* System generated locals */
3908+ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
3909+
3910+ /* Local variables */
3911+ static integer info;
3912+ static doublereal temp;
3913+ static integer i__, j, k;
3914+ static logical lside;
3915+ extern logical lsame_(char *, char *);
3916+ static integer nrowa;
3917+ static logical upper;
3918+ extern /* Subroutine */ int xerbla_(char *, integer *);
3919+ static logical nounit;
3920+
3921+
3922+/*
3923+ Purpose
3924+ =======
3925+
3926+ DTRMM performs one of the matrix-matrix operations
3927+
3928+ B := alpha*op( A )*B, or B := alpha*B*op( A ),
3929+
3930+ where alpha is a scalar, B is an m by n matrix, A is a unit, or
3931+ non-unit, upper or lower triangular matrix and op( A ) is one of
3932+
3933+ op( A ) = A or op( A ) = A'.
3934+
3935+ Arguments
3936+ ==========
3937+
3938+ SIDE - CHARACTER*1.
3939+ On entry, SIDE specifies whether op( A ) multiplies B from
3940+ the left or right as follows:
3941+
3942+ SIDE = 'L' or 'l' B := alpha*op( A )*B.
3943+
3944+ SIDE = 'R' or 'r' B := alpha*B*op( A ).
3945+
3946+ Unchanged on exit.
3947+
3948+ UPLO - CHARACTER*1.
3949+ On entry, UPLO specifies whether the matrix A is an upper or
3950+ lower triangular matrix as follows:
3951+
3952+ UPLO = 'U' or 'u' A is an upper triangular matrix.
3953+
3954+ UPLO = 'L' or 'l' A is a lower triangular matrix.
3955+
3956+ Unchanged on exit.
3957+
3958+ TRANSA - CHARACTER*1.
3959+ On entry, TRANSA specifies the form of op( A ) to be used in
3960+ the matrix multiplication as follows:
3961+
3962+ TRANSA = 'N' or 'n' op( A ) = A.
3963+
3964+ TRANSA = 'T' or 't' op( A ) = A'.
3965+
3966+ TRANSA = 'C' or 'c' op( A ) = A'.
3967+
3968+ Unchanged on exit.
3969+
3970+ DIAG - CHARACTER*1.
3971+ On entry, DIAG specifies whether or not A is unit triangular
3972+ as follows:
3973+
3974+ DIAG = 'U' or 'u' A is assumed to be unit triangular.
3975+
3976+ DIAG = 'N' or 'n' A is not assumed to be unit
3977+ triangular.
3978+
3979+ Unchanged on exit.
3980+
3981+ M - INTEGER.
3982+ On entry, M specifies the number of rows of B. M must be at
3983+ least zero.
3984+ Unchanged on exit.
3985+
3986+ N - INTEGER.
3987+ On entry, N specifies the number of columns of B. N must be
3988+ at least zero.
3989+ Unchanged on exit.
3990+
3991+ ALPHA - DOUBLE PRECISION.
3992+ On entry, ALPHA specifies the scalar alpha. When alpha is
3993+ zero then A is not referenced and B need not be set before
3994+ entry.
3995+ Unchanged on exit.
3996+
3997+ A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
3998+ when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
3999+ Before entry with UPLO = 'U' or 'u', the leading k by k
4000+ upper triangular part of the array A must contain the upper
4001+ triangular matrix and the strictly lower triangular part of
4002+ A is not referenced.
4003+ Before entry with UPLO = 'L' or 'l', the leading k by k
4004+ lower triangular part of the array A must contain the lower
4005+ triangular matrix and the strictly upper triangular part of
4006+ A is not referenced.
4007+ Note that when DIAG = 'U' or 'u', the diagonal elements of
4008+ A are not referenced either, but are assumed to be unity.
4009+ Unchanged on exit.
4010+
4011+ LDA - INTEGER.
4012+ On entry, LDA specifies the first dimension of A as declared
4013+ in the calling (sub) program. When SIDE = 'L' or 'l' then
4014+ LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
4015+ then LDA must be at least max( 1, n ).
4016+ Unchanged on exit.
4017+
4018+ B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
4019+ Before entry, the leading m by n part of the array B must
4020+ contain the matrix B, and on exit is overwritten by the
4021+ transformed matrix.
4022+
4023+ LDB - INTEGER.
4024+ On entry, LDB specifies the first dimension of B as declared
4025+ in the calling (sub) program. LDB must be at least
4026+ max( 1, m ).
4027+ Unchanged on exit.
4028+
4029+
4030+ Level 3 Blas routine.
4031+
4032+ -- Written on 8-February-1989.
4033+ Jack Dongarra, Argonne National Laboratory.
4034+ Iain Duff, AERE Harwell.
4035+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
4036+ Sven Hammarling, Numerical Algorithms Group Ltd.
4037+
4038+
4039+ Test the input parameters.
4040+*/
4041+
4042+ /* Parameter adjustments */
4043+ a_dim1 = *lda;
4044+ a_offset = 1 + a_dim1 * 1;
4045+ a -= a_offset;
4046+ b_dim1 = *ldb;
4047+ b_offset = 1 + b_dim1 * 1;
4048+ b -= b_offset;
4049+
4050+ /* Function Body */
4051+ lside = lsame_(side, "L");
4052+ if (lside) {
4053+ nrowa = *m;
4054+ } else {
4055+ nrowa = *n;
4056+ }
4057+ nounit = lsame_(diag, "N");
4058+ upper = lsame_(uplo, "U");
4059+
4060+ info = 0;
4061+ if (! lside && ! lsame_(side, "R")) {
4062+ info = 1;
4063+ } else if (! upper && ! lsame_(uplo, "L")) {
4064+ info = 2;
4065+ } else if (! lsame_(transa, "N") && ! lsame_(transa,
4066+ "T") && ! lsame_(transa, "C")) {
4067+ info = 3;
4068+ } else if (! lsame_(diag, "U") && ! lsame_(diag,
4069+ "N")) {
4070+ info = 4;
4071+ } else if (*m < 0) {
4072+ info = 5;
4073+ } else if (*n < 0) {
4074+ info = 6;
4075+ } else if (*lda < max(1,nrowa)) {
4076+ info = 9;
4077+ } else if (*ldb < max(1,*m)) {
4078+ info = 11;
4079+ }
4080+ if (info != 0) {
4081+ xerbla_("DTRMM ", &info);
4082+ return 0;
4083+ }
4084+
4085+/* Quick return if possible. */
4086+
4087+ if (*n == 0) {
4088+ return 0;
4089+ }
4090+
4091+/* And when alpha.eq.zero. */
4092+
4093+ if (*alpha == 0.) {
4094+ i__1 = *n;
4095+ for (j = 1; j <= i__1; ++j) {
4096+ i__2 = *m;
4097+ for (i__ = 1; i__ <= i__2; ++i__) {
4098+ b[i__ + j * b_dim1] = 0.;
4099+/* L10: */
4100+ }
4101+/* L20: */
4102+ }
4103+ return 0;
4104+ }
4105+
4106+/* Start the operations. */
4107+
4108+ if (lside) {
4109+ if (lsame_(transa, "N")) {
4110+
4111+/* Form B := alpha*A*B. */
4112+
4113+ if (upper) {
4114+ i__1 = *n;
4115+ for (j = 1; j <= i__1; ++j) {
4116+ i__2 = *m;
4117+ for (k = 1; k <= i__2; ++k) {
4118+ if (b[k + j * b_dim1] != 0.) {
4119+ temp = *alpha * b[k + j * b_dim1];
4120+ i__3 = k - 1;
4121+ for (i__ = 1; i__ <= i__3; ++i__) {
4122+ b[i__ + j * b_dim1] += temp * a[i__ + k *
4123+ a_dim1];
4124+/* L30: */
4125+ }
4126+ if (nounit) {
4127+ temp *= a[k + k * a_dim1];
4128+ }
4129+ b[k + j * b_dim1] = temp;
4130+ }
4131+/* L40: */
4132+ }
4133+/* L50: */
4134+ }
4135+ } else {
4136+ i__1 = *n;
4137+ for (j = 1; j <= i__1; ++j) {
4138+ for (k = *m; k >= 1; --k) {
4139+ if (b[k + j * b_dim1] != 0.) {
4140+ temp = *alpha * b[k + j * b_dim1];
4141+ b[k + j * b_dim1] = temp;
4142+ if (nounit) {
4143+ b[k + j * b_dim1] *= a[k + k * a_dim1];
4144+ }
4145+ i__2 = *m;
4146+ for (i__ = k + 1; i__ <= i__2; ++i__) {
4147+ b[i__ + j * b_dim1] += temp * a[i__ + k *
4148+ a_dim1];
4149+/* L60: */
4150+ }
4151+ }
4152+/* L70: */
4153+ }
4154+/* L80: */
4155+ }
4156+ }
4157+ } else {
4158+
4159+/* Form B := alpha*A'*B. */
4160+
4161+ if (upper) {
4162+ i__1 = *n;
4163+ for (j = 1; j <= i__1; ++j) {
4164+ for (i__ = *m; i__ >= 1; --i__) {
4165+ temp = b[i__ + j * b_dim1];
4166+ if (nounit) {
4167+ temp *= a[i__ + i__ * a_dim1];
4168+ }
4169+ i__2 = i__ - 1;
4170+ for (k = 1; k <= i__2; ++k) {
4171+ temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
4172+/* L90: */
4173+ }
4174+ b[i__ + j * b_dim1] = *alpha * temp;
4175+/* L100: */
4176+ }
4177+/* L110: */
4178+ }
4179+ } else {
4180+ i__1 = *n;
4181+ for (j = 1; j <= i__1; ++j) {
4182+ i__2 = *m;
4183+ for (i__ = 1; i__ <= i__2; ++i__) {
4184+ temp = b[i__ + j * b_dim1];
4185+ if (nounit) {
4186+ temp *= a[i__ + i__ * a_dim1];
4187+ }
4188+ i__3 = *m;
4189+ for (k = i__ + 1; k <= i__3; ++k) {
4190+ temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
4191+/* L120: */
4192+ }
4193+ b[i__ + j * b_dim1] = *alpha * temp;
4194+/* L130: */
4195+ }
4196+/* L140: */
4197+ }
4198+ }
4199+ }
4200+ } else {
4201+ if (lsame_(transa, "N")) {
4202+
4203+/* Form B := alpha*B*A. */
4204+
4205+ if (upper) {
4206+ for (j = *n; j >= 1; --j) {
4207+ temp = *alpha;
4208+ if (nounit) {
4209+ temp *= a[j + j * a_dim1];
4210+ }
4211+ i__1 = *m;
4212+ for (i__ = 1; i__ <= i__1; ++i__) {
4213+ b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
4214+/* L150: */
4215+ }
4216+ i__1 = j - 1;
4217+ for (k = 1; k <= i__1; ++k) {
4218+ if (a[k + j * a_dim1] != 0.) {
4219+ temp = *alpha * a[k + j * a_dim1];
4220+ i__2 = *m;
4221+ for (i__ = 1; i__ <= i__2; ++i__) {
4222+ b[i__ + j * b_dim1] += temp * b[i__ + k *
4223+ b_dim1];
4224+/* L160: */
4225+ }
4226+ }
4227+/* L170: */
4228+ }
4229+/* L180: */
4230+ }
4231+ } else {
4232+ i__1 = *n;
4233+ for (j = 1; j <= i__1; ++j) {
4234+ temp = *alpha;
4235+ if (nounit) {
4236+ temp *= a[j + j * a_dim1];
4237+ }
4238+ i__2 = *m;
4239+ for (i__ = 1; i__ <= i__2; ++i__) {
4240+ b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
4241+/* L190: */
4242+ }
4243+ i__2 = *n;
4244+ for (k = j + 1; k <= i__2; ++k) {
4245+ if (a[k + j * a_dim1] != 0.) {
4246+ temp = *alpha * a[k + j * a_dim1];
4247+ i__3 = *m;
4248+ for (i__ = 1; i__ <= i__3; ++i__) {
4249+ b[i__ + j * b_dim1] += temp * b[i__ + k *
4250+ b_dim1];
4251+/* L200: */
4252+ }
4253+ }
4254+/* L210: */
4255+ }
4256+/* L220: */
4257+ }
4258+ }
4259+ } else {
4260+
4261+/* Form B := alpha*B*A'. */
4262+
4263+ if (upper) {
4264+ i__1 = *n;
4265+ for (k = 1; k <= i__1; ++k) {
4266+ i__2 = k - 1;
4267+ for (j = 1; j <= i__2; ++j) {
4268+ if (a[j + k * a_dim1] != 0.) {
4269+ temp = *alpha * a[j + k * a_dim1];
4270+ i__3 = *m;
4271+ for (i__ = 1; i__ <= i__3; ++i__) {
4272+ b[i__ + j * b_dim1] += temp * b[i__ + k *
4273+ b_dim1];
4274+/* L230: */
4275+ }
4276+ }
4277+/* L240: */
4278+ }
4279+ temp = *alpha;
4280+ if (nounit) {
4281+ temp *= a[k + k * a_dim1];
4282+ }
4283+ if (temp != 1.) {
4284+ i__2 = *m;
4285+ for (i__ = 1; i__ <= i__2; ++i__) {
4286+ b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
4287+/* L250: */
4288+ }
4289+ }
4290+/* L260: */
4291+ }
4292+ } else {
4293+ for (k = *n; k >= 1; --k) {
4294+ i__1 = *n;
4295+ for (j = k + 1; j <= i__1; ++j) {
4296+ if (a[j + k * a_dim1] != 0.) {
4297+ temp = *alpha * a[j + k * a_dim1];
4298+ i__2 = *m;
4299+ for (i__ = 1; i__ <= i__2; ++i__) {
4300+ b[i__ + j * b_dim1] += temp * b[i__ + k *
4301+ b_dim1];
4302+/* L270: */
4303+ }
4304+ }
4305+/* L280: */
4306+ }
4307+ temp = *alpha;
4308+ if (nounit) {
4309+ temp *= a[k + k * a_dim1];
4310+ }
4311+ if (temp != 1.) {
4312+ i__1 = *m;
4313+ for (i__ = 1; i__ <= i__1; ++i__) {
4314+ b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
4315+/* L290: */
4316+ }
4317+ }
4318+/* L300: */
4319+ }
4320+ }
4321+ }
4322+ }
4323+
4324+ return 0;
4325+
4326+/* End of DTRMM . */
4327+
4328+} /* dtrmm_ */
4329+
4330+/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n,
4331+ doublereal *a, integer *lda, doublereal *x, integer *incx)
4332+{
4333+ /* System generated locals */
4334+ integer a_dim1, a_offset, i__1, i__2;
4335+
4336+ /* Local variables */
4337+ static integer info;
4338+ static doublereal temp;
4339+ static integer i__, j;
4340+ extern logical lsame_(char *, char *);
4341+ static integer ix, jx, kx;
4342+ extern /* Subroutine */ int xerbla_(char *, integer *);
4343+ static logical nounit;
4344+
4345+
4346+/*
4347+ Purpose
4348+ =======
4349+
4350+ DTRMV performs one of the matrix-vector operations
4351+
4352+ x := A*x, or x := A'*x,
4353+
4354+ where x is an n element vector and A is an n by n unit, or non-unit,
4355+ upper or lower triangular matrix.
4356+
4357+ Arguments
4358+ ==========
4359+
4360+ UPLO - CHARACTER*1.
4361+ On entry, UPLO specifies whether the matrix is an upper or
4362+ lower triangular matrix as follows:
4363+
4364+ UPLO = 'U' or 'u' A is an upper triangular matrix.
4365+
4366+ UPLO = 'L' or 'l' A is a lower triangular matrix.
4367+
4368+ Unchanged on exit.
4369+
4370+ TRANS - CHARACTER*1.
4371+ On entry, TRANS specifies the operation to be performed as
4372+ follows:
4373+
4374+ TRANS = 'N' or 'n' x := A*x.
4375+
4376+ TRANS = 'T' or 't' x := A'*x.
4377+
4378+ TRANS = 'C' or 'c' x := A'*x.
4379+
4380+ Unchanged on exit.
4381+
4382+ DIAG - CHARACTER*1.
4383+ On entry, DIAG specifies whether or not A is unit
4384+ triangular as follows:
4385+
4386+ DIAG = 'U' or 'u' A is assumed to be unit triangular.
4387+
4388+ DIAG = 'N' or 'n' A is not assumed to be unit
4389+ triangular.
4390+
4391+ Unchanged on exit.
4392+
4393+ N - INTEGER.
4394+ On entry, N specifies the order of the matrix A.
4395+ N must be at least zero.
4396+ Unchanged on exit.
4397+
4398+ A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
4399+ Before entry with UPLO = 'U' or 'u', the leading n by n
4400+ upper triangular part of the array A must contain the upper
4401+ triangular matrix and the strictly lower triangular part of
4402+ A is not referenced.
4403+ Before entry with UPLO = 'L' or 'l', the leading n by n
4404+ lower triangular part of the array A must contain the lower
4405+ triangular matrix and the strictly upper triangular part of
4406+ A is not referenced.
4407+ Note that when DIAG = 'U' or 'u', the diagonal elements of
4408+ A are not referenced either, but are assumed to be unity.
4409+ Unchanged on exit.
4410+
4411+ LDA - INTEGER.
4412+ On entry, LDA specifies the first dimension of A as declared
4413+ in the calling (sub) program. LDA must be at least
4414+ max( 1, n ).
4415+ Unchanged on exit.
4416+
4417+ X - DOUBLE PRECISION array of dimension at least
4418+ ( 1 + ( n - 1 )*abs( INCX ) ).
4419+ Before entry, the incremented array X must contain the n
4420+ element vector x. On exit, X is overwritten with the
4421+ tranformed vector x.
4422+
4423+ INCX - INTEGER.
4424+ On entry, INCX specifies the increment for the elements of
4425+ X. INCX must not be zero.
4426+ Unchanged on exit.
4427+
4428+
4429+ Level 2 Blas routine.
4430+
4431+ -- Written on 22-October-1986.
4432+ Jack Dongarra, Argonne National Lab.
4433+ Jeremy Du Croz, Nag Central Office.
4434+ Sven Hammarling, Nag Central Office.
4435+ Richard Hanson, Sandia National Labs.
4436+
4437+
4438+ Test the input parameters.
4439+*/
4440+
4441+ /* Parameter adjustments */
4442+ a_dim1 = *lda;
4443+ a_offset = 1 + a_dim1 * 1;
4444+ a -= a_offset;
4445+ --x;
4446+
4447+ /* Function Body */
4448+ info = 0;
4449+ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
4450+ info = 1;
4451+ } else if (! lsame_(trans, "N") && ! lsame_(trans,
4452+ "T") && ! lsame_(trans, "C")) {
4453+ info = 2;
4454+ } else if (! lsame_(diag, "U") && ! lsame_(diag,
4455+ "N")) {
4456+ info = 3;
4457+ } else if (*n < 0) {
4458+ info = 4;
4459+ } else if (*lda < max(1,*n)) {
4460+ info = 6;
4461+ } else if (*incx == 0) {
4462+ info = 8;
4463+ }
4464+ if (info != 0) {
4465+ xerbla_("DTRMV ", &info);
4466+ return 0;
4467+ }
4468+
4469+/* Quick return if possible. */
4470+
4471+ if (*n == 0) {
4472+ return 0;
4473+ }
4474+
4475+ nounit = lsame_(diag, "N");
4476+
4477+/*
4478+ Set up the start point in X if the increment is not unity. This
4479+ will be ( N - 1 )*INCX too small for descending loops.
4480+*/
4481+
4482+ if (*incx <= 0) {
4483+ kx = 1 - (*n - 1) * *incx;
4484+ } else if (*incx != 1) {
4485+ kx = 1;
4486+ }
4487+
4488+/*
4489+ Start the operations. In this version the elements of A are
4490+ accessed sequentially with one pass through A.
4491+*/
4492+
4493+ if (lsame_(trans, "N")) {
4494+
4495+/* Form x := A*x. */
4496+
4497+ if (lsame_(uplo, "U")) {
4498+ if (*incx == 1) {
4499+ i__1 = *n;
4500+ for (j = 1; j <= i__1; ++j) {
4501+ if (x[j] != 0.) {
4502+ temp = x[j];
4503+ i__2 = j - 1;
4504+ for (i__ = 1; i__ <= i__2; ++i__) {
4505+ x[i__] += temp * a[i__ + j * a_dim1];
4506+/* L10: */
4507+ }
4508+ if (nounit) {
4509+ x[j] *= a[j + j * a_dim1];
4510+ }
4511+ }
4512+/* L20: */
4513+ }
4514+ } else {
4515+ jx = kx;
4516+ i__1 = *n;
4517+ for (j = 1; j <= i__1; ++j) {
4518+ if (x[jx] != 0.) {
4519+ temp = x[jx];
4520+ ix = kx;
4521+ i__2 = j - 1;
4522+ for (i__ = 1; i__ <= i__2; ++i__) {
4523+ x[ix] += temp * a[i__ + j * a_dim1];
4524+ ix += *incx;
4525+/* L30: */
4526+ }
4527+ if (nounit) {
4528+ x[jx] *= a[j + j * a_dim1];
4529+ }
4530+ }
4531+ jx += *incx;
4532+/* L40: */
4533+ }
4534+ }
4535+ } else {
4536+ if (*incx == 1) {
4537+ for (j = *n; j >= 1; --j) {
4538+ if (x[j] != 0.) {
4539+ temp = x[j];
4540+ i__1 = j + 1;
4541+ for (i__ = *n; i__ >= i__1; --i__) {
4542+ x[i__] += temp * a[i__ + j * a_dim1];
4543+/* L50: */
4544+ }
4545+ if (nounit) {
4546+ x[j] *= a[j + j * a_dim1];
4547+ }
4548+ }
4549+/* L60: */
4550+ }
4551+ } else {
4552+ kx += (*n - 1) * *incx;
4553+ jx = kx;
4554+ for (j = *n; j >= 1; --j) {
4555+ if (x[jx] != 0.) {
4556+ temp = x[jx];
4557+ ix = kx;
4558+ i__1 = j + 1;
4559+ for (i__ = *n; i__ >= i__1; --i__) {
4560+ x[ix] += temp * a[i__ + j * a_dim1];
4561+ ix -= *incx;
4562+/* L70: */
4563+ }
4564+ if (nounit) {
4565+ x[jx] *= a[j + j * a_dim1];
4566+ }
4567+ }
4568+ jx -= *incx;
4569+/* L80: */
4570+ }
4571+ }
4572+ }
4573+ } else {
4574+
4575+/* Form x := A'*x. */
4576+
4577+ if (lsame_(uplo, "U")) {
4578+ if (*incx == 1) {
4579+ for (j = *n; j >= 1; --j) {
4580+ temp = x[j];
4581+ if (nounit) {
4582+ temp *= a[j + j * a_dim1];
4583+ }
4584+ for (i__ = j - 1; i__ >= 1; --i__) {
4585+ temp += a[i__ + j * a_dim1] * x[i__];
4586+/* L90: */
4587+ }
4588+ x[j] = temp;
4589+/* L100: */
4590+ }
4591+ } else {
4592+ jx = kx + (*n - 1) * *incx;
4593+ for (j = *n; j >= 1; --j) {
4594+ temp = x[jx];
4595+ ix = jx;
4596+ if (nounit) {
4597+ temp *= a[j + j * a_dim1];
4598+ }
4599+ for (i__ = j - 1; i__ >= 1; --i__) {
4600+ ix -= *incx;
4601+ temp += a[i__ + j * a_dim1] * x[ix];
4602+/* L110: */
4603+ }
4604+ x[jx] = temp;
4605+ jx -= *incx;
4606+/* L120: */
4607+ }
4608+ }
4609+ } else {
4610+ if (*incx == 1) {
4611+ i__1 = *n;
4612+ for (j = 1; j <= i__1; ++j) {
4613+ temp = x[j];
4614+ if (nounit) {
4615+ temp *= a[j + j * a_dim1];
4616+ }
4617+ i__2 = *n;
4618+ for (i__ = j + 1; i__ <= i__2; ++i__) {
4619+ temp += a[i__ + j * a_dim1] * x[i__];
4620+/* L130: */
4621+ }
4622+ x[j] = temp;
4623+/* L140: */
4624+ }
4625+ } else {
4626+ jx = kx;
4627+ i__1 = *n;
4628+ for (j = 1; j <= i__1; ++j) {
4629+ temp = x[jx];
4630+ ix = jx;
4631+ if (nounit) {
4632+ temp *= a[j + j * a_dim1];
4633+ }
4634+ i__2 = *n;
4635+ for (i__ = j + 1; i__ <= i__2; ++i__) {
4636+ ix += *incx;
4637+ temp += a[i__ + j * a_dim1] * x[ix];
4638+/* L150: */
4639+ }
4640+ x[jx] = temp;
4641+ jx += *incx;
4642+/* L160: */
4643+ }
4644+ }
4645+ }
4646+ }
4647+
4648+ return 0;
4649+
4650+/* End of DTRMV . */
4651+
4652+} /* dtrmv_ */
4653+
4654+/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag,
4655+ integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
4656+ lda, doublereal *b, integer *ldb)
4657+{
4658+ /* System generated locals */
4659+ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
4660+
4661+ /* Local variables */
4662+ static integer info;
4663+ static doublereal temp;
4664+ static integer i__, j, k;
4665+ static logical lside;
4666+ extern logical lsame_(char *, char *);
4667+ static integer nrowa;
4668+ static logical upper;
4669+ extern /* Subroutine */ int xerbla_(char *, integer *);
4670+ static logical nounit;
4671+
4672+
4673+/*
4674+ Purpose
4675+ =======
4676+
4677+ DTRSM solves one of the matrix equations
4678+
4679+ op( A )*X = alpha*B, or X*op( A ) = alpha*B,
4680+
4681+ where alpha is a scalar, X and B are m by n matrices, A is a unit, or
4682+ non-unit, upper or lower triangular matrix and op( A ) is one of
4683+
4684+ op( A ) = A or op( A ) = A'.
4685+
4686+ The matrix X is overwritten on B.
4687+
4688+ Arguments
4689+ ==========
4690+
4691+ SIDE - CHARACTER*1.
4692+ On entry, SIDE specifies whether op( A ) appears on the left
4693+ or right of X as follows:
4694+
4695+ SIDE = 'L' or 'l' op( A )*X = alpha*B.
4696+
4697+ SIDE = 'R' or 'r' X*op( A ) = alpha*B.
4698+
4699+ Unchanged on exit.
4700+
4701+ UPLO - CHARACTER*1.
4702+ On entry, UPLO specifies whether the matrix A is an upper or
4703+ lower triangular matrix as follows:
4704+
4705+ UPLO = 'U' or 'u' A is an upper triangular matrix.
4706+
4707+ UPLO = 'L' or 'l' A is a lower triangular matrix.
4708+
4709+ Unchanged on exit.
4710+
4711+ TRANSA - CHARACTER*1.
4712+ On entry, TRANSA specifies the form of op( A ) to be used in
4713+ the matrix multiplication as follows:
4714+
4715+ TRANSA = 'N' or 'n' op( A ) = A.
4716+
4717+ TRANSA = 'T' or 't' op( A ) = A'.
4718+
4719+ TRANSA = 'C' or 'c' op( A ) = A'.
4720+
4721+ Unchanged on exit.
4722+
4723+ DIAG - CHARACTER*1.
4724+ On entry, DIAG specifies whether or not A is unit triangular
4725+ as follows:
4726+
4727+ DIAG = 'U' or 'u' A is assumed to be unit triangular.
4728+
4729+ DIAG = 'N' or 'n' A is not assumed to be unit
4730+ triangular.
4731+
4732+ Unchanged on exit.
4733+
4734+ M - INTEGER.
4735+ On entry, M specifies the number of rows of B. M must be at
4736+ least zero.
4737+ Unchanged on exit.
4738+
4739+ N - INTEGER.
4740+ On entry, N specifies the number of columns of B. N must be
4741+ at least zero.
4742+ Unchanged on exit.
4743+
4744+ ALPHA - DOUBLE PRECISION.
4745+ On entry, ALPHA specifies the scalar alpha. When alpha is
4746+ zero then A is not referenced and B need not be set before
4747+ entry.
4748+ Unchanged on exit.
4749+
4750+ A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
4751+ when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
4752+ Before entry with UPLO = 'U' or 'u', the leading k by k
4753+ upper triangular part of the array A must contain the upper
4754+ triangular matrix and the strictly lower triangular part of
4755+ A is not referenced.
4756+ Before entry with UPLO = 'L' or 'l', the leading k by k
4757+ lower triangular part of the array A must contain the lower
4758+ triangular matrix and the strictly upper triangular part of
4759+ A is not referenced.
4760+ Note that when DIAG = 'U' or 'u', the diagonal elements of
4761+ A are not referenced either, but are assumed to be unity.
4762+ Unchanged on exit.
4763+
4764+ LDA - INTEGER.
4765+ On entry, LDA specifies the first dimension of A as declared
4766+ in the calling (sub) program. When SIDE = 'L' or 'l' then
4767+ LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
4768+ then LDA must be at least max( 1, n ).
4769+ Unchanged on exit.
4770+
4771+ B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
4772+ Before entry, the leading m by n part of the array B must
4773+ contain the right-hand side matrix B, and on exit is
4774+ overwritten by the solution matrix X.
4775+
4776+ LDB - INTEGER.
4777+ On entry, LDB specifies the first dimension of B as declared
4778+ in the calling (sub) program. LDB must be at least
4779+ max( 1, m ).
4780+ Unchanged on exit.
4781+
4782+
4783+ Level 3 Blas routine.
4784+
4785+
4786+ -- Written on 8-February-1989.
4787+ Jack Dongarra, Argonne National Laboratory.
4788+ Iain Duff, AERE Harwell.
4789+ Jeremy Du Croz, Numerical Algorithms Group Ltd.
4790+ Sven Hammarling, Numerical Algorithms Group Ltd.
4791+
4792+
4793+ Test the input parameters.
4794+*/
4795+
4796+ /* Parameter adjustments */
4797+ a_dim1 = *lda;
4798+ a_offset = 1 + a_dim1 * 1;
4799+ a -= a_offset;
4800+ b_dim1 = *ldb;
4801+ b_offset = 1 + b_dim1 * 1;
4802+ b -= b_offset;
4803+
4804+ /* Function Body */
4805+ lside = lsame_(side, "L");
4806+ if (lside) {
4807+ nrowa = *m;
4808+ } else {
4809+ nrowa = *n;
4810+ }
4811+ nounit = lsame_(diag, "N");
4812+ upper = lsame_(uplo, "U");
4813+
4814+ info = 0;
4815+ if (! lside && ! lsame_(side, "R")) {
4816+ info = 1;
4817+ } else if (! upper && ! lsame_(uplo, "L")) {
4818+ info = 2;
4819+ } else if (! lsame_(transa, "N") && ! lsame_(transa,
4820+ "T") && ! lsame_(transa, "C")) {
4821+ info = 3;
4822+ } else if (! lsame_(diag, "U") && ! lsame_(diag,
4823+ "N")) {
4824+ info = 4;
4825+ } else if (*m < 0) {
4826+ info = 5;
4827+ } else if (*n < 0) {
4828+ info = 6;
4829+ } else if (*lda < max(1,nrowa)) {
4830+ info = 9;
4831+ } else if (*ldb < max(1,*m)) {
4832+ info = 11;
4833+ }
4834+ if (info != 0) {
4835+ xerbla_("DTRSM ", &info);
4836+ return 0;
4837+ }
4838+
4839+/* Quick return if possible. */
4840+
4841+ if (*n == 0) {
4842+ return 0;
4843+ }
4844+
4845+/* And when alpha.eq.zero. */
4846+
4847+ if (*alpha == 0.) {
4848+ i__1 = *n;
4849+ for (j = 1; j <= i__1; ++j) {
4850+ i__2 = *m;
4851+ for (i__ = 1; i__ <= i__2; ++i__) {
4852+ b[i__ + j * b_dim1] = 0.;
4853+/* L10: */
4854+ }
4855+/* L20: */
4856+ }
4857+ return 0;
4858+ }
4859+
4860+/* Start the operations. */
4861+
4862+ if (lside) {
4863+ if (lsame_(transa, "N")) {
4864+
4865+/* Form B := alpha*inv( A )*B. */
4866+
4867+ if (upper) {
4868+ i__1 = *n;
4869+ for (j = 1; j <= i__1; ++j) {
4870+ if (*alpha != 1.) {
4871+ i__2 = *m;
4872+ for (i__ = 1; i__ <= i__2; ++i__) {
4873+ b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
4874+ ;
4875+/* L30: */
4876+ }
4877+ }
4878+ for (k = *m; k >= 1; --k) {
4879+ if (b[k + j * b_dim1] != 0.) {
4880+ if (nounit) {
4881+ b[k + j * b_dim1] /= a[k + k * a_dim1];
4882+ }
4883+ i__2 = k - 1;
4884+ for (i__ = 1; i__ <= i__2; ++i__) {
4885+ b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
4886+ i__ + k * a_dim1];
4887+/* L40: */
4888+ }
4889+ }
4890+/* L50: */
4891+ }
4892+/* L60: */
4893+ }
4894+ } else {
4895+ i__1 = *n;
4896+ for (j = 1; j <= i__1; ++j) {
4897+ if (*alpha != 1.) {
4898+ i__2 = *m;
4899+ for (i__ = 1; i__ <= i__2; ++i__) {
4900+ b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
4901+ ;
4902+/* L70: */
4903+ }
4904+ }
4905+ i__2 = *m;
4906+ for (k = 1; k <= i__2; ++k) {
4907+ if (b[k + j * b_dim1] != 0.) {
4908+ if (nounit) {
4909+ b[k + j * b_dim1] /= a[k + k * a_dim1];
4910+ }
4911+ i__3 = *m;
4912+ for (i__ = k + 1; i__ <= i__3; ++i__) {
4913+ b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
4914+ i__ + k * a_dim1];
4915+/* L80: */
4916+ }
4917+ }
4918+/* L90: */
4919+ }
4920+/* L100: */
4921+ }
4922+ }
4923+ } else {
4924+
4925+/* Form B := alpha*inv( A' )*B. */
4926+
4927+ if (upper) {
4928+ i__1 = *n;
4929+ for (j = 1; j <= i__1; ++j) {
4930+ i__2 = *m;
4931+ for (i__ = 1; i__ <= i__2; ++i__) {
4932+ temp = *alpha * b[i__ + j * b_dim1];
4933+ i__3 = i__ - 1;
4934+ for (k = 1; k <= i__3; ++k) {
4935+ temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
4936+/* L110: */
4937+ }
4938+ if (nounit) {
4939+ temp /= a[i__ + i__ * a_dim1];
4940+ }
4941+ b[i__ + j * b_dim1] = temp;
4942+/* L120: */
4943+ }
4944+/* L130: */
4945+ }
4946+ } else {
4947+ i__1 = *n;
4948+ for (j = 1; j <= i__1; ++j) {
4949+ for (i__ = *m; i__ >= 1; --i__) {
4950+ temp = *alpha * b[i__ + j * b_dim1];
4951+ i__2 = *m;
4952+ for (k = i__ + 1; k <= i__2; ++k) {
4953+ temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
4954+/* L140: */
4955+ }
4956+ if (nounit) {
4957+ temp /= a[i__ + i__ * a_dim1];
4958+ }
4959+ b[i__ + j * b_dim1] = temp;
4960+/* L150: */
4961+ }
4962+/* L160: */
4963+ }
4964+ }
4965+ }
4966+ } else {
4967+ if (lsame_(transa, "N")) {
4968+
4969+/* Form B := alpha*B*inv( A ). */
4970+
4971+ if (upper) {
4972+ i__1 = *n;
4973+ for (j = 1; j <= i__1; ++j) {
4974+ if (*alpha != 1.) {
4975+ i__2 = *m;
4976+ for (i__ = 1; i__ <= i__2; ++i__) {
4977+ b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
4978+ ;
4979+/* L170: */
4980+ }
4981+ }
4982+ i__2 = j - 1;
4983+ for (k = 1; k <= i__2; ++k) {
4984+ if (a[k + j * a_dim1] != 0.) {
4985+ i__3 = *m;
4986+ for (i__ = 1; i__ <= i__3; ++i__) {
4987+ b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
4988+ i__ + k * b_dim1];
4989+/* L180: */
4990+ }
4991+ }
4992+/* L190: */
4993+ }
4994+ if (nounit) {
4995+ temp = 1. / a[j + j * a_dim1];
4996+ i__2 = *m;
4997+ for (i__ = 1; i__ <= i__2; ++i__) {
4998+ b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
4999+/* L200: */
5000+ }
The diff has been truncated for viewing.

Subscribers

People subscribed via source and target branches