LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ ssytrs()

subroutine ssytrs ( character  uplo,
integer  n,
integer  nrhs,
real, dimension( lda, * )  a,
integer  lda,
integer, dimension( * )  ipiv,
real, dimension( ldb, * )  b,
integer  ldb,
integer  info 
)

SSYTRS

Download SSYTRS + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SSYTRS solves a system of linear equations A*X = B with a real
 symmetric matrix A using the factorization A = U*D*U**T or
 A = L*D*L**T computed by SSYTRF.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*L**T.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by SSYTRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 119 of file ssytrs.f.

120*
121* -- LAPACK computational routine --
122* -- LAPACK is a software package provided by Univ. of Tennessee, --
123* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124*
125* .. Scalar Arguments ..
126 CHARACTER UPLO
127 INTEGER INFO, LDA, LDB, N, NRHS
128* ..
129* .. Array Arguments ..
130 INTEGER IPIV( * )
131 REAL A( LDA, * ), B( LDB, * )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 REAL ONE
138 parameter( one = 1.0e+0 )
139* ..
140* .. Local Scalars ..
141 LOGICAL UPPER
142 INTEGER J, K, KP
143 REAL AK, AKM1, AKM1K, BK, BKM1, DENOM
144* ..
145* .. External Functions ..
146 LOGICAL LSAME
147 EXTERNAL lsame
148* ..
149* .. External Subroutines ..
150 EXTERNAL sgemv, sger, sscal, sswap, xerbla
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max
154* ..
155* .. Executable Statements ..
156*
157 info = 0
158 upper = lsame( uplo, 'U' )
159 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
160 info = -1
161 ELSE IF( n.LT.0 ) THEN
162 info = -2
163 ELSE IF( nrhs.LT.0 ) THEN
164 info = -3
165 ELSE IF( lda.LT.max( 1, n ) ) THEN
166 info = -5
167 ELSE IF( ldb.LT.max( 1, n ) ) THEN
168 info = -8
169 END IF
170 IF( info.NE.0 ) THEN
171 CALL xerbla( 'SSYTRS', -info )
172 RETURN
173 END IF
174*
175* Quick return if possible
176*
177 IF( n.EQ.0 .OR. nrhs.EQ.0 )
178 $ RETURN
179*
180 IF( upper ) THEN
181*
182* Solve A*X = B, where A = U*D*U**T.
183*
184* First solve U*D*X = B, overwriting B with X.
185*
186* K is the main loop index, decreasing from N to 1 in steps of
187* 1 or 2, depending on the size of the diagonal blocks.
188*
189 k = n
190 10 CONTINUE
191*
192* If K < 1, exit from loop.
193*
194 IF( k.LT.1 )
195 $ GO TO 30
196*
197 IF( ipiv( k ).GT.0 ) THEN
198*
199* 1 x 1 diagonal block
200*
201* Interchange rows K and IPIV(K).
202*
203 kp = ipiv( k )
204 IF( kp.NE.k )
205 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
206*
207* Multiply by inv(U(K)), where U(K) is the transformation
208* stored in column K of A.
209*
210 CALL sger( k-1, nrhs, -one, a( 1, k ), 1, b( k, 1 ), ldb,
211 $ b( 1, 1 ), ldb )
212*
213* Multiply by the inverse of the diagonal block.
214*
215 CALL sscal( nrhs, one / a( k, k ), b( k, 1 ), ldb )
216 k = k - 1
217 ELSE
218*
219* 2 x 2 diagonal block
220*
221* Interchange rows K-1 and -IPIV(K).
222*
223 kp = -ipiv( k )
224 IF( kp.NE.k-1 )
225 $ CALL sswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
226*
227* Multiply by inv(U(K)), where U(K) is the transformation
228* stored in columns K-1 and K of A.
229*
230 CALL sger( k-2, nrhs, -one, a( 1, k ), 1, b( k, 1 ), ldb,
231 $ b( 1, 1 ), ldb )
232 CALL sger( k-2, nrhs, -one, a( 1, k-1 ), 1, b( k-1, 1 ),
233 $ ldb, b( 1, 1 ), ldb )
234*
235* Multiply by the inverse of the diagonal block.
236*
237 akm1k = a( k-1, k )
238 akm1 = a( k-1, k-1 ) / akm1k
239 ak = a( k, k ) / akm1k
240 denom = akm1*ak - one
241 DO 20 j = 1, nrhs
242 bkm1 = b( k-1, j ) / akm1k
243 bk = b( k, j ) / akm1k
244 b( k-1, j ) = ( ak*bkm1-bk ) / denom
245 b( k, j ) = ( akm1*bk-bkm1 ) / denom
246 20 CONTINUE
247 k = k - 2
248 END IF
249*
250 GO TO 10
251 30 CONTINUE
252*
253* Next solve U**T *X = B, overwriting B with X.
254*
255* K is the main loop index, increasing from 1 to N in steps of
256* 1 or 2, depending on the size of the diagonal blocks.
257*
258 k = 1
259 40 CONTINUE
260*
261* If K > N, exit from loop.
262*
263 IF( k.GT.n )
264 $ GO TO 50
265*
266 IF( ipiv( k ).GT.0 ) THEN
267*
268* 1 x 1 diagonal block
269*
270* Multiply by inv(U**T(K)), where U(K) is the transformation
271* stored in column K of A.
272*
273 CALL sgemv( 'Transpose', k-1, nrhs, -one, b, ldb, a( 1, k ),
274 $ 1, one, b( k, 1 ), ldb )
275*
276* Interchange rows K and IPIV(K).
277*
278 kp = ipiv( k )
279 IF( kp.NE.k )
280 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
281 k = k + 1
282 ELSE
283*
284* 2 x 2 diagonal block
285*
286* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
287* stored in columns K and K+1 of A.
288*
289 CALL sgemv( 'Transpose', k-1, nrhs, -one, b, ldb, a( 1, k ),
290 $ 1, one, b( k, 1 ), ldb )
291 CALL sgemv( 'Transpose', k-1, nrhs, -one, b, ldb,
292 $ a( 1, k+1 ), 1, one, b( k+1, 1 ), ldb )
293*
294* Interchange rows K and -IPIV(K).
295*
296 kp = -ipiv( k )
297 IF( kp.NE.k )
298 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
299 k = k + 2
300 END IF
301*
302 GO TO 40
303 50 CONTINUE
304*
305 ELSE
306*
307* Solve A*X = B, where A = L*D*L**T.
308*
309* First solve L*D*X = B, overwriting B with X.
310*
311* K is the main loop index, increasing from 1 to N in steps of
312* 1 or 2, depending on the size of the diagonal blocks.
313*
314 k = 1
315 60 CONTINUE
316*
317* If K > N, exit from loop.
318*
319 IF( k.GT.n )
320 $ GO TO 80
321*
322 IF( ipiv( k ).GT.0 ) THEN
323*
324* 1 x 1 diagonal block
325*
326* Interchange rows K and IPIV(K).
327*
328 kp = ipiv( k )
329 IF( kp.NE.k )
330 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
331*
332* Multiply by inv(L(K)), where L(K) is the transformation
333* stored in column K of A.
334*
335 IF( k.LT.n )
336 $ CALL sger( n-k, nrhs, -one, a( k+1, k ), 1, b( k, 1 ),
337 $ ldb, b( k+1, 1 ), ldb )
338*
339* Multiply by the inverse of the diagonal block.
340*
341 CALL sscal( nrhs, one / a( k, k ), b( k, 1 ), ldb )
342 k = k + 1
343 ELSE
344*
345* 2 x 2 diagonal block
346*
347* Interchange rows K+1 and -IPIV(K).
348*
349 kp = -ipiv( k )
350 IF( kp.NE.k+1 )
351 $ CALL sswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
352*
353* Multiply by inv(L(K)), where L(K) is the transformation
354* stored in columns K and K+1 of A.
355*
356 IF( k.LT.n-1 ) THEN
357 CALL sger( n-k-1, nrhs, -one, a( k+2, k ), 1, b( k, 1 ),
358 $ ldb, b( k+2, 1 ), ldb )
359 CALL sger( n-k-1, nrhs, -one, a( k+2, k+1 ), 1,
360 $ b( k+1, 1 ), ldb, b( k+2, 1 ), ldb )
361 END IF
362*
363* Multiply by the inverse of the diagonal block.
364*
365 akm1k = a( k+1, k )
366 akm1 = a( k, k ) / akm1k
367 ak = a( k+1, k+1 ) / akm1k
368 denom = akm1*ak - one
369 DO 70 j = 1, nrhs
370 bkm1 = b( k, j ) / akm1k
371 bk = b( k+1, j ) / akm1k
372 b( k, j ) = ( ak*bkm1-bk ) / denom
373 b( k+1, j ) = ( akm1*bk-bkm1 ) / denom
374 70 CONTINUE
375 k = k + 2
376 END IF
377*
378 GO TO 60
379 80 CONTINUE
380*
381* Next solve L**T *X = B, overwriting B with X.
382*
383* K is the main loop index, decreasing from N to 1 in steps of
384* 1 or 2, depending on the size of the diagonal blocks.
385*
386 k = n
387 90 CONTINUE
388*
389* If K < 1, exit from loop.
390*
391 IF( k.LT.1 )
392 $ GO TO 100
393*
394 IF( ipiv( k ).GT.0 ) THEN
395*
396* 1 x 1 diagonal block
397*
398* Multiply by inv(L**T(K)), where L(K) is the transformation
399* stored in column K of A.
400*
401 IF( k.LT.n )
402 $ CALL sgemv( 'Transpose', n-k, nrhs, -one, b( k+1, 1 ),
403 $ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
404*
405* Interchange rows K and IPIV(K).
406*
407 kp = ipiv( k )
408 IF( kp.NE.k )
409 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
410 k = k - 1
411 ELSE
412*
413* 2 x 2 diagonal block
414*
415* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
416* stored in columns K-1 and K of A.
417*
418 IF( k.LT.n ) THEN
419 CALL sgemv( 'Transpose', n-k, nrhs, -one, b( k+1, 1 ),
420 $ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
421 CALL sgemv( 'Transpose', n-k, nrhs, -one, b( k+1, 1 ),
422 $ ldb, a( k+1, k-1 ), 1, one, b( k-1, 1 ),
423 $ ldb )
424 END IF
425*
426* Interchange rows K and -IPIV(K).
427*
428 kp = -ipiv( k )
429 IF( kp.NE.k )
430 $ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
431 k = k - 2
432 END IF
433*
434 GO TO 90
435 100 CONTINUE
436 END IF
437*
438 RETURN
439*
440* End of SSYTRS
441*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
sgemv
subroutine sgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
SGEMV
Definition sgemv.f:158
sger
subroutine sger(m, n, alpha, x, incx, y, incy, a, lda)
SGER
Definition sger.f:130
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
sscal
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
sswap
subroutine sswap(n, sx, incx, sy, incy)
SSWAP
Definition sswap.f:82
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