LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sspgst()

 subroutine sspgst ( integer ITYPE, character UPLO, integer N, real, dimension( * ) AP, real, dimension( * ) BP, integer INFO )

SSPGST

Purpose:
``` SSPGST reduces a real symmetric-definite generalized eigenproblem
to standard form, using packed storage.

If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.

B must have been previously factorized as U**T*U or L*L**T by SPPTRF.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T*A*L.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored and B is factored as U**T*U; = 'L': Lower triangle of A is stored and B is factored as L*L**T.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] AP ``` AP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, if INFO = 0, the transformed matrix, stored in the same format as A.``` [in] BP ``` BP is REAL array, dimension (N*(N+1)/2) The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by SPPTRF.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 112 of file sspgst.f.

113 *
114 * -- LAPACK computational routine --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 *
118 * .. Scalar Arguments ..
119  CHARACTER UPLO
120  INTEGER INFO, ITYPE, N
121 * ..
122 * .. Array Arguments ..
123  REAL AP( * ), BP( * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  REAL ONE, HALF
130  parameter( one = 1.0, half = 0.5 )
131 * ..
132 * .. Local Scalars ..
133  LOGICAL UPPER
134  INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
135  REAL AJJ, AKK, BJJ, BKK, CT
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL saxpy, sscal, sspmv, sspr2, stpmv, stpsv,
139  \$ xerbla
140 * ..
141 * .. External Functions ..
142  LOGICAL LSAME
143  REAL SDOT
144  EXTERNAL lsame, sdot
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  upper = lsame( uplo, 'U' )
152  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
153  info = -1
154  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
155  info = -2
156  ELSE IF( n.LT.0 ) THEN
157  info = -3
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'SSPGST', -info )
161  RETURN
162  END IF
163 *
164  IF( itype.EQ.1 ) THEN
165  IF( upper ) THEN
166 *
167 * Compute inv(U**T)*A*inv(U)
168 *
169 * J1 and JJ are the indices of A(1,j) and A(j,j)
170 *
171  jj = 0
172  DO 10 j = 1, n
173  j1 = jj + 1
174  jj = jj + j
175 *
176 * Compute the j-th column of the upper triangle of A
177 *
178  bjj = bp( jj )
179  CALL stpsv( uplo, 'Transpose', 'Nonunit', j, bp,
180  \$ ap( j1 ), 1 )
181  CALL sspmv( uplo, j-1, -one, ap, bp( j1 ), 1, one,
182  \$ ap( j1 ), 1 )
183  CALL sscal( j-1, one / bjj, ap( j1 ), 1 )
184  ap( jj ) = ( ap( jj )-sdot( j-1, ap( j1 ), 1, bp( j1 ),
185  \$ 1 ) ) / bjj
186  10 CONTINUE
187  ELSE
188 *
189 * Compute inv(L)*A*inv(L**T)
190 *
191 * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
192 *
193  kk = 1
194  DO 20 k = 1, n
195  k1k1 = kk + n - k + 1
196 *
197 * Update the lower triangle of A(k:n,k:n)
198 *
199  akk = ap( kk )
200  bkk = bp( kk )
201  akk = akk / bkk**2
202  ap( kk ) = akk
203  IF( k.LT.n ) THEN
204  CALL sscal( n-k, one / bkk, ap( kk+1 ), 1 )
205  ct = -half*akk
206  CALL saxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
207  CALL sspr2( uplo, n-k, -one, ap( kk+1 ), 1,
208  \$ bp( kk+1 ), 1, ap( k1k1 ) )
209  CALL saxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
210  CALL stpsv( uplo, 'No transpose', 'Non-unit', n-k,
211  \$ bp( k1k1 ), ap( kk+1 ), 1 )
212  END IF
213  kk = k1k1
214  20 CONTINUE
215  END IF
216  ELSE
217  IF( upper ) THEN
218 *
219 * Compute U*A*U**T
220 *
221 * K1 and KK are the indices of A(1,k) and A(k,k)
222 *
223  kk = 0
224  DO 30 k = 1, n
225  k1 = kk + 1
226  kk = kk + k
227 *
228 * Update the upper triangle of A(1:k,1:k)
229 *
230  akk = ap( kk )
231  bkk = bp( kk )
232  CALL stpmv( uplo, 'No transpose', 'Non-unit', k-1, bp,
233  \$ ap( k1 ), 1 )
234  ct = half*akk
235  CALL saxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
236  CALL sspr2( uplo, k-1, one, ap( k1 ), 1, bp( k1 ), 1,
237  \$ ap )
238  CALL saxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
239  CALL sscal( k-1, bkk, ap( k1 ), 1 )
240  ap( kk ) = akk*bkk**2
241  30 CONTINUE
242  ELSE
243 *
244 * Compute L**T *A*L
245 *
246 * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
247 *
248  jj = 1
249  DO 40 j = 1, n
250  j1j1 = jj + n - j + 1
251 *
252 * Compute the j-th column of the lower triangle of A
253 *
254  ajj = ap( jj )
255  bjj = bp( jj )
256  ap( jj ) = ajj*bjj + sdot( n-j, ap( jj+1 ), 1,
257  \$ bp( jj+1 ), 1 )
258  CALL sscal( n-j, bjj, ap( jj+1 ), 1 )
259  CALL sspmv( uplo, n-j, one, ap( j1j1 ), bp( jj+1 ), 1,
260  \$ one, ap( jj+1 ), 1 )
261  CALL stpmv( uplo, 'Transpose', 'Non-unit', n-j+1,
262  \$ bp( jj ), ap( jj ), 1 )
263  jj = j1j1
264  40 CONTINUE
265  END IF
266  END IF
267  RETURN
268 *
269 * End of SSPGST
270 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:142
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
Definition: sspmv.f:147
subroutine stpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPSV
Definition: stpsv.f:144
subroutine sspr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
SSPR2
Definition: sspr2.f:142
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