LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sspsv()

subroutine sspsv ( character  uplo,
integer  n,
integer  nrhs,
real, dimension( * )  ap,
integer, dimension( * )  ipiv,
real, dimension( ldb, * )  b,
integer  ldb,
integer  info 
)

SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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

Purpose:
 SSPSV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N symmetric matrix stored in packed format and X
 and B are N-by-NRHS matrices.

 The diagonal pivoting method is used to factor A as
    A = U * D * U**T,  if UPLO = 'U', or
    A = L * D * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, D is symmetric and block diagonal with 1-by-1
 and 2-by-2 diagonal blocks.  The factored form of A is then used to
 solve the system of equations A * X = B.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
[in]N
          N is INTEGER
          The number of linear equations, i.e., 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,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.
          See below for further details.

          On exit, the block diagonal matrix D and the multipliers used
          to obtain the factor U or L from the factorization
          A = U*D*U**T or A = L*D*L**T as computed by SSPTRF, stored as
          a packed triangular matrix in the same storage format as A.
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D, as
          determined by SSPTRF.  If IPIV(k) > 0, then rows and columns
          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
          then rows and columns k-1 and -IPIV(k) were interchanged and
          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
          diagonal block.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS 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
          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
                has been completed, but the block diagonal matrix D is
                exactly singular, so the solution could not be
                computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  The packed storage scheme is illustrated by the following example
  when N = 4, UPLO = 'U':

  Two-dimensional storage of the symmetric matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = aji)
                 a44

  Packed storage of the upper triangle of A:

  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 161 of file sspsv.f.

162*
163* -- LAPACK driver routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER UPLO
169 INTEGER INFO, LDB, N, NRHS
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * )
173 REAL AP( * ), B( LDB, * )
174* ..
175*
176* =====================================================================
177*
178* .. External Functions ..
179 LOGICAL LSAME
180 EXTERNAL lsame
181* ..
182* .. External Subroutines ..
183 EXTERNAL ssptrf, ssptrs, xerbla
184* ..
185* .. Intrinsic Functions ..
186 INTRINSIC max
187* ..
188* .. Executable Statements ..
189*
190* Test the input parameters.
191*
192 info = 0
193 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194 info = -1
195 ELSE IF( n.LT.0 ) THEN
196 info = -2
197 ELSE IF( nrhs.LT.0 ) THEN
198 info = -3
199 ELSE IF( ldb.LT.max( 1, n ) ) THEN
200 info = -7
201 END IF
202 IF( info.NE.0 ) THEN
203 CALL xerbla( 'SSPSV ', -info )
204 RETURN
205 END IF
206*
207* Compute the factorization A = U*D*U**T or A = L*D*L**T.
208*
209 CALL ssptrf( uplo, n, ap, ipiv, info )
210 IF( info.EQ.0 ) THEN
211*
212* Solve the system A*X = B, overwriting B with X.
213*
214 CALL ssptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
215*
216 END IF
217 RETURN
218*
219* End of SSPSV
220*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssptrf(uplo, n, ap, ipiv, info)
SSPTRF
Definition ssptrf.f:157
subroutine ssptrs(uplo, n, nrhs, ap, ipiv, b, ldb, info)
SSPTRS
Definition ssptrs.f:115
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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