Move LAPACK trunk into position.

1 files changed, 151 insertions, 0 deletions

diff --git a/SRC/spbsv.f b/SRC/spbsv.f
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+      SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
+*
+*  -- LAPACK driver routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      REAL               AB( LDAB, * ), B( LDB, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  SPBSV computes the solution to a real system of linear equations
+*     A * X = B,
+*  where A is an N-by-N symmetric positive definite band matrix and X
+*  and B are N-by-NRHS matrices.
+*
+*  The Cholesky decomposition is used to factor A as
+*     A = U**T * U,  if UPLO = 'U', or
+*     A = L * L**T,  if UPLO = 'L',
+*  where U is an upper triangular band matrix, and L is a lower
+*  triangular band matrix, with the same number of superdiagonals or
+*  subdiagonals as A.  The factored form of A is then used to solve the
+*  system of equations A * X = B.
+*
+*  Arguments
+*  =========
+*
+*  UPLO    (input) CHARACTER*1
+*          = 'U':  Upper triangle of A is stored;
+*          = 'L':  Lower triangle of A is stored.
+*
+*  N       (input) INTEGER
+*          The number of linear equations, i.e., the order of the
+*          matrix A.  N >= 0.
+*
+*  KD      (input) INTEGER
+*          The number of superdiagonals of the matrix A if UPLO = 'U',
+*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
+*
+*  NRHS    (input) INTEGER
+*          The number of right hand sides, i.e., the number of columns
+*          of the matrix B.  NRHS >= 0.
+*
+*  AB      (input/output) REAL array, dimension (LDAB,N)
+*          On entry, the upper or lower triangle of the symmetric band
+*          matrix A, stored in the first KD+1 rows of the array.  The
+*          j-th column of A is stored in the j-th column of the array AB
+*          as follows:
+*          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
+*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
+*          See below for further details.
+*
+*          On exit, if INFO = 0, the triangular factor U or L from the
+*          Cholesky factorization A = U**T*U or A = L*L**T of the band
+*          matrix A, in the same storage format as A.
+*
+*  LDAB    (input) INTEGER
+*          The leading dimension of the array AB.  LDAB >= KD+1.
+*
+*  B       (input/output) 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.
+*
+*  LDB     (input) INTEGER
+*          The leading dimension of the array B.  LDB >= max(1,N).
+*
+*  INFO    (output) INTEGER
+*          = 0:  successful exit
+*          < 0:  if INFO = -i, the i-th argument had an illegal value
+*          > 0:  if INFO = i, the leading minor of order i of A is not
+*                positive definite, so the factorization could not be
+*                completed, and the solution has not been computed.
+*
+*  Further Details
+*  ===============
+*
+*  The band storage scheme is illustrated by the following example, when
+*  N = 6, KD = 2, and UPLO = 'U':
+*
+*  On entry:                       On exit:
+*
+*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
+*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
+*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
+*
+*  Similarly, if UPLO = 'L' the format of A is as follows:
+*
+*  On entry:                       On exit:
+*
+*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
+*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
+*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
+*
+*  Array elements marked * are not used by the routine.
+*
+*  =====================================================================
+*
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SPBTRF, SPBTRS, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( KD.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -4
+      ELSE IF( LDAB.LT.KD+1 ) THEN
+         INFO = -6
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'SPBSV ', -INFO )
+         RETURN
+      END IF
+*
+*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*
+      CALL SPBTRF( UPLO, N, KD, AB, LDAB, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+         CALL SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
+*
+      END IF
+      RETURN
+*
+*     End of SPBSV
+*
+      END