Contents

• NAME
• SYNOPSIS
  • F95 INTERFACE
  • C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

     spbtrs - solve a system of linear equations A*X = B  with  a
     symmetric positive definite band matrix A using the Cholesky
     factorization A = U**T*U or A = L*L**T computed by SPBTRF

SYNOPSIS

     SUBROUTINE SPBTRS(UPLO, N, KD, NRHS, A, LDA, B, LDB, INFO)

     CHARACTER * 1 UPLO
     INTEGER N, KD, NRHS, LDA, LDB, INFO
     REAL A(LDA,*), B(LDB,*)

     SUBROUTINE SPBTRS_64(UPLO, N, KD, NRHS, A, LDA, B, LDB, INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 N, KD, NRHS, LDA, LDB, INFO
     REAL A(LDA,*), B(LDB,*)

  F95 INTERFACE
     SUBROUTINE PBTRS(UPLO, [N], KD, [NRHS], A, [LDA], B, [LDB], [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER :: N, KD, NRHS, LDA, LDB, INFO
     REAL, DIMENSION(:,:) :: A, B

     SUBROUTINE PBTRS_64(UPLO, [N], KD, [NRHS], A, [LDA], B, [LDB],
            [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER(8) :: N, KD, NRHS, LDA, LDB, INFO
     REAL, DIMENSION(:,:) :: A, B

  C INTERFACE
     #include <sunperf.h>

     void spbtrs(char uplo, int n, int kd, int  nrhs,  float  *a,
               int lda, float *b, int ldb, int *info);

     void spbtrs_64(char uplo, long n, long kd, long nrhs,  float
               *a, long lda, float *b, long ldb, long *info);

PURPOSE

     spbtrs solves a system of linear equations A*X =  B  with  a
     symmetric positive definite band matrix A using the Cholesky
     factorization A = U**T*U or A = L*L**T computed by SPBTRF.

ARGUMENTS

     UPLO (input)
               = 'U':  Upper triangular factor stored in A;
               = 'L':  Lower triangular factor stored in A.

     N (input) The order of the matrix A.  N >= 0.

     KD (input)
               The number of superdiagonals of the  matrix  A  if
               UPLO  = 'U', or the number of subdiagonals if UPLO
               = 'L'.  KD >= 0.

     NRHS (input)
               The number of right hand sides, i.e.,  the  number
               of columns of the matrix B.  NRHS >= 0.

     A (input) The triangular factor U or  L  from  the  Cholesky
               factorization A = U**T*U or A = L*L**T of the band
               matrix A, stored in the first  KD+1  rows  of  the
               array.  The j-th column of U or L is stored in the
               j-th column of the array A as  follows:   if  UPLO
               ='U',   A(kd+1+i-j,j)   =   U(i,j)   for  max(1,j-
               kd)<=i<=j; if UPLO ='L',  A(1+i-j,j)     =  L(i,j)
               for j<=i<=min(n,j+kd).

     LDA (input)
               The leading dimension of  the  array  A.   LDA  >=
               KD+1.

     B (input/output)
               On entry, the right hand side matrix B.  On  exit,
               the solution matrix X.

     LDB (input)
               The leading dimension of  the  array  B.   LDB  >=
               max(1,N).

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value