STBT03 computes the residual for the solution to a scaled triangular


 system of equations  A*x = s*b  or  A'*x = s*b  when A is a


 triangular band matrix. Here A' is the transpose of A, s is a scalar,


 and x and b are N by NRHS matrices.  The test ratio is the maximum


 over the number of right hand sides of


    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),


 where op(A) denotes A or A' and EPS is the machine epsilon.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1


          Specifies the operation applied to A.


          = 'N':  A *x = b  (No transpose)


          = 'T':  A'*x = b  (Transpose)


          = 'C':  A'*x = b  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

KD

          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.

NRHS

          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrices X and B.  NRHS >= 0.

AB

          AB is REAL array, dimension (LDAB,N)


          The upper or lower triangular 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).

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

SCALE

          SCALE is REAL


          The scaling factor s used in solving the triangular system.

CNORM

          CNORM is REAL array, dimension (N)


          The 1-norms of the columns of A, not counting the diagonal.

TSCAL

          TSCAL is REAL


          The scaling factor used in computing the 1-norms in CNORM.


          CNORM actually contains the column norms of TSCAL*A.

X

          X is REAL array, dimension (LDX,NRHS)


          The computed solution vectors for the system of linear


          equations.

LDX

          LDX is INTEGER


          The leading dimension of the array X.  LDX >= max(1,N).

B

          B is REAL array, dimension (LDB,NRHS)


          The right hand side vectors for the system of linear


          equations.

LDB

          LDB is INTEGER


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

WORK

          WORK is REAL array, dimension (N)

RESID

          RESID is REAL


          The maximum over the number of right hand sides of


          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

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