CTPT03 computes the residual for the solution to a scaled triangular


 system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,


 when the triangular matrix A is stored in packed format.  Here A**T


 denotes the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, 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 = s*b     (No transpose)


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


          = 'C':  A**H *x = s*b  (Conjugate 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.

NRHS

          NRHS is INTEGER


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


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

AP

          AP is COMPLEX array, dimension (N*(N+1)/2)


          The upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

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 COMPLEX 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 COMPLEX 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 COMPLEX 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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