SLATRS3 solves one of the triangular systems


    A * X = B * diag(scale)  or  A**T * X = B * diag(scale)


 with scaling to prevent overflow.  Here A is an upper or lower


 triangular matrix, A**T denotes the transpose of A. X and B are


 n by nrhs matrices and scale is an nrhs element vector of scaling


 factors. A scaling factor scale(j) is usually less than or equal


 to 1, chosen such that X(:,j) is less than the overflow threshold.


 If the matrix A is singular (A(j,j) = 0 for some j), then


 a non-trivial solution to A*X = 0 is returned. If the system is


 so badly scaled that the solution cannot be represented as


 (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.


 This is a BLAS-3 version of LATRS for solving several right


 hand sides simultaneously.

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':  Solve A * x = s*b  (No transpose)


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


          = 'C':  Solve A**T* x = s*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

NORMIN

          NORMIN is CHARACTER*1


          Specifies whether CNORM has been set or not.


          = 'Y':  CNORM contains the column norms on entry


          = 'N':  CNORM is not set on entry.  On exit, the norms will


                  be computed and stored in CNORM.

N

          N is INTEGER


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

NRHS

          NRHS is INTEGER


          The number of columns of X.  NRHS >= 0.

A

          A is REAL array, dimension (LDA,N)


          The triangular matrix A.  If UPLO = 'U', the leading n by n


          upper triangular part of the array A contains the upper


          triangular matrix, and the strictly lower triangular part of


          A is not referenced.  If UPLO = 'L', the leading n by n lower


          triangular part of the array A contains the lower triangular


          matrix, and the strictly upper triangular part of A is not


          referenced.  If DIAG = 'U', the diagonal elements of A are


          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max (1,N).

X

          X is REAL array, dimension (LDX,NRHS)


          On entry, the right hand side B of the triangular system.


          On exit, X is overwritten by the solution matrix X.

LDX

          LDX is INTEGER


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

SCALE

          SCALE is REAL array, dimension (NRHS)


          The scaling factor s(k) is for the triangular system


          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).


          If SCALE = 0, the matrix A is singular or badly scaled.


          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)


          that is an exact or approximate solution to A*x(:,k) = 0


          is returned. If the system so badly scaled that solution


          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0


          is returned.

CNORM

          CNORM is REAL array, dimension (N)


          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)


          contains the norm of the off-diagonal part of the j-th column


          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal


          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)


          must be greater than or equal to the 1-norm.


          If NORMIN = 'N', CNORM is an output argument and CNORM(j)


          returns the 1-norm of the offdiagonal part of the j-th column


          of A.

WORK

          WORK is REAL array, dimension (LWORK).


          On exit, if INFO = 0, WORK(1) returns the optimal size of


          WORK.

LWORK LWORK is INTEGER LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where NBA = (N + NB - 1)/NB and NB is the optimal block size.

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -k, the k-th argument had an illegal value

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