LA_GERCOND - 5.2 English - 68552

LA_GERCOND estimates the Skeel condition number for a general matrix.

Purpose:

 LA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
 where op2 is determined by CMODE as follows
 CMODE =  1    op2(C) = C
 CMODE =  0    op2(C) = I
 CMODE = -1    op2(C) = inv(C)
 The Skeel condition number cond(A) = norminf(|inv(A)||A|)
 is computed by computing scaling factors R such that
 diag(R)*A*op2(C) is row equilibrated and computing the standard
 infinity-norm condition number.

Parameters:

• TRANS – [in]

  TRANS is CHARACTER*1

  Specifies the form of the system of equations:

  = ‘N’: A * X = B (No transpose)

  = ‘T’: A**T * X = B (Transpose)

  = ‘C’: A**H * X = B (Conjugate Transpose = Transpose)

• N – [in]

  N is INTEGER

  The number of linear equations, i.e., the order of the matrix A. N >= 0.

• A – [in]

  A is REAL array, dimension (LDA,N)

  On entry, the N-by-N matrix A.

• LDA – [in]

  LDA is INTEGER

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

• AF – [in]

  AF is REAL array, dimension (LDAF,N)

  The factors L and U from the factorization A = P*L*U as computed by SGETRF.

• LDAF – [in]

  LDAF is INTEGER

  The leading dimension of the array AF. LDAF >= fla_max(1,N).

• IPIV – [in]

  IPIV is INTEGER array, dimension (N)

  The pivot indices from the factorization A = P*L*U as computed by SGETRF; row i of the matrix was interchanged with row IPIV(i).

• CMODE – [in]

  CMODE is INTEGER

  Determines op2(C) in the formula op(A) * op2(C) as follows:

  CMODE = 1 op2(C) = C

  CMODE = 0 op2(C) = I

  CMODE = -1 op2(C) = inv(C)

• C – [in]

  C is REAL array, dimension (N)

  The vector C in the formula op(A) * op2(C).

• INFO – [out]

  INFO is INTEGER

  = 0: Successful exit.

  i > 0: The ith argument is invalid.

• WORK – [out]

  WORK is REAL array, dimension (3*N).

  Workspace.

• IWORK – [out]

  IWORK is INTEGER array, dimension (N).

  Workspace.2