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---
:name: cla_lin_berr
:md5sum: 6b8eeecaaa46d0e73b99de53d6d4b511
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- nz:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- res:
:type: doublereal
:intent: input
:dims:
- n
- nrhs
- ayb:
:type: doublereal
:intent: input
:dims:
- n
- nrhs
- berr:
:type: complex
:intent: output
:dims:
- nrhs
:substitutions: {}
:fortran_help: " SUBROUTINE CLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLA_LIN_BERR computes componentwise relative backward error from\n\
* the formula\n\
* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )\n\
* where abs(Z) is the componentwise absolute value of the matrix\n\
* or vector Z.\n\
*\n\n\
* N (input) INTEGER\n\
* The number of linear equations, i.e., the order of the\n\
* matrix A. N >= 0.\n\
*\n\
* NZ (input) INTEGER\n\
* We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to\n\
* guard against spuriously zero residuals. Default value is N.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrices AYB, RES, and BERR. NRHS >= 0.\n\
*\n\
* RES (input) DOUBLE PRECISION array, dimension (N,NRHS)\n\
* The residual matrix, i.e., the matrix R in the relative backward\n\
* error formula above.\n\
*\n\
* AYB (input) DOUBLE PRECISION array, dimension (N, NRHS)\n\
* The denominator in the relative backward error formula above, i.e.,\n\
* the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B\n\
* are from iterative refinement (see cla_gerfsx_extended.f).\n\
* \n\
* BERR (output) COMPLEX array, dimension (NRHS)\n\
* The componentwise relative backward error from the formula above.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n REAL TMP\n INTEGER I, J\n COMPLEX CDUM\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC ABS, REAL, AIMAG, MAX\n\
* ..\n\
* .. External Functions ..\n EXTERNAL SLAMCH\n REAL SLAMCH\n REAL SAFE1\n\
* ..\n\
* .. Statement Functions ..\n COMPLEX CABS1\n\
* ..\n\
* .. Statement Function Definitions ..\n CABS1( CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )\n\
* ..\n"
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