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---
:name: zla_gbrcond_x
:md5sum: 82710e74ceba14453857104a1281a7b2
:category: :function
:type: doublereal
:arguments:
- trans:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- afb:
:type: doublecomplex
:intent: input
:dims:
- ldafb
- n
- ldafb:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: input
:dims:
- n
- x:
:type: doublecomplex
:intent: input
:dims:
- n
- info:
:type: integer
:intent: output
- work:
:type: doublecomplex
:intent: input
:dims:
- 2*n
- rwork:
:type: doublereal
:intent: input
:dims:
- n
:substitutions: {}
:fortran_help: " DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLA_GBRCOND_X Computes the infinity norm condition number of\n\
* op(A) * diag(X) where X is a COMPLEX*16 vector.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* Specifies the form of the system of equations:\n\
* = 'N': A * X = B (No transpose)\n\
* = 'T': A**T * X = B (Transpose)\n\
* = 'C': A**H * X = B (Conjugate Transpose = Transpose)\n\
*\n\
* N (input) INTEGER\n\
* The number of linear equations, i.e., the order of the\n\
* matrix A. N >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals within the band of A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals within the band of A. KU >= 0.\n\
*\n\
* AB (input) COMPLEX*16 array, dimension (LDAB,N)\n\
* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KL+KU+1.\n\
*\n\
* AFB (input) COMPLEX*16 array, dimension (LDAFB,N)\n\
* Details of the LU factorization of the band matrix A, as\n\
* computed by ZGBTRF. U is stored as an upper triangular\n\
* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,\n\
* and the multipliers used during the factorization are stored\n\
* in rows KL+KU+2 to 2*KL+KU+1.\n\
*\n\
* LDAFB (input) INTEGER\n\
* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N)\n\
* The pivot indices from the factorization A = P*L*U\n\
* as computed by ZGBTRF; row i of the matrix was interchanged\n\
* with row IPIV(i).\n\
*\n\
* X (input) COMPLEX*16 array, dimension (N)\n\
* The vector X in the formula op(A) * diag(X).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: Successful exit.\n\
* i > 0: The ith argument is invalid.\n\
*\n\
* WORK (input) COMPLEX*16 array, dimension (2*N).\n\
* Workspace.\n\
*\n\
* RWORK (input) DOUBLE PRECISION array, dimension (N).\n\
* Workspace.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL NOTRANS\n INTEGER KASE, I, J\n DOUBLE PRECISION AINVNM, ANORM, TMP\n COMPLEX*16 ZDUM\n\
* ..\n\
* .. Local Arrays ..\n INTEGER ISAVE( 3 )\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL ZLACN2, ZGBTRS, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC ABS, MAX\n\
* ..\n\
* .. Statement Functions ..\n DOUBLE PRECISION CABS1\n\
* ..\n\
* .. Statement Function Definitions ..\n CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )\n\
* ..\n"
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