349 lines
11 KiB
C++
349 lines
11 KiB
C++
/* fortran/zlanhe.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* > \brief \b ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele
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ment of largest absolute value of a complex Hermitian matrix. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download ZLANHE + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhe.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhe.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhe.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER NORM, UPLO */
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/* INTEGER LDA, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION WORK( * ) */
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/* COMPLEX*16 A( LDA, * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > ZLANHE returns the value of the one norm, or the Frobenius norm, or */
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/* > the infinity norm, or the element of largest absolute value of a */
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/* > complex hermitian matrix A. */
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/* > \endverbatim */
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/* > */
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/* > \return ZLANHE */
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/* > \verbatim */
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/* > */
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/* > ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
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/* > ( */
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/* > ( norm1(A), NORM = '1', 'O' or 'o' */
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/* > ( */
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/* > ( normI(A), NORM = 'I' or 'i' */
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/* > ( */
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/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
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/* > */
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/* > where norm1 denotes the one norm of a matrix (maximum column sum), */
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/* > normI denotes the infinity norm of a matrix (maximum row sum) and */
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/* > normF denotes the Frobenius norm of a matrix (square root of sum of */
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/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] NORM */
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/* > \verbatim */
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/* > NORM is CHARACTER*1 */
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/* > Specifies the value to be returned in ZLANHE as described */
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/* > above. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > Specifies whether the upper or lower triangular part of the */
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/* > hermitian matrix A is to be referenced. */
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/* > = 'U': Upper triangular part of A is referenced */
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/* > = 'L': Lower triangular part of A is referenced */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix A. N >= 0. When N = 0, ZLANHE is */
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/* > set to zero. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] A */
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/* > \verbatim */
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/* > A is COMPLEX*16 array, dimension (LDA,N) */
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/* > The hermitian matrix A. If UPLO = 'U', the leading n by n */
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/* > upper triangular part of A contains the upper triangular part */
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/* > of the matrix A, and the strictly lower triangular part of A */
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/* > is not referenced. If UPLO = 'L', the leading n by n lower */
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/* > triangular part of A contains the lower triangular part of */
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/* > the matrix A, and the strictly upper triangular part of A is */
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/* > not referenced. Note that the imaginary parts of the diagonal */
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/* > elements need not be set and are assumed to be zero. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(N,1). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
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/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */
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/* > WORK is not referenced. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup complex16HEauxiliary */
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/* ===================================================================== */
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doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a,
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integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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doublereal ret_val, d__1;
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/* Builtin functions */
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double z_abs(doublecomplex *), sqrt(doublereal);
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/* Local variables */
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integer i__, j;
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doublereal sum, absa, scale;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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doublereal value;
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extern logical disnan_(doublereal *);
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extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
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doublereal *, doublereal *);
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/* -- LAPACK auxiliary routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--work;
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/* Function Body */
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if (*n == 0) {
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value = 0.;
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} else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) {
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/* Find max(abs(A(i,j))). */
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value = 0.;
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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sum = z_abs(&a[i__ + j * a_dim1]);
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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/* L10: */
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}
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i__2 = j + j * a_dim1;
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sum = (d__1 = a[i__2].r, abs(d__1));
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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/* L20: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j + j * a_dim1;
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sum = (d__1 = a[i__2].r, abs(d__1));
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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i__2 = *n;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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sum = z_abs(&a[i__ + j * a_dim1]);
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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/* L30: */
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}
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/* L40: */
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}
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}
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} else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", (
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ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') {
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/* Find normI(A) ( = norm1(A), since A is hermitian). */
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value = 0.;
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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sum = 0.;
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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absa = z_abs(&a[i__ + j * a_dim1]);
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sum += absa;
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work[i__] += absa;
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/* L50: */
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}
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i__2 = j + j * a_dim1;
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work[j] = sum + (d__1 = a[i__2].r, abs(d__1));
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/* L60: */
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}
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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sum = work[i__];
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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/* L70: */
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}
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} else {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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work[i__] = 0.;
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/* L80: */
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j + j * a_dim1;
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sum = work[j] + (d__1 = a[i__2].r, abs(d__1));
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i__2 = *n;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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absa = z_abs(&a[i__ + j * a_dim1]);
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sum += absa;
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work[i__] += absa;
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/* L90: */
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}
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if (value < sum || disnan_(&sum)) {
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value = sum;
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}
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/* L100: */
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}
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}
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} else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", (
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ftnlen)1, (ftnlen)1)) {
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/* Find normF(A). */
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scale = 0.;
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sum = 1.;
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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i__2 = j - 1;
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zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
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/* L110: */
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}
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} else {
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n - j;
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zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
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/* L120: */
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}
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}
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sum *= 2;
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = i__ + i__ * a_dim1;
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if (a[i__2].r != 0.) {
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i__2 = i__ + i__ * a_dim1;
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absa = (d__1 = a[i__2].r, abs(d__1));
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if (scale < absa) {
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/* Computing 2nd power */
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d__1 = scale / absa;
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sum = sum * (d__1 * d__1) + 1.;
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scale = absa;
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} else {
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/* Computing 2nd power */
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d__1 = absa / scale;
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sum += d__1 * d__1;
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}
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}
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/* L130: */
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}
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value = scale * sqrt(sum);
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}
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ret_val = value;
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return ret_val;
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/* End of ZLANHE */
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} /* zlanhe_ */
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#ifdef __cplusplus
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}
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#endif
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