Add graph references
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Abdelrahman Said
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/* -- translated by f2c (version 20240504).
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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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#include "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 DLANSY 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 real symmetric 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 DLANSY + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.
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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/dlansy.
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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/dlansy.
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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 DLANSY( NORM, UPLO, N, A, LDA, WORK )
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CHARACTER NORM, UPLO
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INTEGER LDA, N
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DOUBLE PRECISION A( LDA, * ), WORK( * )
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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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> DLANSY 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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> real symmetric matrix A.
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> \endverbatim
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>
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> \return DLANSY
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> \verbatim
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>
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> DLANSY = ( 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 DLANSY 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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> symmetric 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, DLANSY 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 DOUBLE PRECISION array, dimension (LDA,N)
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> The symmetric 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.
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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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> \date September 2012
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> \ingroup doubleSYauxiliary
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===================================================================== */
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doublereal igraphdlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer
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*lda, doublereal *work)
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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 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 igraphlsame_(char *, char *);
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doublereal value;
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extern logical igraphdisnan_(doublereal *);
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extern /* Subroutine */ int igraphdlassq_(integer *, doublereal *, integer *,
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doublereal *, doublereal *);
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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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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September 2012
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=====================================================================
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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 (igraphlsame_(norm, "M")) {
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/* Find max(abs(A(i,j))). */
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value = 0.;
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if (igraphlsame_(uplo, "U")) {
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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;
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for (i__ = 1; i__ <= i__2; ++i__) {
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sum = (d__1 = a[i__ + j * a_dim1], abs(d__1));
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if (value < sum || igraphdisnan_(&sum)) {
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value = sum;
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}
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/* L10: */
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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 = *n;
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for (i__ = j; i__ <= i__2; ++i__) {
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sum = (d__1 = a[i__ + j * a_dim1], abs(d__1));
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if (value < sum || igraphdisnan_(&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 (igraphlsame_(norm, "I") || igraphlsame_(norm, "O") || *(unsigned char *)norm == '1') {
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/* Find normI(A) ( = norm1(A), since A is symmetric). */
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value = 0.;
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if (igraphlsame_(uplo, "U")) {
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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 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
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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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work[j] = sum + (d__1 = a[j + j * a_dim1], 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 || igraphdisnan_(&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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sum = work[j] + (d__1 = a[j + j * a_dim1], 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 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
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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 || igraphdisnan_(&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 (igraphlsame_(norm, "F") || igraphlsame_(norm, "E")) {
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/* Find normF(A). */
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scale = 0.;
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sum = 1.;
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if (igraphlsame_(uplo, "U")) {
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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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igraphdlassq_(&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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igraphdlassq_(&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 = *lda + 1;
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igraphdlassq_(n, &a[a_offset], &i__1, &scale, &sum);
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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 DLANSY */
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} /* igraphdlansy_ */
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