/* -- translated by f2c (version 20100827).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
/* > \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele
ment of largest absolute value of a real symmetric matrix.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLANSY + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansy.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
CHARACTER NORM, UPLO
INTEGER LDA, N
DOUBLE PRECISION A( LDA, * ), WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLANSY returns the value of the one norm, or the Frobenius norm, or
> the infinity norm, or the element of largest absolute value of a
> real symmetric matrix A.
> \endverbatim
>
> \return DLANSY
> \verbatim
>
> DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
> (
> ( norm1(A), NORM = '1', 'O' or 'o'
> (
> ( normI(A), NORM = 'I' or 'i'
> (
> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
>
> where norm1 denotes the one norm of a matrix (maximum column sum),
> normI denotes the infinity norm of a matrix (maximum row sum) and
> normF denotes the Frobenius norm of a matrix (square root of sum of
> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
> \endverbatim
Arguments:
==========
> \param[in] NORM
> \verbatim
> NORM is CHARACTER*1
> Specifies the value to be returned in DLANSY as described
> above.
> \endverbatim
>
> \param[in] UPLO
> \verbatim
> UPLO is CHARACTER*1
> Specifies whether the upper or lower triangular part of the
> symmetric matrix A is to be referenced.
> = 'U': Upper triangular part of A is referenced
> = 'L': Lower triangular part of A is referenced
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0. When N = 0, DLANSY is
> set to zero.
> \endverbatim
>
> \param[in] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,N)
> The symmetric matrix A. If UPLO = 'U', the leading n by n
> upper triangular part of A contains the upper triangular part
> of the matrix A, and the strictly lower triangular part of A
> is not referenced. If UPLO = 'L', the leading n by n lower
> triangular part of A contains the lower triangular part of
> the matrix A, and the strictly upper triangular part of A is
> not referenced.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(N,1).
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
> WORK is not referenced.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleSYauxiliary
===================================================================== */
doublereal igraphdlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer
*lda, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal ret_val, d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j;
doublereal sum, absa, scale;
extern logical igraphlsame_(char *, char *);
doublereal value = 0.;
extern logical igraphdisnan_(doublereal *);
extern /* Subroutine */ int igraphdlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (igraphlsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (igraphlsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
sum = (d__1 = a[i__ + j * a_dim1], abs(d__1));
if (value < sum || igraphdisnan_(&sum)) {
value = sum;
}
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
sum = (d__1 = a[i__ + j * a_dim1], abs(d__1));
if (value < sum || igraphdisnan_(&sum)) {
value = sum;
}
/* L30: */
}
/* L40: */
}
}
} else if (igraphlsame_(norm, "I") || igraphlsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is symmetric). */
value = 0.;
if (igraphlsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
absa = (d__1 = a[i__ + j * a_dim1], abs(d__1));
sum += absa;
work[i__] += absa;
/* L50: */
}
work[j] = sum + (d__1 = a[j + j * a_dim1], abs(d__1));
/* L60: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
sum = work[i__];
if (value < sum || igraphdisnan_(&sum)) {
value = sum;
}
/* L70: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L80: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = work[j] + (d__1 = a[j + j * a_dim1], abs(d__1));
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = (d__1 = a[i__ + j * a_dim1], abs(d__1));
sum += absa;
work[i__] += absa;
/* L90: */
}
if (value < sum || igraphdisnan_(&sum)) {
value = sum;
}
/* L100: */
}
}
} else if (igraphlsame_(norm, "F") || igraphlsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (igraphlsame_(uplo, "U")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
igraphdlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L110: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
igraphdlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
/* L120: */
}
}
sum *= 2;
i__1 = *lda + 1;
igraphdlassq_(n, &a[a_offset], &i__1, &scale, &sum);
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANSY */
} /* igraphdlansy_ */