2010-07-16 20:54:53 +08:00
|
|
|
/* dlansy.f -- translated by f2c (version 20061008).
|
|
|
|
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
|
|
|
|
*/
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
#include "clapack.h"
|
|
|
|
|
2010-07-16 20:54:53 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
/* Table of constant values */
|
|
|
|
|
|
|
|
static integer c__1 = 1;
|
|
|
|
|
|
|
|
doublereal dlansy_(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, d__2, d__3;
|
|
|
|
|
|
|
|
/* Builtin functions */
|
|
|
|
double sqrt(doublereal);
|
|
|
|
|
|
|
|
/* Local variables */
|
|
|
|
integer i__, j;
|
|
|
|
doublereal sum, absa, scale;
|
|
|
|
extern logical lsame_(char *, char *);
|
|
|
|
doublereal value;
|
|
|
|
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
|
|
|
|
doublereal *, doublereal *);
|
|
|
|
|
|
|
|
|
2010-07-16 20:54:53 +08:00
|
|
|
/* -- LAPACK auxiliary routine (version 3.2) -- */
|
2010-05-12 01:44:00 +08:00
|
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
|
|
|
/* November 2006 */
|
|
|
|
|
|
|
|
/* .. Scalar Arguments .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. Array Arguments .. */
|
|
|
|
/* .. */
|
|
|
|
|
|
|
|
/* Purpose */
|
|
|
|
/* ======= */
|
|
|
|
|
|
|
|
/* 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. */
|
|
|
|
|
|
|
|
/* Description */
|
|
|
|
/* =========== */
|
|
|
|
|
|
|
|
/* DLANSY returns the value */
|
|
|
|
|
|
|
|
/* 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. */
|
|
|
|
|
|
|
|
/* Arguments */
|
|
|
|
/* ========= */
|
|
|
|
|
|
|
|
/* NORM (input) CHARACTER*1 */
|
|
|
|
/* Specifies the value to be returned in DLANSY as described */
|
|
|
|
/* above. */
|
|
|
|
|
|
|
|
/* UPLO (input) 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 */
|
|
|
|
|
|
|
|
/* N (input) INTEGER */
|
|
|
|
/* The order of the matrix A. N >= 0. When N = 0, DLANSY is */
|
|
|
|
/* set to zero. */
|
|
|
|
|
|
|
|
/* A (input) 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. */
|
|
|
|
|
|
|
|
/* LDA (input) INTEGER */
|
|
|
|
/* The leading dimension of the array A. LDA >= max(N,1). */
|
|
|
|
|
|
|
|
/* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
|
|
|
|
/* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */
|
|
|
|
/* WORK is not referenced. */
|
|
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
|
|
/* .. Parameters .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. Local Scalars .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. External Subroutines .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. External Functions .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. Intrinsic Functions .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. Executable Statements .. */
|
|
|
|
|
|
|
|
/* Parameter adjustments */
|
|
|
|
a_dim1 = *lda;
|
|
|
|
a_offset = 1 + a_dim1;
|
|
|
|
a -= a_offset;
|
|
|
|
--work;
|
|
|
|
|
|
|
|
/* Function Body */
|
|
|
|
if (*n == 0) {
|
|
|
|
value = 0.;
|
|
|
|
} else if (lsame_(norm, "M")) {
|
|
|
|
|
|
|
|
/* Find max(abs(A(i,j))). */
|
|
|
|
|
|
|
|
value = 0.;
|
|
|
|
if (lsame_(uplo, "U")) {
|
|
|
|
i__1 = *n;
|
|
|
|
for (j = 1; j <= i__1; ++j) {
|
|
|
|
i__2 = j;
|
|
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
|
|
/* Computing MAX */
|
|
|
|
d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
|
|
|
|
d__1));
|
|
|
|
value = max(d__2,d__3);
|
|
|
|
/* L10: */
|
|
|
|
}
|
|
|
|
/* L20: */
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
i__1 = *n;
|
|
|
|
for (j = 1; j <= i__1; ++j) {
|
|
|
|
i__2 = *n;
|
|
|
|
for (i__ = j; i__ <= i__2; ++i__) {
|
|
|
|
/* Computing MAX */
|
|
|
|
d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
|
|
|
|
d__1));
|
|
|
|
value = max(d__2,d__3);
|
|
|
|
/* L30: */
|
|
|
|
}
|
|
|
|
/* L40: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') {
|
|
|
|
|
|
|
|
/* Find normI(A) ( = norm1(A), since A is symmetric). */
|
|
|
|
|
|
|
|
value = 0.;
|
|
|
|
if (lsame_(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__) {
|
|
|
|
/* Computing MAX */
|
|
|
|
d__1 = value, d__2 = work[i__];
|
|
|
|
value = max(d__1,d__2);
|
|
|
|
/* 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: */
|
|
|
|
}
|
|
|
|
value = max(value,sum);
|
|
|
|
/* L100: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
|
|
|
|
|
|
|
|
/* Find normF(A). */
|
|
|
|
|
|
|
|
scale = 0.;
|
|
|
|
sum = 1.;
|
|
|
|
if (lsame_(uplo, "U")) {
|
|
|
|
i__1 = *n;
|
|
|
|
for (j = 2; j <= i__1; ++j) {
|
|
|
|
i__2 = j - 1;
|
|
|
|
dlassq_(&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;
|
|
|
|
dlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
|
|
|
|
/* L120: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
sum *= 2;
|
|
|
|
i__1 = *lda + 1;
|
|
|
|
dlassq_(n, &a[a_offset], &i__1, &scale, &sum);
|
|
|
|
value = scale * sqrt(sum);
|
|
|
|
}
|
|
|
|
|
|
|
|
ret_val = value;
|
|
|
|
return ret_val;
|
|
|
|
|
|
|
|
/* End of DLANSY */
|
|
|
|
|
|
|
|
} /* dlansy_ */
|