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/* dlansp.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
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
doublereal dlansp_(char *norm, char *uplo, integer *n, doublereal *ap,
doublereal *work)
{
/* System generated locals */
integer i__1, i__2;
doublereal ret_val, d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal sum, absa, scale;
extern logical lsame_(char *, char *);
doublereal value;
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLANSP 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, supplied in packed form. */
/* Description */
/* =========== */
/* DLANSP returns the value */
/* DLANSP = ( 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 DLANSP as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* symmetric matrix A is supplied. */
/* = 'U': Upper triangular part of A is supplied */
/* = 'L': Lower triangular part of A is supplied */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. When N = 0, DLANSP is */
/* set to zero. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The upper or lower triangle of the symmetric matrix A, packed */
/* columnwise in a linear array. The j-th column of A is stored */
/* in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* 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 */
--work;
--ap;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (lsame_(uplo, "U")) {
k = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = k + j - 1;
for (i__ = k; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ap[i__], abs(d__1));
value = max(d__2,d__3);
/* L10: */
}
k += j;
/* L20: */
}
} else {
k = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = k + *n - j;
for (i__ = k; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ap[i__], abs(d__1));
value = max(d__2,d__3);
/* L30: */
}
k = k + *n - j + 1;
/* L40: */
}
}
} else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is symmetric). */
value = 0.;
k = 1;
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 = ap[k], abs(d__1));
sum += absa;
work[i__] += absa;
++k;
/* L50: */
}
work[j] = sum + (d__1 = ap[k], abs(d__1));
++k;
/* 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 = ap[k], abs(d__1));
++k;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = (d__1 = ap[k], abs(d__1));
sum += absa;
work[i__] += absa;
++k;
/* L90: */
}
value = max(value,sum);
/* L100: */
}
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
k = 2;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
dlassq_(&i__2, &ap[k], &c__1, &scale, &sum);
k += j;
/* L110: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
dlassq_(&i__2, &ap[k], &c__1, &scale, &sum);
k = k + *n - j + 1;
/* L120: */
}
}
sum *= 2;
k = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (ap[k] != 0.) {
absa = (d__1 = ap[k], abs(d__1));
if (scale < absa) {
/* Computing 2nd power */
d__1 = scale / absa;
sum = sum * (d__1 * d__1) + 1.;
scale = absa;
} else {
/* Computing 2nd power */
d__1 = absa / scale;
sum += d__1 * d__1;
}
}
if (lsame_(uplo, "U")) {
k = k + i__ + 1;
} else {
k = k + *n - i__ + 1;
}
/* L130: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANSP */
} /* dlansp_ */
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