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/* ../../../dependencies/lapack/src/zlanhe.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"
/* Table of constant values */
static integer c__1 = 1;
doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a,
integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal ret_val, d__1, d__2, d__3;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublereal sum, absa, scale;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLANHE returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of a */
/* complex hermitian matrix A. */
/* Description */
/* =========== */
/* ZLANHE returns the value */
/* ZLANHE = ( 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 matrix norm. */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies the value to be returned in ZLANHE as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* hermitian 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, ZLANHE is */
/* set to zero. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The hermitian 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. Note that the imaginary parts of the diagonal */
/* elements need not be set and are assumed to be zero. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(N,1). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), */
/* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */
/* WORK is not referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. 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", (ftnlen)1, (ftnlen)1)) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* Computing MAX */
i__2 = j + j * a_dim1;
d__2 = value, d__3 = (d__1 = a[i__2].r, abs(d__1));
value = max(d__2,d__3);
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j + j * a_dim1;
d__2 = value, d__3 = (d__1 = a[i__2].r, abs(d__1));
value = max(d__2,d__3);
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L30: */
}
/* L40: */
}
}
} else if (lsame_(norm, "I", (ftnlen)1, (ftnlen)1) || lsame_(norm, "O", (
ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is hermitian). */
value = 0.;
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L50: */
}
i__2 = j + j * a_dim1;
work[j] = sum + (d__1 = a[i__2].r, 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) {
i__2 = j + j * a_dim1;
sum = work[j] + (d__1 = a[i__2].r, abs(d__1));
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L90: */
}
value = max(value,sum);
/* L100: */
}
}
} else if (lsame_(norm, "F", (ftnlen)1, (ftnlen)1) || lsame_(norm, "E", (
ftnlen)1, (ftnlen)1)) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
zlassq_(&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;
zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
/* L120: */
}
}
sum *= 2;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
if (a[i__2].r != 0.) {
i__2 = i__ + i__ * a_dim1;
absa = (d__1 = a[i__2].r, 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;
}
}
/* L130: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANHE */
} /* zlanhe_ */
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