dlansp.c

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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_ */