hypre/lapack/dlansy.c

#include "hypre_lapack.h"
#include "f2c.h"

doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer 
	*lda, doublereal *work)
{
/*  -- 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   


    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  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 (LWORK),   
            where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,   
            WORK is not referenced.   

   =====================================================================   


       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* 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 */
    static doublereal absa;
    static integer i__, j;
    static doublereal scale;
    extern logical lsame_(char *, char *);
    static doublereal value;
    extern /* Subroutine */ HYPRE_Int dlassq_(integer *, doublereal *, integer *, 
	    doublereal *, doublereal *);
    static doublereal sum;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    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_ref(i__, j), 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_ref(i__, j), 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_ref(i__, j), abs(d__1));
		    sum += absa;
		    work[i__] += absa;
/* L50: */
		}
		work[j] = sum + (d__1 = a_ref(j, j), 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_ref(j, j), abs(d__1));
		i__2 = *n;
		for (i__ = j + 1; i__ <= i__2; ++i__) {
		    absa = (d__1 = a_ref(i__, j), 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_ref(1, j), &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_ref(j + 1, j), &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_ */

#undef a_ref