dlansb.c

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/* dlansb.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 dlansb_(char *norm, char *uplo, integer *n, integer *k, doublereal 
        *ab, integer *ldab, doublereal *work)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
    doublereal ret_val, d__1, d__2, d__3;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__, j, l;
    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 */
/*  ======= */

/*  DLANSB  returns the value of the one norm,  or the Frobenius norm, or */
/*  the  infinity norm,  or the element of  largest absolute value  of an */
/*  n by n symmetric band matrix A,  with k super-diagonals. */

/*  Description */
/*  =========== */

/*  DLANSB returns the value */

/*     DLANSB = ( 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 DLANSB as described */
/*          above. */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          band matrix A is supplied. */
/*          = 'U':  Upper triangular part is supplied */
/*          = 'L':  Lower triangular part is supplied */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0.  When N = 0, DLANSB is */
/*          set to zero. */

/*  K       (input) INTEGER */
/*          The number of super-diagonals or sub-diagonals of the */
/*          band matrix A.  K >= 0. */

/*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          The upper or lower triangle of the symmetric band matrix A, */
/*          stored in the first K+1 rows of AB.  The j-th column of A is */
/*          stored in the j-th column of the array AB as follows: */
/*          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k). */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= K+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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_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) {
/* Computing MAX */
                i__2 = *k + 2 - j;
                i__3 = *k + 1;
                for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
                    d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1], abs(
                            d__1));
                    value = max(d__2,d__3);
/* L10: */
                }
/* L20: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                i__2 = *n + 1 - j, i__4 = *k + 1;
                i__3 = min(i__2,i__4);
                for (i__ = 1; i__ <= i__3; ++i__) {
/* Computing MAX */
                    d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_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.;
                l = *k + 1 - j;
/* Computing MAX */
                i__3 = 1, i__2 = j - *k;
                i__4 = j - 1;
                for (i__ = max(i__3,i__2); i__ <= i__4; ++i__) {
                    absa = (d__1 = ab[l + i__ + j * ab_dim1], abs(d__1));
                    sum += absa;
                    work[i__] += absa;
/* L50: */
                }
                work[j] = sum + (d__1 = ab[*k + 1 + j * ab_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 = ab[j * ab_dim1 + 1], abs(d__1));
                l = 1 - j;
/* Computing MIN */
                i__3 = *n, i__2 = j + *k;
                i__4 = min(i__3,i__2);
                for (i__ = j + 1; i__ <= i__4; ++i__) {
                    absa = (d__1 = ab[l + i__ + j * ab_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 (*k > 0) {
            if (lsame_(uplo, "U")) {
                i__1 = *n;
                for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
                    i__3 = j - 1;
                    i__4 = min(i__3,*k);
/* Computing MAX */
                    i__2 = *k + 2 - j;
                    dlassq_(&i__4, &ab[max(i__2, 1)+ j * ab_dim1], &c__1, &
                            scale, &sum);
/* L110: */
                }
                l = *k + 1;
            } else {
                i__1 = *n - 1;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__3 = *n - j;
                    i__4 = min(i__3,*k);
                    dlassq_(&i__4, &ab[j * ab_dim1 + 2], &c__1, &scale, &sum);
/* L120: */
                }
                l = 1;
            }
            sum *= 2;
        } else {
            l = 1;
        }
        dlassq_(n, &ab[l + ab_dim1], ldab, &scale, &sum);
        value = scale * sqrt(sum);
    }

    ret_val = value;
    return ret_val;

/*     End of DLANSB */

} /* dlansb_ */