dlantp.c

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/* dlantp.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 dlantp_(char *norm, char *uplo, char *diag, 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, scale;
    logical udiag;
    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 */
/*  ======= */

/*  DLANTP  returns the value of the one norm,  or the Frobenius norm, or */
/*  the  infinity norm,  or the  element of  largest absolute value  of a */
/*  triangular matrix A, supplied in packed form. */

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

/*  DLANTP returns the value */

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

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

/*  DIAG    (input) CHARACTER*1 */
/*          Specifies whether or not the matrix A is unit triangular. */
/*          = 'N':  Non-unit triangular */
/*          = 'U':  Unit triangular */

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

/*  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/*          The upper or lower triangular 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. */
/*          Note that when DIAG = 'U', the elements of the array AP */
/*          corresponding to the diagonal elements of the matrix A are */
/*          not referenced, but are assumed to be one. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/*          where LWORK >= N when NORM = 'I'; 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))). */

        k = 1;
        if (lsame_(diag, "U")) {
            value = 1.;
            if (lsame_(uplo, "U")) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = k + j - 2;
                    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 {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = k + *n - j;
                    for (i__ = k + 1; 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 {
            value = 0.;
            if (lsame_(uplo, "U")) {
                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);
/* L50: */
                    }
                    k += j;
/* L60: */
                }
            } else {
                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);
/* L70: */
                    }
                    k = k + *n - j + 1;
/* L80: */
                }
            }
        }
    } else if (lsame_(norm, "O") || *(unsigned char *)
            norm == '1') {

/*        Find norm1(A). */

        value = 0.;
        k = 1;
        udiag = lsame_(diag, "U");
        if (lsame_(uplo, "U")) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (udiag) {
                    sum = 1.;
                    i__2 = k + j - 2;
                    for (i__ = k; i__ <= i__2; ++i__) {
                        sum += (d__1 = ap[i__], abs(d__1));
/* L90: */
                    }
                } else {
                    sum = 0.;
                    i__2 = k + j - 1;
                    for (i__ = k; i__ <= i__2; ++i__) {
                        sum += (d__1 = ap[i__], abs(d__1));
/* L100: */
                    }
                }
                k += j;
                value = max(value,sum);
/* L110: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (udiag) {
                    sum = 1.;
                    i__2 = k + *n - j;
                    for (i__ = k + 1; i__ <= i__2; ++i__) {
                        sum += (d__1 = ap[i__], abs(d__1));
/* L120: */
                    }
                } else {
                    sum = 0.;
                    i__2 = k + *n - j;
                    for (i__ = k; i__ <= i__2; ++i__) {
                        sum += (d__1 = ap[i__], abs(d__1));
/* L130: */
                    }
                }
                k = k + *n - j + 1;
                value = max(value,sum);
/* L140: */
            }
        }
    } else if (lsame_(norm, "I")) {

/*        Find normI(A). */

        k = 1;
        if (lsame_(uplo, "U")) {
            if (lsame_(diag, "U")) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 1.;
/* L150: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = j - 1;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        work[i__] += (d__1 = ap[k], abs(d__1));
                        ++k;
/* L160: */
                    }
                    ++k;
/* L170: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 0.;
/* L180: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = j;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        work[i__] += (d__1 = ap[k], abs(d__1));
                        ++k;
/* L190: */
                    }
/* L200: */
                }
            }
        } else {
            if (lsame_(diag, "U")) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 1.;
/* L210: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    ++k;
                    i__2 = *n;
                    for (i__ = j + 1; i__ <= i__2; ++i__) {
                        work[i__] += (d__1 = ap[k], abs(d__1));
                        ++k;
/* L220: */
                    }
/* L230: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 0.;
/* L240: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = *n;
                    for (i__ = j; i__ <= i__2; ++i__) {
                        work[i__] += (d__1 = ap[k], abs(d__1));
                        ++k;
/* L250: */
                    }
/* L260: */
                }
            }
        }
        value = 0.;
        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);
/* L270: */
        }
    } else if (lsame_(norm, "F") || lsame_(norm, "E")) {

/*        Find normF(A). */

        if (lsame_(uplo, "U")) {
            if (lsame_(diag, "U")) {
                scale = 1.;
                sum = (doublereal) (*n);
                k = 2;
                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;
/* L280: */
                }
            } else {
                scale = 0.;
                sum = 1.;
                k = 1;
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    dlassq_(&j, &ap[k], &c__1, &scale, &sum);
                    k += j;
/* L290: */
                }
            }
        } else {
            if (lsame_(diag, "U")) {
                scale = 1.;
                sum = (doublereal) (*n);
                k = 2;
                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;
/* L300: */
                }
            } else {
                scale = 0.;
                sum = 1.;
                k = 1;
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = *n - j + 1;
                    dlassq_(&i__2, &ap[k], &c__1, &scale, &sum);
                    k = k + *n - j + 1;
/* L310: */
                }
            }
        }
        value = scale * sqrt(sum);
    }

    ret_val = value;
    return ret_val;

/*     End of DLANTP */

} /* dlantp_ */