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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_ */
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