/* slansf.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 slansf_(char *norm, char *transr, char *uplo, integer *n, real *a, real *work) { /* System generated locals */ integer i__1, i__2; real ret_val, r__1, r__2, r__3; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, k, l; real s; integer n1; real aa; integer lda, ifm, noe, ilu; real scale; extern logical lsame_(char *, char *); real value; extern integer isamax_(integer *, real *, integer *); extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *, real *); /* -- LAPACK routine (version 3.2) -- */ /* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */ /* -- November 2008 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SLANSF 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 in RFP format. */ /* Description */ /* =========== */ /* SLANSF returns the value */ /* SLANSF = ( 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 */ /* Specifies the value to be returned in SLANSF as described */ /* above. */ /* TRANSR (input) CHARACTER */ /* Specifies whether the RFP format of A is normal or */ /* transposed format. */ /* = 'N': RFP format is Normal; */ /* = 'T': RFP format is Transpose. */ /* UPLO (input) CHARACTER */ /* On entry, UPLO specifies whether the RFP matrix A came from */ /* an upper or lower triangular matrix as follows: */ /* = 'U': RFP A came from an upper triangular matrix; */ /* = 'L': RFP A came from a lower triangular matrix. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. When N = 0, SLANSF is */ /* set to zero. */ /* A (input) REAL array, dimension ( N*(N+1)/2 ); */ /* On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') */ /* part of the symmetric matrix A stored in RFP format. See the */ /* "Notes" below for more details. */ /* Unchanged on exit. */ /* WORK (workspace) REAL array, dimension (MAX(1,LWORK)), */ /* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */ /* WORK is not referenced. */ /* Notes */ /* ===== */ /* We first consider Rectangular Full Packed (RFP) Format when N is */ /* even. We give an example where N = 6. */ /* AP is Upper AP is Lower */ /* 00 01 02 03 04 05 00 */ /* 11 12 13 14 15 10 11 */ /* 22 23 24 25 20 21 22 */ /* 33 34 35 30 31 32 33 */ /* 44 45 40 41 42 43 44 */ /* 55 50 51 52 53 54 55 */ /* Let TRANSR = 'N'. RFP holds AP as follows: */ /* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */ /* three columns of AP upper. The lower triangle A(4:6,0:2) consists of */ /* the transpose of the first three columns of AP upper. */ /* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */ /* three columns of AP lower. The upper triangle A(0:2,0:2) consists of */ /* the transpose of the last three columns of AP lower. */ /* This covers the case N even and TRANSR = 'N'. */ /* RFP A RFP A */ /* 03 04 05 33 43 53 */ /* 13 14 15 00 44 54 */ /* 23 24 25 10 11 55 */ /* 33 34 35 20 21 22 */ /* 00 44 45 30 31 32 */ /* 01 11 55 40 41 42 */ /* 02 12 22 50 51 52 */ /* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ /* transpose of RFP A above. One therefore gets: */ /* RFP A RFP A */ /* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */ /* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */ /* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */ /* We first consider Rectangular Full Packed (RFP) Format when N is */ /* odd. We give an example where N = 5. */ /* AP is Upper AP is Lower */ /* 00 01 02 03 04 00 */ /* 11 12 13 14 10 11 */ /* 22 23 24 20 21 22 */ /* 33 34 30 31 32 33 */ /* 44 40 41 42 43 44 */ /* Let TRANSR = 'N'. RFP holds AP as follows: */ /* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */ /* three columns of AP upper. The lower triangle A(3:4,0:1) consists of */ /* the transpose of the first two columns of AP upper. */ /* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */ /* three columns of AP lower. The upper triangle A(0:1,1:2) consists of */ /* the transpose of the last two columns of AP lower. */ /* This covers the case N odd and TRANSR = 'N'. */ /* RFP A RFP A */ /* 02 03 04 00 33 43 */ /* 12 13 14 10 11 44 */ /* 22 23 24 20 21 22 */ /* 00 33 34 30 31 32 */ /* 01 11 44 40 41 42 */ /* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ /* transpose of RFP A above. One therefore gets: */ /* RFP A RFP A */ /* 02 12 22 00 01 00 10 20 30 40 50 */ /* 03 13 23 33 11 33 11 21 31 41 51 */ /* 04 14 24 34 44 43 44 22 32 42 52 */ /* Reference */ /* ========= */ /* ===================================================================== */ /* .. */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ if (*n == 0) { ret_val = 0.f; return ret_val; } /* set noe = 1 if n is odd. if n is even set noe=0 */ noe = 1; if (*n % 2 == 0) { noe = 0; } /* set ifm = 0 when form='T or 't' and 1 otherwise */ ifm = 1; if (lsame_(transr, "T")) { ifm = 0; } /* set ilu = 0 when uplo='U or 'u' and 1 otherwise */ ilu = 1; if (lsame_(uplo, "U")) { ilu = 0; } /* set lda = (n+1)/2 when ifm = 0 */ /* set lda = n when ifm = 1 and noe = 1 */ /* set lda = n+1 when ifm = 1 and noe = 0 */ if (ifm == 1) { if (noe == 1) { lda = *n; } else { /* noe=0 */ lda = *n + 1; } } else { /* ifm=0 */ lda = (*n + 1) / 2; } if (lsame_(norm, "M")) { /* Find max(abs(A(i,j))). */ k = (*n + 1) / 2; value = 0.f; if (noe == 1) { /* n is odd */ if (ifm == 1) { /* A is n by k */ i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = *n - 1; for (i__ = 0; i__ <= i__2; ++i__) { /* Computing MAX */ r__2 = value, r__3 = (r__1 = a[i__ + j * lda], dabs( r__1)); value = dmax(r__2,r__3); } } } else { /* xpose case; A is k by n */ i__1 = *n - 1; for (j = 0; j <= i__1; ++j) { i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { /* Computing MAX */ r__2 = value, r__3 = (r__1 = a[i__ + j * lda], dabs( r__1)); value = dmax(r__2,r__3); } } } } else { /* n is even */ if (ifm == 1) { /* A is n+1 by k */ i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = *n; for (i__ = 0; i__ <= i__2; ++i__) { /* Computing MAX */ r__2 = value, r__3 = (r__1 = a[i__ + j * lda], dabs( r__1)); value = dmax(r__2,r__3); } } } else { /* xpose case; A is k by n+1 */ i__1 = *n; for (j = 0; j <= i__1; ++j) { i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { /* Computing MAX */ r__2 = value, r__3 = (r__1 = a[i__ + j * lda], dabs( r__1)); value = dmax(r__2,r__3); } } } } } else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') { /* Find normI(A) ( = norm1(A), since A is symmetric). */ if (ifm == 1) { k = *n / 2; if (noe == 1) { /* n is odd */ if (ilu == 0) { i__1 = k - 1; for (i__ = 0; i__ <= i__1; ++i__) { work[i__] = 0.f; } i__1 = k; for (j = 0; j <= i__1; ++j) { s = 0.f; i__2 = k + j - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(i,j+k) */ s += aa; work[i__] += aa; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,j+k) */ work[j + k] = s + aa; if (i__ == k + k) { goto L10; } ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j,j) */ work[j] += aa; s = 0.f; i__2 = k - 1; for (l = j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(l,j) */ s += aa; work[l] += aa; } work[j] += s; } L10: i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } else { /* ilu = 1 */ ++k; /* k=(n+1)/2 for n odd and ilu=1 */ i__1 = *n - 1; for (i__ = k; i__ <= i__1; ++i__) { work[i__] = 0.f; } for (j = k - 1; j >= 0; --j) { s = 0.f; i__1 = j - 2; for (i__ = 0; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,i+k) */ s += aa; work[i__ + k] += aa; } if (j > 0) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,j+k) */ s += aa; work[i__ + k] += s; /* i=j */ ++i__; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j,j) */ work[j] = aa; s = 0.f; i__1 = *n - 1; for (l = j + 1; l <= i__1; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(l,j) */ s += aa; work[l] += aa; } work[j] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } } else { /* n is even */ if (ilu == 0) { i__1 = k - 1; for (i__ = 0; i__ <= i__1; ++i__) { work[i__] = 0.f; } i__1 = k - 1; for (j = 0; j <= i__1; ++j) { s = 0.f; i__2 = k + j - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(i,j+k) */ s += aa; work[i__] += aa; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,j+k) */ work[j + k] = s + aa; ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j,j) */ work[j] += aa; s = 0.f; i__2 = k - 1; for (l = j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(l,j) */ s += aa; work[l] += aa; } work[j] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } else { /* ilu = 1 */ i__1 = *n - 1; for (i__ = k; i__ <= i__1; ++i__) { work[i__] = 0.f; } for (j = k - 1; j >= 0; --j) { s = 0.f; i__1 = j - 1; for (i__ = 0; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,i+k) */ s += aa; work[i__ + k] += aa; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j+k,j+k) */ s += aa; work[i__ + k] += s; /* i=j */ ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(j,j) */ work[j] = aa; s = 0.f; i__1 = *n - 1; for (l = j + 1; l <= i__1; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* -> A(l,j) */ s += aa; work[l] += aa; } work[j] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } } } else { /* ifm=0 */ k = *n / 2; if (noe == 1) { /* n is odd */ if (ilu == 0) { n1 = k; /* n/2 */ ++k; /* k is the row size and lda */ i__1 = *n - 1; for (i__ = n1; i__ <= i__1; ++i__) { work[i__] = 0.f; } i__1 = n1 - 1; for (j = 0; j <= i__1; ++j) { s = 0.f; i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,n1+i) */ work[i__ + n1] += aa; s += aa; } work[j] = s; } /* j=n1=k-1 is special */ s = (r__1 = a[j * lda], dabs(r__1)); /* A(k-1,k-1) */ i__1 = k - 1; for (i__ = 1; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k-1,i+n1) */ work[i__ + n1] += aa; s += aa; } work[j] += s; i__1 = *n - 1; for (j = k; j <= i__1; ++j) { s = 0.f; i__2 = j - k - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(i,j-k) */ work[i__] += aa; s += aa; } /* i=j-k */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j-k,j-k) */ s += aa; work[j - k] += s; ++i__; s = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,j) */ i__2 = *n - 1; for (l = j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,l) */ work[l] += aa; s += aa; } work[j] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } else { /* ilu=1 */ ++k; /* k=(n+1)/2 for n odd and ilu=1 */ i__1 = *n - 1; for (i__ = k; i__ <= i__1; ++i__) { work[i__] = 0.f; } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { /* process */ s = 0.f; i__2 = j - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,i) */ work[i__] += aa; s += aa; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* i=j so process of A(j,j) */ s += aa; work[j] = s; /* is initialised here */ ++i__; /* i=j process A(j+k,j+k) */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); s = aa; i__2 = *n - 1; for (l = k + j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(l,k+j) */ s += aa; work[l] += aa; } work[k + j] += s; } /* j=k-1 is special :process col A(k-1,0:k-1) */ s = 0.f; i__1 = k - 2; for (i__ = 0; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k,i) */ work[i__] += aa; s += aa; } /* i=k-1 */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k-1,k-1) */ s += aa; work[i__] = s; /* done with col j=k+1 */ i__1 = *n - 1; for (j = k; j <= i__1; ++j) { /* process col j of A = A(j,0:k-1) */ s = 0.f; i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,i) */ work[i__] += aa; s += aa; } work[j] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } } else { /* n is even */ if (ilu == 0) { i__1 = *n - 1; for (i__ = k; i__ <= i__1; ++i__) { work[i__] = 0.f; } i__1 = k - 1; for (j = 0; j <= i__1; ++j) { s = 0.f; i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,i+k) */ work[i__ + k] += aa; s += aa; } work[j] = s; } /* j=k */ aa = (r__1 = a[j * lda], dabs(r__1)); /* A(k,k) */ s = aa; i__1 = k - 1; for (i__ = 1; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k,k+i) */ work[i__ + k] += aa; s += aa; } work[j] += s; i__1 = *n - 1; for (j = k + 1; j <= i__1; ++j) { s = 0.f; i__2 = j - 2 - k; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(i,j-k-1) */ work[i__] += aa; s += aa; } /* i=j-1-k */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j-k-1,j-k-1) */ s += aa; work[j - k - 1] += s; ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,j) */ s = aa; i__2 = *n - 1; for (l = j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j,l) */ work[l] += aa; s += aa; } work[j] += s; } /* j=n */ s = 0.f; i__1 = k - 2; for (i__ = 0; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(i,k-1) */ work[i__] += aa; s += aa; } /* i=k-1 */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k-1,k-1) */ s += aa; work[i__] += s; i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } else { /* ilu=1 */ i__1 = *n - 1; for (i__ = k; i__ <= i__1; ++i__) { work[i__] = 0.f; } /* j=0 is special :process col A(k:n-1,k) */ s = dabs(a[0]); /* A(k,k) */ i__1 = k - 1; for (i__ = 1; i__ <= i__1; ++i__) { aa = (r__1 = a[i__], dabs(r__1)); /* A(k+i,k) */ work[i__ + k] += aa; s += aa; } work[k] += s; i__1 = k - 1; for (j = 1; j <= i__1; ++j) { /* process */ s = 0.f; i__2 = j - 2; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j-1,i) */ work[i__] += aa; s += aa; } aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* i=j-1 so process of A(j-1,j-1) */ s += aa; work[j - 1] = s; /* is initialised here */ ++i__; /* i=j process A(j+k,j+k) */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); s = aa; i__2 = *n - 1; for (l = k + j + 1; l <= i__2; ++l) { ++i__; aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(l,k+j) */ s += aa; work[l] += aa; } work[k + j] += s; } /* j=k is special :process col A(k,0:k-1) */ s = 0.f; i__1 = k - 2; for (i__ = 0; i__ <= i__1; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k,i) */ work[i__] += aa; s += aa; } /* i=k-1 */ aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(k-1,k-1) */ s += aa; work[i__] = s; /* done with col j=k+1 */ i__1 = *n; for (j = k + 1; j <= i__1; ++j) { /* process col j-1 of A = A(j-1,0:k-1) */ s = 0.f; i__2 = k - 1; for (i__ = 0; i__ <= i__2; ++i__) { aa = (r__1 = a[i__ + j * lda], dabs(r__1)); /* A(j-1,i) */ work[i__] += aa; s += aa; } work[j - 1] += s; } i__ = isamax_(n, work, &c__1); value = work[i__ - 1]; } } } } else if (lsame_(norm, "F") || lsame_(norm, "E")) { /* Find normF(A). */ k = (*n + 1) / 2; scale = 0.f; s = 1.f; if (noe == 1) { /* n is odd */ if (ifm == 1) { /* A is normal */ if (ilu == 0) { /* A is upper */ i__1 = k - 3; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 2; slassq_(&i__2, &a[k + j + 1 + j * lda], &c__1, &scale, &s); /* L at A(k,0) */ } i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = k + j - 1; slassq_(&i__2, &a[j * lda], &c__1, &scale, &s); /* trap U at A(0,0) */ } s += s; /* double s for the off diagonal elements */ i__1 = k - 1; i__2 = lda + 1; slassq_(&i__1, &a[k], &i__2, &scale, &s); /* tri L at A(k,0) */ i__1 = lda + 1; slassq_(&k, &a[k - 1], &i__1, &scale, &s); /* tri U at A(k-1,0) */ } else { /* ilu=1 & A is lower */ i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = *n - j - 1; slassq_(&i__2, &a[j + 1 + j * lda], &c__1, &scale, &s) ; /* trap L at A(0,0) */ } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { slassq_(&j, &a[(j + 1) * lda], &c__1, &scale, &s); /* U at A(0,1) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, a, &i__1, &scale, &s); /* tri L at A(0,0) */ i__1 = k - 1; i__2 = lda + 1; slassq_(&i__1, &a[lda], &i__2, &scale, &s); /* tri U at A(0,1) */ } } else { /* A is xpose */ if (ilu == 0) { /* A' is upper */ i__1 = k - 2; for (j = 1; j <= i__1; ++j) { slassq_(&j, &a[(k + j) * lda], &c__1, &scale, &s); /* U at A(0,k) */ } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { slassq_(&k, &a[j * lda], &c__1, &scale, &s); /* k by k-1 rect. at A(0,0) */ } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 1; slassq_(&i__2, &a[j + 1 + (j + k - 1) * lda], &c__1, & scale, &s); /* L at A(0,k-1) */ } s += s; /* double s for the off diagonal elements */ i__1 = k - 1; i__2 = lda + 1; slassq_(&i__1, &a[k * lda], &i__2, &scale, &s); /* tri U at A(0,k) */ i__1 = lda + 1; slassq_(&k, &a[(k - 1) * lda], &i__1, &scale, &s); /* tri L at A(0,k-1) */ } else { /* A' is lower */ i__1 = k - 1; for (j = 1; j <= i__1; ++j) { slassq_(&j, &a[j * lda], &c__1, &scale, &s); /* U at A(0,0) */ } i__1 = *n - 1; for (j = k; j <= i__1; ++j) { slassq_(&k, &a[j * lda], &c__1, &scale, &s); /* k by k-1 rect. at A(0,k) */ } i__1 = k - 3; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 2; slassq_(&i__2, &a[j + 2 + j * lda], &c__1, &scale, &s) ; /* L at A(1,0) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, a, &i__1, &scale, &s); /* tri U at A(0,0) */ i__1 = k - 1; i__2 = lda + 1; slassq_(&i__1, &a[1], &i__2, &scale, &s); /* tri L at A(1,0) */ } } } else { /* n is even */ if (ifm == 1) { /* A is normal */ if (ilu == 0) { /* A is upper */ i__1 = k - 2; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 1; slassq_(&i__2, &a[k + j + 2 + j * lda], &c__1, &scale, &s); /* L at A(k+1,0) */ } i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = k + j; slassq_(&i__2, &a[j * lda], &c__1, &scale, &s); /* trap U at A(0,0) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, &a[k + 1], &i__1, &scale, &s); /* tri L at A(k+1,0) */ i__1 = lda + 1; slassq_(&k, &a[k], &i__1, &scale, &s); /* tri U at A(k,0) */ } else { /* ilu=1 & A is lower */ i__1 = k - 1; for (j = 0; j <= i__1; ++j) { i__2 = *n - j - 1; slassq_(&i__2, &a[j + 2 + j * lda], &c__1, &scale, &s) ; /* trap L at A(1,0) */ } i__1 = k - 1; for (j = 1; j <= i__1; ++j) { slassq_(&j, &a[j * lda], &c__1, &scale, &s); /* U at A(0,0) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, &a[1], &i__1, &scale, &s); /* tri L at A(1,0) */ i__1 = lda + 1; slassq_(&k, a, &i__1, &scale, &s); /* tri U at A(0,0) */ } } else { /* A is xpose */ if (ilu == 0) { /* A' is upper */ i__1 = k - 1; for (j = 1; j <= i__1; ++j) { slassq_(&j, &a[(k + 1 + j) * lda], &c__1, &scale, &s); /* U at A(0,k+1) */ } i__1 = k - 1; for (j = 0; j <= i__1; ++j) { slassq_(&k, &a[j * lda], &c__1, &scale, &s); /* k by k rect. at A(0,0) */ } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 1; slassq_(&i__2, &a[j + 1 + (j + k) * lda], &c__1, & scale, &s); /* L at A(0,k) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, &a[(k + 1) * lda], &i__1, &scale, &s); /* tri U at A(0,k+1) */ i__1 = lda + 1; slassq_(&k, &a[k * lda], &i__1, &scale, &s); /* tri L at A(0,k) */ } else { /* A' is lower */ i__1 = k - 1; for (j = 1; j <= i__1; ++j) { slassq_(&j, &a[(j + 1) * lda], &c__1, &scale, &s); /* U at A(0,1) */ } i__1 = *n; for (j = k + 1; j <= i__1; ++j) { slassq_(&k, &a[j * lda], &c__1, &scale, &s); /* k by k rect. at A(0,k+1) */ } i__1 = k - 2; for (j = 0; j <= i__1; ++j) { i__2 = k - j - 1; slassq_(&i__2, &a[j + 1 + j * lda], &c__1, &scale, &s) ; /* L at A(0,0) */ } s += s; /* double s for the off diagonal elements */ i__1 = lda + 1; slassq_(&k, &a[lda], &i__1, &scale, &s); /* tri L at A(0,1) */ i__1 = lda + 1; slassq_(&k, a, &i__1, &scale, &s); /* tri U at A(0,0) */ } } } value = scale * sqrt(s); } ret_val = value; return ret_val; /* End of SLANSF */ } /* slansf_ */