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608 lines
17 KiB
608 lines
17 KiB
/* dsytf2.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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/* Subroutine */ int dsytf2_(char *uplo, integer *n, doublereal *a, integer * |
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lda, integer *ipiv, integer *info) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, i__1, i__2; |
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doublereal d__1, d__2, d__3; |
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/* Builtin functions */ |
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double sqrt(doublereal); |
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/* Local variables */ |
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integer i__, j, k; |
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doublereal t, r1, d11, d12, d21, d22; |
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integer kk, kp; |
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doublereal wk, wkm1, wkp1; |
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integer imax, jmax; |
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extern /* Subroutine */ int dsyr_(char *, integer *, doublereal *, |
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doublereal *, integer *, doublereal *, integer *); |
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doublereal alpha; |
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, |
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integer *); |
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extern logical lsame_(char *, char *); |
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extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, |
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doublereal *, integer *); |
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integer kstep; |
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logical upper; |
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doublereal absakk; |
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extern integer idamax_(integer *, doublereal *, integer *); |
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extern logical disnan_(doublereal *); |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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doublereal colmax, rowmax; |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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|
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/* Purpose */ |
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/* ======= */ |
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/* DSYTF2 computes the factorization of a real symmetric matrix A using */ |
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/* the Bunch-Kaufman diagonal pivoting method: */ |
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/* A = U*D*U' or A = L*D*L' */ |
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/* where U (or L) is a product of permutation and unit upper (lower) */ |
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/* triangular matrices, U' is the transpose of U, and D is symmetric and */ |
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/* block diagonal with 1-by-1 and 2-by-2 diagonal blocks. */ |
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/* This is the unblocked version of the algorithm, calling Level 2 BLAS. */ |
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/* Arguments */ |
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/* ========= */ |
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/* UPLO (input) CHARACTER*1 */ |
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/* Specifies whether the upper or lower triangular part of the */ |
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/* symmetric matrix A is stored: */ |
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/* = 'U': Upper triangular */ |
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/* = 'L': Lower triangular */ |
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/* N (input) INTEGER */ |
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/* The order of the matrix A. N >= 0. */ |
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ |
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/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ |
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/* n-by-n upper triangular part of A contains the upper */ |
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/* triangular part of the matrix A, and the strictly lower */ |
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/* triangular part of A is not referenced. If UPLO = 'L', the */ |
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/* leading n-by-n lower triangular part of A contains the lower */ |
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/* triangular part of the matrix A, and the strictly upper */ |
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/* triangular part of A is not referenced. */ |
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/* On exit, the block diagonal matrix D and the multipliers used */ |
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/* to obtain the factor U or L (see below for further details). */ |
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/* LDA (input) INTEGER */ |
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/* The leading dimension of the array A. LDA >= max(1,N). */ |
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/* IPIV (output) INTEGER array, dimension (N) */ |
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/* Details of the interchanges and the block structure of D. */ |
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/* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ |
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/* interchanged and D(k,k) is a 1-by-1 diagonal block. */ |
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/* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ |
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/* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ |
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/* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ |
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/* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ |
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/* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit */ |
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/* < 0: if INFO = -k, the k-th argument had an illegal value */ |
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/* > 0: if INFO = k, D(k,k) is exactly zero. The factorization */ |
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/* has been completed, but the block diagonal matrix D is */ |
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/* exactly singular, and division by zero will occur if it */ |
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/* is used to solve a system of equations. */ |
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/* Further Details */ |
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/* =============== */ |
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/* 09-29-06 - patch from */ |
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/* Bobby Cheng, MathWorks */ |
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/* Replace l.204 and l.372 */ |
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/* IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN */ |
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/* by */ |
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/* IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN */ |
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/* 01-01-96 - Based on modifications by */ |
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/* J. Lewis, Boeing Computer Services Company */ |
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/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ |
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/* 1-96 - Based on modifications by J. Lewis, Boeing Computer Services */ |
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/* Company */ |
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/* If UPLO = 'U', then A = U*D*U', where */ |
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/* U = P(n)*U(n)* ... *P(k)U(k)* ..., */ |
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/* i.e., U is a product of terms P(k)*U(k), where k decreases from n to */ |
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/* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ |
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/* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ |
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/* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */ |
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/* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ |
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/* ( I v 0 ) k-s */ |
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/* U(k) = ( 0 I 0 ) s */ |
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/* ( 0 0 I ) n-k */ |
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/* k-s s n-k */ |
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/* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */ |
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/* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */ |
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/* and A(k,k), and v overwrites A(1:k-2,k-1:k). */ |
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/* If UPLO = 'L', then A = L*D*L', where */ |
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/* L = P(1)*L(1)* ... *P(k)*L(k)* ..., */ |
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/* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */ |
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/* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ |
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/* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ |
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/* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */ |
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/* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ |
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/* ( I 0 0 ) k-1 */ |
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/* L(k) = ( 0 I 0 ) s */ |
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/* ( 0 v I ) n-k-s+1 */ |
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/* k-1 s n-k-s+1 */ |
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/* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */ |
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/* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */ |
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/* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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a -= a_offset; |
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--ipiv; |
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/* Function Body */ |
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*info = 0; |
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upper = lsame_(uplo, "U"); |
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if (! upper && ! lsame_(uplo, "L")) { |
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*info = -1; |
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} else if (*n < 0) { |
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*info = -2; |
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} else if (*lda < max(1,*n)) { |
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*info = -4; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DSYTF2", &i__1); |
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return 0; |
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} |
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/* Initialize ALPHA for use in choosing pivot block size. */ |
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alpha = (sqrt(17.) + 1.) / 8.; |
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if (upper) { |
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/* Factorize A as U*D*U' using the upper triangle of A */ |
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/* K is the main loop index, decreasing from N to 1 in steps of */ |
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/* 1 or 2 */ |
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k = *n; |
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L10: |
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/* If K < 1, exit from loop */ |
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if (k < 1) { |
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goto L70; |
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} |
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kstep = 1; |
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/* Determine rows and columns to be interchanged and whether */ |
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/* a 1-by-1 or 2-by-2 pivot block will be used */ |
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absakk = (d__1 = a[k + k * a_dim1], abs(d__1)); |
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/* IMAX is the row-index of the largest off-diagonal element in */ |
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/* column K, and COLMAX is its absolute value */ |
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if (k > 1) { |
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i__1 = k - 1; |
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imax = idamax_(&i__1, &a[k * a_dim1 + 1], &c__1); |
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colmax = (d__1 = a[imax + k * a_dim1], abs(d__1)); |
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} else { |
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colmax = 0.; |
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} |
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if (max(absakk,colmax) == 0. || disnan_(&absakk)) { |
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/* Column K is zero or contains a NaN: set INFO and continue */ |
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if (*info == 0) { |
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*info = k; |
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} |
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kp = k; |
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} else { |
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if (absakk >= alpha * colmax) { |
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/* no interchange, use 1-by-1 pivot block */ |
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kp = k; |
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} else { |
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/* JMAX is the column-index of the largest off-diagonal */ |
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/* element in row IMAX, and ROWMAX is its absolute value */ |
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i__1 = k - imax; |
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jmax = imax + idamax_(&i__1, &a[imax + (imax + 1) * a_dim1], |
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lda); |
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rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1)); |
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if (imax > 1) { |
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i__1 = imax - 1; |
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jmax = idamax_(&i__1, &a[imax * a_dim1 + 1], &c__1); |
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/* Computing MAX */ |
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d__2 = rowmax, d__3 = (d__1 = a[jmax + imax * a_dim1], |
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abs(d__1)); |
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rowmax = max(d__2,d__3); |
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} |
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if (absakk >= alpha * colmax * (colmax / rowmax)) { |
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/* no interchange, use 1-by-1 pivot block */ |
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kp = k; |
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} else if ((d__1 = a[imax + imax * a_dim1], abs(d__1)) >= |
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alpha * rowmax) { |
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/* interchange rows and columns K and IMAX, use 1-by-1 */ |
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/* pivot block */ |
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kp = imax; |
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} else { |
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/* interchange rows and columns K-1 and IMAX, use 2-by-2 */ |
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/* pivot block */ |
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kp = imax; |
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kstep = 2; |
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} |
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} |
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kk = k - kstep + 1; |
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if (kp != kk) { |
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/* Interchange rows and columns KK and KP in the leading */ |
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/* submatrix A(1:k,1:k) */ |
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i__1 = kp - 1; |
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dswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], |
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&c__1); |
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i__1 = kk - kp - 1; |
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dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + |
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1) * a_dim1], lda); |
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t = a[kk + kk * a_dim1]; |
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a[kk + kk * a_dim1] = a[kp + kp * a_dim1]; |
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a[kp + kp * a_dim1] = t; |
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if (kstep == 2) { |
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t = a[k - 1 + k * a_dim1]; |
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a[k - 1 + k * a_dim1] = a[kp + k * a_dim1]; |
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a[kp + k * a_dim1] = t; |
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} |
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} |
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/* Update the leading submatrix */ |
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if (kstep == 1) { |
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/* 1-by-1 pivot block D(k): column k now holds */ |
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/* W(k) = U(k)*D(k) */ |
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/* where U(k) is the k-th column of U */ |
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/* Perform a rank-1 update of A(1:k-1,1:k-1) as */ |
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/* A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' */ |
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r1 = 1. / a[k + k * a_dim1]; |
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i__1 = k - 1; |
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d__1 = -r1; |
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dsyr_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &a[ |
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a_offset], lda); |
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/* Store U(k) in column k */ |
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i__1 = k - 1; |
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dscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1); |
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} else { |
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/* 2-by-2 pivot block D(k): columns k and k-1 now hold */ |
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/* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */ |
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/* where U(k) and U(k-1) are the k-th and (k-1)-th columns */ |
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/* of U */ |
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/* Perform a rank-2 update of A(1:k-2,1:k-2) as */ |
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/* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )' */ |
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/* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' */ |
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if (k > 2) { |
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d12 = a[k - 1 + k * a_dim1]; |
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d22 = a[k - 1 + (k - 1) * a_dim1] / d12; |
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d11 = a[k + k * a_dim1] / d12; |
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t = 1. / (d11 * d22 - 1.); |
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d12 = t / d12; |
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for (j = k - 2; j >= 1; --j) { |
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wkm1 = d12 * (d11 * a[j + (k - 1) * a_dim1] - a[j + k |
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* a_dim1]); |
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wk = d12 * (d22 * a[j + k * a_dim1] - a[j + (k - 1) * |
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a_dim1]); |
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for (i__ = j; i__ >= 1; --i__) { |
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a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__ |
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+ k * a_dim1] * wk - a[i__ + (k - 1) * |
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a_dim1] * wkm1; |
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/* L20: */ |
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} |
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a[j + k * a_dim1] = wk; |
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a[j + (k - 1) * a_dim1] = wkm1; |
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/* L30: */ |
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} |
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} |
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} |
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} |
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/* Store details of the interchanges in IPIV */ |
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if (kstep == 1) { |
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ipiv[k] = kp; |
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} else { |
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ipiv[k] = -kp; |
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ipiv[k - 1] = -kp; |
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} |
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/* Decrease K and return to the start of the main loop */ |
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k -= kstep; |
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goto L10; |
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} else { |
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/* Factorize A as L*D*L' using the lower triangle of A */ |
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/* K is the main loop index, increasing from 1 to N in steps of */ |
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/* 1 or 2 */ |
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k = 1; |
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L40: |
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/* If K > N, exit from loop */ |
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if (k > *n) { |
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goto L70; |
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} |
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kstep = 1; |
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/* Determine rows and columns to be interchanged and whether */ |
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/* a 1-by-1 or 2-by-2 pivot block will be used */ |
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absakk = (d__1 = a[k + k * a_dim1], abs(d__1)); |
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/* IMAX is the row-index of the largest off-diagonal element in */ |
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/* column K, and COLMAX is its absolute value */ |
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if (k < *n) { |
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i__1 = *n - k; |
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imax = k + idamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1); |
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colmax = (d__1 = a[imax + k * a_dim1], abs(d__1)); |
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} else { |
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colmax = 0.; |
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} |
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if (max(absakk,colmax) == 0. || disnan_(&absakk)) { |
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/* Column K is zero or contains a NaN: set INFO and continue */ |
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if (*info == 0) { |
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*info = k; |
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} |
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kp = k; |
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} else { |
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if (absakk >= alpha * colmax) { |
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/* no interchange, use 1-by-1 pivot block */ |
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kp = k; |
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} else { |
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/* JMAX is the column-index of the largest off-diagonal */ |
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/* element in row IMAX, and ROWMAX is its absolute value */ |
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i__1 = imax - k; |
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jmax = k - 1 + idamax_(&i__1, &a[imax + k * a_dim1], lda); |
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rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1)); |
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if (imax < *n) { |
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i__1 = *n - imax; |
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jmax = imax + idamax_(&i__1, &a[imax + 1 + imax * a_dim1], |
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&c__1); |
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/* Computing MAX */ |
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d__2 = rowmax, d__3 = (d__1 = a[jmax + imax * a_dim1], |
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abs(d__1)); |
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rowmax = max(d__2,d__3); |
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} |
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if (absakk >= alpha * colmax * (colmax / rowmax)) { |
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/* no interchange, use 1-by-1 pivot block */ |
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kp = k; |
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} else if ((d__1 = a[imax + imax * a_dim1], abs(d__1)) >= |
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alpha * rowmax) { |
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/* interchange rows and columns K and IMAX, use 1-by-1 */ |
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/* pivot block */ |
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kp = imax; |
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} else { |
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/* interchange rows and columns K+1 and IMAX, use 2-by-2 */ |
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/* pivot block */ |
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kp = imax; |
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kstep = 2; |
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} |
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} |
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kk = k + kstep - 1; |
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if (kp != kk) { |
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/* Interchange rows and columns KK and KP in the trailing */ |
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/* submatrix A(k:n,k:n) */ |
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if (kp < *n) { |
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i__1 = *n - kp; |
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dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1 |
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+ kp * a_dim1], &c__1); |
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} |
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i__1 = kp - kk - 1; |
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dswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk + |
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1) * a_dim1], lda); |
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t = a[kk + kk * a_dim1]; |
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a[kk + kk * a_dim1] = a[kp + kp * a_dim1]; |
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a[kp + kp * a_dim1] = t; |
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if (kstep == 2) { |
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t = a[k + 1 + k * a_dim1]; |
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a[k + 1 + k * a_dim1] = a[kp + k * a_dim1]; |
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a[kp + k * a_dim1] = t; |
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} |
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} |
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/* Update the trailing submatrix */ |
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if (kstep == 1) { |
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/* 1-by-1 pivot block D(k): column k now holds */ |
|
|
|
/* W(k) = L(k)*D(k) */ |
|
|
|
/* where L(k) is the k-th column of L */ |
|
|
|
if (k < *n) { |
|
|
|
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */ |
|
|
|
/* A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' */ |
|
|
|
d11 = 1. / a[k + k * a_dim1]; |
|
i__1 = *n - k; |
|
d__1 = -d11; |
|
dsyr_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &c__1, & |
|
a[k + 1 + (k + 1) * a_dim1], lda); |
|
|
|
/* Store L(k) in column K */ |
|
|
|
i__1 = *n - k; |
|
dscal_(&i__1, &d11, &a[k + 1 + k * a_dim1], &c__1); |
|
} |
|
} else { |
|
|
|
/* 2-by-2 pivot block D(k) */ |
|
|
|
if (k < *n - 1) { |
|
|
|
/* Perform a rank-2 update of A(k+2:n,k+2:n) as */ |
|
|
|
/* A := A - ( (A(k) A(k+1))*D(k)**(-1) ) * (A(k) A(k+1))' */ |
|
|
|
/* where L(k) and L(k+1) are the k-th and (k+1)-th */ |
|
/* columns of L */ |
|
|
|
d21 = a[k + 1 + k * a_dim1]; |
|
d11 = a[k + 1 + (k + 1) * a_dim1] / d21; |
|
d22 = a[k + k * a_dim1] / d21; |
|
t = 1. / (d11 * d22 - 1.); |
|
d21 = t / d21; |
|
|
|
i__1 = *n; |
|
for (j = k + 2; j <= i__1; ++j) { |
|
|
|
wk = d21 * (d11 * a[j + k * a_dim1] - a[j + (k + 1) * |
|
a_dim1]); |
|
wkp1 = d21 * (d22 * a[j + (k + 1) * a_dim1] - a[j + k |
|
* a_dim1]); |
|
|
|
i__2 = *n; |
|
for (i__ = j; i__ <= i__2; ++i__) { |
|
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__ |
|
+ k * a_dim1] * wk - a[i__ + (k + 1) * |
|
a_dim1] * wkp1; |
|
/* L50: */ |
|
} |
|
|
|
a[j + k * a_dim1] = wk; |
|
a[j + (k + 1) * a_dim1] = wkp1; |
|
|
|
/* L60: */ |
|
} |
|
} |
|
} |
|
} |
|
|
|
/* Store details of the interchanges in IPIV */ |
|
|
|
if (kstep == 1) { |
|
ipiv[k] = kp; |
|
} else { |
|
ipiv[k] = -kp; |
|
ipiv[k + 1] = -kp; |
|
} |
|
|
|
/* Increase K and return to the start of the main loop */ |
|
|
|
k += kstep; |
|
goto L40; |
|
|
|
} |
|
|
|
L70: |
|
|
|
return 0; |
|
|
|
/* End of DSYTF2 */ |
|
|
|
} /* dsytf2_ */
|
|
|