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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDA, N 00010 REAL AMAX, SCOND 00011 * .. 00012 * .. Array Arguments .. 00013 REAL A( LDA, * ), S( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SPOEQU computes row and column scalings intended to equilibrate a 00020 * symmetric positive definite matrix A and reduce its condition number 00021 * (with respect to the two-norm). S contains the scale factors, 00022 * S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with 00023 * elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This 00024 * choice of S puts the condition number of B within a factor N of the 00025 * smallest possible condition number over all possible diagonal 00026 * scalings. 00027 * 00028 * Arguments 00029 * ========= 00030 * 00031 * N (input) INTEGER 00032 * The order of the matrix A. N >= 0. 00033 * 00034 * A (input) REAL array, dimension (LDA,N) 00035 * The N-by-N symmetric positive definite matrix whose scaling 00036 * factors are to be computed. Only the diagonal elements of A 00037 * are referenced. 00038 * 00039 * LDA (input) INTEGER 00040 * The leading dimension of the array A. LDA >= max(1,N). 00041 * 00042 * S (output) REAL array, dimension (N) 00043 * If INFO = 0, S contains the scale factors for A. 00044 * 00045 * SCOND (output) REAL 00046 * If INFO = 0, S contains the ratio of the smallest S(i) to 00047 * the largest S(i). If SCOND >= 0.1 and AMAX is neither too 00048 * large nor too small, it is not worth scaling by S. 00049 * 00050 * AMAX (output) REAL 00051 * Absolute value of largest matrix element. If AMAX is very 00052 * close to overflow or very close to underflow, the matrix 00053 * should be scaled. 00054 * 00055 * INFO (output) INTEGER 00056 * = 0: successful exit 00057 * < 0: if INFO = -i, the i-th argument had an illegal value 00058 * > 0: if INFO = i, the i-th diagonal element is nonpositive. 00059 * 00060 * ===================================================================== 00061 * 00062 * .. Parameters .. 00063 REAL ZERO, ONE 00064 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00065 * .. 00066 * .. Local Scalars .. 00067 INTEGER I 00068 REAL SMIN 00069 * .. 00070 * .. External Subroutines .. 00071 EXTERNAL XERBLA 00072 * .. 00073 * .. Intrinsic Functions .. 00074 INTRINSIC MAX, MIN, SQRT 00075 * .. 00076 * .. Executable Statements .. 00077 * 00078 * Test the input parameters. 00079 * 00080 INFO = 0 00081 IF( N.LT.0 ) THEN 00082 INFO = -1 00083 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00084 INFO = -3 00085 END IF 00086 IF( INFO.NE.0 ) THEN 00087 CALL XERBLA( 'SPOEQU', -INFO ) 00088 RETURN 00089 END IF 00090 * 00091 * Quick return if possible 00092 * 00093 IF( N.EQ.0 ) THEN 00094 SCOND = ONE 00095 AMAX = ZERO 00096 RETURN 00097 END IF 00098 * 00099 * Find the minimum and maximum diagonal elements. 00100 * 00101 S( 1 ) = A( 1, 1 ) 00102 SMIN = S( 1 ) 00103 AMAX = S( 1 ) 00104 DO 10 I = 2, N 00105 S( I ) = A( I, I ) 00106 SMIN = MIN( SMIN, S( I ) ) 00107 AMAX = MAX( AMAX, S( I ) ) 00108 10 CONTINUE 00109 * 00110 IF( SMIN.LE.ZERO ) THEN 00111 * 00112 * Find the first non-positive diagonal element and return. 00113 * 00114 DO 20 I = 1, N 00115 IF( S( I ).LE.ZERO ) THEN 00116 INFO = I 00117 RETURN 00118 END IF 00119 20 CONTINUE 00120 ELSE 00121 * 00122 * Set the scale factors to the reciprocals 00123 * of the diagonal elements. 00124 * 00125 DO 30 I = 1, N 00126 S( I ) = ONE / SQRT( S( I ) ) 00127 30 CONTINUE 00128 * 00129 * Compute SCOND = min(S(I)) / max(S(I)) 00130 * 00131 SCOND = SQRT( SMIN ) / SQRT( AMAX ) 00132 END IF 00133 RETURN 00134 * 00135 * End of SPOEQU 00136 * 00137 END
1.7.3 
