Annotation of rpl/lapack/lapack/zppequ.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, N
! 11: DOUBLE PRECISION AMAX, SCOND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION S( * )
! 15: COMPLEX*16 AP( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZPPEQU computes row and column scalings intended to equilibrate a
! 22: * Hermitian positive definite matrix A in packed storage and reduce
! 23: * its condition number (with respect to the two-norm). S contains the
! 24: * scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
! 25: * B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
! 26: * This choice of S puts the condition number of B within a factor N of
! 27: * the smallest possible condition number over all possible diagonal
! 28: * scalings.
! 29: *
! 30: * Arguments
! 31: * =========
! 32: *
! 33: * UPLO (input) CHARACTER*1
! 34: * = 'U': Upper triangle of A is stored;
! 35: * = 'L': Lower triangle of A is stored.
! 36: *
! 37: * N (input) INTEGER
! 38: * The order of the matrix A. N >= 0.
! 39: *
! 40: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
! 41: * The upper or lower triangle of the Hermitian matrix A, packed
! 42: * columnwise in a linear array. The j-th column of A is stored
! 43: * in the array AP as follows:
! 44: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 45: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 46: *
! 47: * S (output) DOUBLE PRECISION array, dimension (N)
! 48: * If INFO = 0, S contains the scale factors for A.
! 49: *
! 50: * SCOND (output) DOUBLE PRECISION
! 51: * If INFO = 0, S contains the ratio of the smallest S(i) to
! 52: * the largest S(i). If SCOND >= 0.1 and AMAX is neither too
! 53: * large nor too small, it is not worth scaling by S.
! 54: *
! 55: * AMAX (output) DOUBLE PRECISION
! 56: * Absolute value of largest matrix element. If AMAX is very
! 57: * close to overflow or very close to underflow, the matrix
! 58: * should be scaled.
! 59: *
! 60: * INFO (output) INTEGER
! 61: * = 0: successful exit
! 62: * < 0: if INFO = -i, the i-th argument had an illegal value
! 63: * > 0: if INFO = i, the i-th diagonal element is nonpositive.
! 64: *
! 65: * =====================================================================
! 66: *
! 67: * .. Parameters ..
! 68: DOUBLE PRECISION ONE, ZERO
! 69: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 70: * ..
! 71: * .. Local Scalars ..
! 72: LOGICAL UPPER
! 73: INTEGER I, JJ
! 74: DOUBLE PRECISION SMIN
! 75: * ..
! 76: * .. External Functions ..
! 77: LOGICAL LSAME
! 78: EXTERNAL LSAME
! 79: * ..
! 80: * .. External Subroutines ..
! 81: EXTERNAL XERBLA
! 82: * ..
! 83: * .. Intrinsic Functions ..
! 84: INTRINSIC DBLE, MAX, MIN, SQRT
! 85: * ..
! 86: * .. Executable Statements ..
! 87: *
! 88: * Test the input parameters.
! 89: *
! 90: INFO = 0
! 91: UPPER = LSAME( UPLO, 'U' )
! 92: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 93: INFO = -1
! 94: ELSE IF( N.LT.0 ) THEN
! 95: INFO = -2
! 96: END IF
! 97: IF( INFO.NE.0 ) THEN
! 98: CALL XERBLA( 'ZPPEQU', -INFO )
! 99: RETURN
! 100: END IF
! 101: *
! 102: * Quick return if possible
! 103: *
! 104: IF( N.EQ.0 ) THEN
! 105: SCOND = ONE
! 106: AMAX = ZERO
! 107: RETURN
! 108: END IF
! 109: *
! 110: * Initialize SMIN and AMAX.
! 111: *
! 112: S( 1 ) = DBLE( AP( 1 ) )
! 113: SMIN = S( 1 )
! 114: AMAX = S( 1 )
! 115: *
! 116: IF( UPPER ) THEN
! 117: *
! 118: * UPLO = 'U': Upper triangle of A is stored.
! 119: * Find the minimum and maximum diagonal elements.
! 120: *
! 121: JJ = 1
! 122: DO 10 I = 2, N
! 123: JJ = JJ + I
! 124: S( I ) = DBLE( AP( JJ ) )
! 125: SMIN = MIN( SMIN, S( I ) )
! 126: AMAX = MAX( AMAX, S( I ) )
! 127: 10 CONTINUE
! 128: *
! 129: ELSE
! 130: *
! 131: * UPLO = 'L': Lower triangle of A is stored.
! 132: * Find the minimum and maximum diagonal elements.
! 133: *
! 134: JJ = 1
! 135: DO 20 I = 2, N
! 136: JJ = JJ + N - I + 2
! 137: S( I ) = DBLE( AP( JJ ) )
! 138: SMIN = MIN( SMIN, S( I ) )
! 139: AMAX = MAX( AMAX, S( I ) )
! 140: 20 CONTINUE
! 141: END IF
! 142: *
! 143: IF( SMIN.LE.ZERO ) THEN
! 144: *
! 145: * Find the first non-positive diagonal element and return.
! 146: *
! 147: DO 30 I = 1, N
! 148: IF( S( I ).LE.ZERO ) THEN
! 149: INFO = I
! 150: RETURN
! 151: END IF
! 152: 30 CONTINUE
! 153: ELSE
! 154: *
! 155: * Set the scale factors to the reciprocals
! 156: * of the diagonal elements.
! 157: *
! 158: DO 40 I = 1, N
! 159: S( I ) = ONE / SQRT( S( I ) )
! 160: 40 CONTINUE
! 161: *
! 162: * Compute SCOND = min(S(I)) / max(S(I))
! 163: *
! 164: SCOND = SQRT( SMIN ) / SQRT( AMAX )
! 165: END IF
! 166: RETURN
! 167: *
! 168: * End of ZPPEQU
! 169: *
! 170: END
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