Annotation of rpl/lapack/lapack/zla_syrcond_c.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_C( UPLO, N, A, LDA, AF,
! 2: $ LDAF, IPIV, C, CAPPLY,
! 3: $ INFO, WORK, RWORK )
! 4: *
! 5: * -- LAPACK routine (version 3.2.1) --
! 6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 7: * -- Jason Riedy of Univ. of California Berkeley. --
! 8: * -- April 2009 --
! 9: *
! 10: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 11: * -- Univ. of California Berkeley and NAG Ltd. --
! 12: *
! 13: IMPLICIT NONE
! 14: * ..
! 15: * .. Scalar Arguments ..
! 16: CHARACTER UPLO
! 17: LOGICAL CAPPLY
! 18: INTEGER N, LDA, LDAF, INFO
! 19: * ..
! 20: * .. Array Arguments ..
! 21: INTEGER IPIV( * )
! 22: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
! 23: DOUBLE PRECISION C( * ), RWORK( * )
! 24: * ..
! 25: *
! 26: * Purpose
! 27: * =======
! 28: *
! 29: * ZLA_SYRCOND_C Computes the infinity norm condition number of
! 30: * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * UPLO (input) CHARACTER*1
! 36: * = 'U': Upper triangle of A is stored;
! 37: * = 'L': Lower triangle of A is stored.
! 38: *
! 39: * N (input) INTEGER
! 40: * The number of linear equations, i.e., the order of the
! 41: * matrix A. N >= 0.
! 42: *
! 43: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 44: * On entry, the N-by-N matrix A
! 45: *
! 46: * LDA (input) INTEGER
! 47: * The leading dimension of the array A. LDA >= max(1,N).
! 48: *
! 49: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 50: * The block diagonal matrix D and the multipliers used to
! 51: * obtain the factor U or L as computed by ZSYTRF.
! 52: *
! 53: * LDAF (input) INTEGER
! 54: * The leading dimension of the array AF. LDAF >= max(1,N).
! 55: *
! 56: * IPIV (input) INTEGER array, dimension (N)
! 57: * Details of the interchanges and the block structure of D
! 58: * as determined by ZSYTRF.
! 59: *
! 60: * C (input) DOUBLE PRECISION array, dimension (N)
! 61: * The vector C in the formula op(A) * inv(diag(C)).
! 62: *
! 63: * CAPPLY (input) LOGICAL
! 64: * If .TRUE. then access the vector C in the formula above.
! 65: *
! 66: * INFO (output) INTEGER
! 67: * = 0: Successful exit.
! 68: * i > 0: The ith argument is invalid.
! 69: *
! 70: * WORK (input) COMPLEX*16 array, dimension (2*N).
! 71: * Workspace.
! 72: *
! 73: * RWORK (input) DOUBLE PRECISION array, dimension (N).
! 74: * Workspace.
! 75: *
! 76: * =====================================================================
! 77: *
! 78: * .. Local Scalars ..
! 79: INTEGER KASE
! 80: DOUBLE PRECISION AINVNM, ANORM, TMP
! 81: INTEGER I, J
! 82: LOGICAL UP
! 83: COMPLEX*16 ZDUM
! 84: * ..
! 85: * .. Local Arrays ..
! 86: INTEGER ISAVE( 3 )
! 87: * ..
! 88: * .. External Functions ..
! 89: LOGICAL LSAME
! 90: EXTERNAL LSAME
! 91: * ..
! 92: * .. External Subroutines ..
! 93: EXTERNAL ZLACN2, ZSYTRS, XERBLA
! 94: * ..
! 95: * .. Intrinsic Functions ..
! 96: INTRINSIC ABS, MAX
! 97: * ..
! 98: * .. Statement Functions ..
! 99: DOUBLE PRECISION CABS1
! 100: * ..
! 101: * .. Statement Function Definitions ..
! 102: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 103: * ..
! 104: * .. Executable Statements ..
! 105: *
! 106: ZLA_SYRCOND_C = 0.0D+0
! 107: *
! 108: INFO = 0
! 109: IF( N.LT.0 ) THEN
! 110: INFO = -2
! 111: END IF
! 112: IF( INFO.NE.0 ) THEN
! 113: CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
! 114: RETURN
! 115: END IF
! 116: UP = .FALSE.
! 117: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
! 118: *
! 119: * Compute norm of op(A)*op2(C).
! 120: *
! 121: ANORM = 0.0D+0
! 122: IF ( UP ) THEN
! 123: DO I = 1, N
! 124: TMP = 0.0D+0
! 125: IF ( CAPPLY ) THEN
! 126: DO J = 1, I
! 127: TMP = TMP + CABS1( A( J, I ) ) / C( J )
! 128: END DO
! 129: DO J = I+1, N
! 130: TMP = TMP + CABS1( A( I, J ) ) / C( J )
! 131: END DO
! 132: ELSE
! 133: DO J = 1, I
! 134: TMP = TMP + CABS1( A( J, I ) )
! 135: END DO
! 136: DO J = I+1, N
! 137: TMP = TMP + CABS1( A( I, J ) )
! 138: END DO
! 139: END IF
! 140: RWORK( I ) = TMP
! 141: ANORM = MAX( ANORM, TMP )
! 142: END DO
! 143: ELSE
! 144: DO I = 1, N
! 145: TMP = 0.0D+0
! 146: IF ( CAPPLY ) THEN
! 147: DO J = 1, I
! 148: TMP = TMP + CABS1( A( I, J ) ) / C( J )
! 149: END DO
! 150: DO J = I+1, N
! 151: TMP = TMP + CABS1( A( J, I ) ) / C( J )
! 152: END DO
! 153: ELSE
! 154: DO J = 1, I
! 155: TMP = TMP + CABS1( A( I, J ) )
! 156: END DO
! 157: DO J = I+1, N
! 158: TMP = TMP + CABS1( A( J, I ) )
! 159: END DO
! 160: END IF
! 161: RWORK( I ) = TMP
! 162: ANORM = MAX( ANORM, TMP )
! 163: END DO
! 164: END IF
! 165: *
! 166: * Quick return if possible.
! 167: *
! 168: IF( N.EQ.0 ) THEN
! 169: ZLA_SYRCOND_C = 1.0D+0
! 170: RETURN
! 171: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
! 172: RETURN
! 173: END IF
! 174: *
! 175: * Estimate the norm of inv(op(A)).
! 176: *
! 177: AINVNM = 0.0D+0
! 178: *
! 179: KASE = 0
! 180: 10 CONTINUE
! 181: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 182: IF( KASE.NE.0 ) THEN
! 183: IF( KASE.EQ.2 ) THEN
! 184: *
! 185: * Multiply by R.
! 186: *
! 187: DO I = 1, N
! 188: WORK( I ) = WORK( I ) * RWORK( I )
! 189: END DO
! 190: *
! 191: IF ( UP ) THEN
! 192: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
! 193: $ WORK, N, INFO )
! 194: ELSE
! 195: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
! 196: $ WORK, N, INFO )
! 197: ENDIF
! 198: *
! 199: * Multiply by inv(C).
! 200: *
! 201: IF ( CAPPLY ) THEN
! 202: DO I = 1, N
! 203: WORK( I ) = WORK( I ) * C( I )
! 204: END DO
! 205: END IF
! 206: ELSE
! 207: *
! 208: * Multiply by inv(C').
! 209: *
! 210: IF ( CAPPLY ) THEN
! 211: DO I = 1, N
! 212: WORK( I ) = WORK( I ) * C( I )
! 213: END DO
! 214: END IF
! 215: *
! 216: IF ( UP ) THEN
! 217: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
! 218: $ WORK, N, INFO )
! 219: ELSE
! 220: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
! 221: $ WORK, N, INFO )
! 222: END IF
! 223: *
! 224: * Multiply by R.
! 225: *
! 226: DO I = 1, N
! 227: WORK( I ) = WORK( I ) * RWORK( I )
! 228: END DO
! 229: END IF
! 230: GO TO 10
! 231: END IF
! 232: *
! 233: * Compute the estimate of the reciprocal condition number.
! 234: *
! 235: IF( AINVNM .NE. 0.0D+0 )
! 236: $ ZLA_SYRCOND_C = 1.0D+0 / AINVNM
! 237: *
! 238: RETURN
! 239: *
! 240: END
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