Annotation of rpl/lapack/lapack/zlanhp.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK )
! 2: *
! 3: * -- LAPACK auxiliary 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 NORM, UPLO
! 10: INTEGER N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION WORK( * )
! 14: COMPLEX*16 AP( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLANHP returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of a
! 22: * complex hermitian matrix A, supplied in packed form.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANHP returns the value
! 28: *
! 29: * ZLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 30: * (
! 31: * ( norm1(A), NORM = '1', 'O' or 'o'
! 32: * (
! 33: * ( normI(A), NORM = 'I' or 'i'
! 34: * (
! 35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 36: *
! 37: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 38: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 39: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 41: *
! 42: * Arguments
! 43: * =========
! 44: *
! 45: * NORM (input) CHARACTER*1
! 46: * Specifies the value to be returned in ZLANHP as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the upper or lower triangular part of the
! 51: * hermitian matrix A is supplied.
! 52: * = 'U': Upper triangular part of A is supplied
! 53: * = 'L': Lower triangular part of A is supplied
! 54: *
! 55: * N (input) INTEGER
! 56: * The order of the matrix A. N >= 0. When N = 0, ZLANHP is
! 57: * set to zero.
! 58: *
! 59: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
! 60: * The upper or lower triangle of the hermitian matrix A, packed
! 61: * columnwise in a linear array. The j-th column of A is stored
! 62: * in the array AP as follows:
! 63: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 64: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 65: * Note that the imaginary parts of the diagonal elements need
! 66: * not be set and are assumed to be zero.
! 67: *
! 68: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 69: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 70: * WORK is not referenced.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Parameters ..
! 75: DOUBLE PRECISION ONE, ZERO
! 76: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 77: * ..
! 78: * .. Local Scalars ..
! 79: INTEGER I, J, K
! 80: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 81: * ..
! 82: * .. External Functions ..
! 83: LOGICAL LSAME
! 84: EXTERNAL LSAME
! 85: * ..
! 86: * .. External Subroutines ..
! 87: EXTERNAL ZLASSQ
! 88: * ..
! 89: * .. Intrinsic Functions ..
! 90: INTRINSIC ABS, DBLE, MAX, SQRT
! 91: * ..
! 92: * .. Executable Statements ..
! 93: *
! 94: IF( N.EQ.0 ) THEN
! 95: VALUE = ZERO
! 96: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 97: *
! 98: * Find max(abs(A(i,j))).
! 99: *
! 100: VALUE = ZERO
! 101: IF( LSAME( UPLO, 'U' ) ) THEN
! 102: K = 0
! 103: DO 20 J = 1, N
! 104: DO 10 I = K + 1, K + J - 1
! 105: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 106: 10 CONTINUE
! 107: K = K + J
! 108: VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
! 109: 20 CONTINUE
! 110: ELSE
! 111: K = 1
! 112: DO 40 J = 1, N
! 113: VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
! 114: DO 30 I = K + 1, K + N - J
! 115: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 116: 30 CONTINUE
! 117: K = K + N - J + 1
! 118: 40 CONTINUE
! 119: END IF
! 120: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 121: $ ( NORM.EQ.'1' ) ) THEN
! 122: *
! 123: * Find normI(A) ( = norm1(A), since A is hermitian).
! 124: *
! 125: VALUE = ZERO
! 126: K = 1
! 127: IF( LSAME( UPLO, 'U' ) ) THEN
! 128: DO 60 J = 1, N
! 129: SUM = ZERO
! 130: DO 50 I = 1, J - 1
! 131: ABSA = ABS( AP( K ) )
! 132: SUM = SUM + ABSA
! 133: WORK( I ) = WORK( I ) + ABSA
! 134: K = K + 1
! 135: 50 CONTINUE
! 136: WORK( J ) = SUM + ABS( DBLE( AP( K ) ) )
! 137: K = K + 1
! 138: 60 CONTINUE
! 139: DO 70 I = 1, N
! 140: VALUE = MAX( VALUE, WORK( I ) )
! 141: 70 CONTINUE
! 142: ELSE
! 143: DO 80 I = 1, N
! 144: WORK( I ) = ZERO
! 145: 80 CONTINUE
! 146: DO 100 J = 1, N
! 147: SUM = WORK( J ) + ABS( DBLE( AP( K ) ) )
! 148: K = K + 1
! 149: DO 90 I = J + 1, N
! 150: ABSA = ABS( AP( K ) )
! 151: SUM = SUM + ABSA
! 152: WORK( I ) = WORK( I ) + ABSA
! 153: K = K + 1
! 154: 90 CONTINUE
! 155: VALUE = MAX( VALUE, SUM )
! 156: 100 CONTINUE
! 157: END IF
! 158: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 159: *
! 160: * Find normF(A).
! 161: *
! 162: SCALE = ZERO
! 163: SUM = ONE
! 164: K = 2
! 165: IF( LSAME( UPLO, 'U' ) ) THEN
! 166: DO 110 J = 2, N
! 167: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
! 168: K = K + J
! 169: 110 CONTINUE
! 170: ELSE
! 171: DO 120 J = 1, N - 1
! 172: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
! 173: K = K + N - J + 1
! 174: 120 CONTINUE
! 175: END IF
! 176: SUM = 2*SUM
! 177: K = 1
! 178: DO 130 I = 1, N
! 179: IF( DBLE( AP( K ) ).NE.ZERO ) THEN
! 180: ABSA = ABS( DBLE( AP( K ) ) )
! 181: IF( SCALE.LT.ABSA ) THEN
! 182: SUM = ONE + SUM*( SCALE / ABSA )**2
! 183: SCALE = ABSA
! 184: ELSE
! 185: SUM = SUM + ( ABSA / SCALE )**2
! 186: END IF
! 187: END IF
! 188: IF( LSAME( UPLO, 'U' ) ) THEN
! 189: K = K + I + 1
! 190: ELSE
! 191: K = K + N - I + 1
! 192: END IF
! 193: 130 CONTINUE
! 194: VALUE = SCALE*SQRT( SUM )
! 195: END IF
! 196: *
! 197: ZLANHP = VALUE
! 198: RETURN
! 199: *
! 200: * End of ZLANHP
! 201: *
! 202: END
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