Annotation of rpl/lapack/lapack/zlansp.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANSP( 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: * ZLANSP 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 symmetric matrix A, supplied in packed form.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANSP returns the value
! 28: *
! 29: * ZLANSP = ( 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 ZLANSP as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the upper or lower triangular part of the
! 51: * symmetric 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, ZLANSP 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 symmetric 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: *
! 66: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 67: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 68: * WORK is not referenced.
! 69: *
! 70: * =====================================================================
! 71: *
! 72: * .. Parameters ..
! 73: DOUBLE PRECISION ONE, ZERO
! 74: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 75: * ..
! 76: * .. Local Scalars ..
! 77: INTEGER I, J, K
! 78: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 79: * ..
! 80: * .. External Functions ..
! 81: LOGICAL LSAME
! 82: EXTERNAL LSAME
! 83: * ..
! 84: * .. External Subroutines ..
! 85: EXTERNAL ZLASSQ
! 86: * ..
! 87: * .. Intrinsic Functions ..
! 88: INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
! 89: * ..
! 90: * .. Executable Statements ..
! 91: *
! 92: IF( N.EQ.0 ) THEN
! 93: VALUE = ZERO
! 94: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 95: *
! 96: * Find max(abs(A(i,j))).
! 97: *
! 98: VALUE = ZERO
! 99: IF( LSAME( UPLO, 'U' ) ) THEN
! 100: K = 1
! 101: DO 20 J = 1, N
! 102: DO 10 I = K, K + J - 1
! 103: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 104: 10 CONTINUE
! 105: K = K + J
! 106: 20 CONTINUE
! 107: ELSE
! 108: K = 1
! 109: DO 40 J = 1, N
! 110: DO 30 I = K, K + N - J
! 111: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 112: 30 CONTINUE
! 113: K = K + N - J + 1
! 114: 40 CONTINUE
! 115: END IF
! 116: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 117: $ ( NORM.EQ.'1' ) ) THEN
! 118: *
! 119: * Find normI(A) ( = norm1(A), since A is symmetric).
! 120: *
! 121: VALUE = ZERO
! 122: K = 1
! 123: IF( LSAME( UPLO, 'U' ) ) THEN
! 124: DO 60 J = 1, N
! 125: SUM = ZERO
! 126: DO 50 I = 1, J - 1
! 127: ABSA = ABS( AP( K ) )
! 128: SUM = SUM + ABSA
! 129: WORK( I ) = WORK( I ) + ABSA
! 130: K = K + 1
! 131: 50 CONTINUE
! 132: WORK( J ) = SUM + ABS( AP( K ) )
! 133: K = K + 1
! 134: 60 CONTINUE
! 135: DO 70 I = 1, N
! 136: VALUE = MAX( VALUE, WORK( I ) )
! 137: 70 CONTINUE
! 138: ELSE
! 139: DO 80 I = 1, N
! 140: WORK( I ) = ZERO
! 141: 80 CONTINUE
! 142: DO 100 J = 1, N
! 143: SUM = WORK( J ) + ABS( AP( K ) )
! 144: K = K + 1
! 145: DO 90 I = J + 1, N
! 146: ABSA = ABS( AP( K ) )
! 147: SUM = SUM + ABSA
! 148: WORK( I ) = WORK( I ) + ABSA
! 149: K = K + 1
! 150: 90 CONTINUE
! 151: VALUE = MAX( VALUE, SUM )
! 152: 100 CONTINUE
! 153: END IF
! 154: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 155: *
! 156: * Find normF(A).
! 157: *
! 158: SCALE = ZERO
! 159: SUM = ONE
! 160: K = 2
! 161: IF( LSAME( UPLO, 'U' ) ) THEN
! 162: DO 110 J = 2, N
! 163: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
! 164: K = K + J
! 165: 110 CONTINUE
! 166: ELSE
! 167: DO 120 J = 1, N - 1
! 168: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
! 169: K = K + N - J + 1
! 170: 120 CONTINUE
! 171: END IF
! 172: SUM = 2*SUM
! 173: K = 1
! 174: DO 130 I = 1, N
! 175: IF( DBLE( AP( K ) ).NE.ZERO ) THEN
! 176: ABSA = ABS( DBLE( AP( K ) ) )
! 177: IF( SCALE.LT.ABSA ) THEN
! 178: SUM = ONE + SUM*( SCALE / ABSA )**2
! 179: SCALE = ABSA
! 180: ELSE
! 181: SUM = SUM + ( ABSA / SCALE )**2
! 182: END IF
! 183: END IF
! 184: IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
! 185: ABSA = ABS( DIMAG( AP( K ) ) )
! 186: IF( SCALE.LT.ABSA ) THEN
! 187: SUM = ONE + SUM*( SCALE / ABSA )**2
! 188: SCALE = ABSA
! 189: ELSE
! 190: SUM = SUM + ( ABSA / SCALE )**2
! 191: END IF
! 192: END IF
! 193: IF( LSAME( UPLO, 'U' ) ) THEN
! 194: K = K + I + 1
! 195: ELSE
! 196: K = K + N - I + 1
! 197: END IF
! 198: 130 CONTINUE
! 199: VALUE = SCALE*SQRT( SUM )
! 200: END IF
! 201: *
! 202: ZLANSP = VALUE
! 203: RETURN
! 204: *
! 205: * End of ZLANSP
! 206: *
! 207: END
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