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