Annotation of rpl/lapack/lapack/zlanhb.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
! 2: $ WORK )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER NORM, UPLO
! 11: INTEGER K, LDAB, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION WORK( * )
! 15: COMPLEX*16 AB( LDAB, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLANHB returns the value of the one norm, or the Frobenius norm, or
! 22: * the infinity norm, or the element of largest absolute value of an
! 23: * n by n hermitian band matrix A, with k super-diagonals.
! 24: *
! 25: * Description
! 26: * ===========
! 27: *
! 28: * ZLANHB returns the value
! 29: *
! 30: * ZLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 31: * (
! 32: * ( norm1(A), NORM = '1', 'O' or 'o'
! 33: * (
! 34: * ( normI(A), NORM = 'I' or 'i'
! 35: * (
! 36: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 37: *
! 38: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 39: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 40: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 41: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 42: *
! 43: * Arguments
! 44: * =========
! 45: *
! 46: * NORM (input) CHARACTER*1
! 47: * Specifies the value to be returned in ZLANHB as described
! 48: * above.
! 49: *
! 50: * UPLO (input) CHARACTER*1
! 51: * Specifies whether the upper or lower triangular part of the
! 52: * band matrix A is supplied.
! 53: * = 'U': Upper triangular
! 54: * = 'L': Lower triangular
! 55: *
! 56: * N (input) INTEGER
! 57: * The order of the matrix A. N >= 0. When N = 0, ZLANHB is
! 58: * set to zero.
! 59: *
! 60: * K (input) INTEGER
! 61: * The number of super-diagonals or sub-diagonals of the
! 62: * band matrix A. K >= 0.
! 63: *
! 64: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 65: * The upper or lower triangle of the hermitian band matrix A,
! 66: * stored in the first K+1 rows of AB. The j-th column of A is
! 67: * stored in the j-th column of the array AB as follows:
! 68: * if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
! 69: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
! 70: * Note that the imaginary parts of the diagonal elements need
! 71: * not be set and are assumed to be zero.
! 72: *
! 73: * LDAB (input) INTEGER
! 74: * The leading dimension of the array AB. LDAB >= K+1.
! 75: *
! 76: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 77: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 78: * WORK is not referenced.
! 79: *
! 80: * =====================================================================
! 81: *
! 82: * .. Parameters ..
! 83: DOUBLE PRECISION ONE, ZERO
! 84: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 85: * ..
! 86: * .. Local Scalars ..
! 87: INTEGER I, J, L
! 88: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 89: * ..
! 90: * .. External Functions ..
! 91: LOGICAL LSAME
! 92: EXTERNAL LSAME
! 93: * ..
! 94: * .. External Subroutines ..
! 95: EXTERNAL ZLASSQ
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC ABS, DBLE, MAX, MIN, SQRT
! 99: * ..
! 100: * .. Executable Statements ..
! 101: *
! 102: IF( N.EQ.0 ) THEN
! 103: VALUE = ZERO
! 104: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 105: *
! 106: * Find max(abs(A(i,j))).
! 107: *
! 108: VALUE = ZERO
! 109: IF( LSAME( UPLO, 'U' ) ) THEN
! 110: DO 20 J = 1, N
! 111: DO 10 I = MAX( K+2-J, 1 ), K
! 112: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 113: 10 CONTINUE
! 114: VALUE = MAX( VALUE, ABS( DBLE( AB( K+1, J ) ) ) )
! 115: 20 CONTINUE
! 116: ELSE
! 117: DO 40 J = 1, N
! 118: VALUE = MAX( VALUE, ABS( DBLE( AB( 1, J ) ) ) )
! 119: DO 30 I = 2, MIN( N+1-J, K+1 )
! 120: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 121: 30 CONTINUE
! 122: 40 CONTINUE
! 123: END IF
! 124: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 125: $ ( NORM.EQ.'1' ) ) THEN
! 126: *
! 127: * Find normI(A) ( = norm1(A), since A is hermitian).
! 128: *
! 129: VALUE = ZERO
! 130: IF( LSAME( UPLO, 'U' ) ) THEN
! 131: DO 60 J = 1, N
! 132: SUM = ZERO
! 133: L = K + 1 - J
! 134: DO 50 I = MAX( 1, J-K ), J - 1
! 135: ABSA = ABS( AB( L+I, J ) )
! 136: SUM = SUM + ABSA
! 137: WORK( I ) = WORK( I ) + ABSA
! 138: 50 CONTINUE
! 139: WORK( J ) = SUM + ABS( DBLE( AB( K+1, J ) ) )
! 140: 60 CONTINUE
! 141: DO 70 I = 1, N
! 142: VALUE = MAX( VALUE, WORK( I ) )
! 143: 70 CONTINUE
! 144: ELSE
! 145: DO 80 I = 1, N
! 146: WORK( I ) = ZERO
! 147: 80 CONTINUE
! 148: DO 100 J = 1, N
! 149: SUM = WORK( J ) + ABS( DBLE( AB( 1, J ) ) )
! 150: L = 1 - J
! 151: DO 90 I = J + 1, MIN( N, J+K )
! 152: ABSA = ABS( AB( L+I, J ) )
! 153: SUM = SUM + ABSA
! 154: WORK( I ) = WORK( I ) + ABSA
! 155: 90 CONTINUE
! 156: VALUE = MAX( VALUE, SUM )
! 157: 100 CONTINUE
! 158: END IF
! 159: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 160: *
! 161: * Find normF(A).
! 162: *
! 163: SCALE = ZERO
! 164: SUM = ONE
! 165: IF( K.GT.0 ) THEN
! 166: IF( LSAME( UPLO, 'U' ) ) THEN
! 167: DO 110 J = 2, N
! 168: CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
! 169: $ 1, SCALE, SUM )
! 170: 110 CONTINUE
! 171: L = K + 1
! 172: ELSE
! 173: DO 120 J = 1, N - 1
! 174: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
! 175: $ SUM )
! 176: 120 CONTINUE
! 177: L = 1
! 178: END IF
! 179: SUM = 2*SUM
! 180: ELSE
! 181: L = 1
! 182: END IF
! 183: DO 130 J = 1, N
! 184: IF( DBLE( AB( L, J ) ).NE.ZERO ) THEN
! 185: ABSA = ABS( DBLE( AB( L, J ) ) )
! 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: 130 CONTINUE
! 194: VALUE = SCALE*SQRT( SUM )
! 195: END IF
! 196: *
! 197: ZLANHB = VALUE
! 198: RETURN
! 199: *
! 200: * End of ZLANHB
! 201: *
! 202: END
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