Annotation of rpl/lapack/lapack/zlantp.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, 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 DIAG, NORM, UPLO
! 10: INTEGER N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION WORK( * )
! 14: COMPLEX*16 AP( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLANTP 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: * triangular matrix A, supplied in packed form.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANTP returns the value
! 28: *
! 29: * ZLANTP = ( 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 ZLANTP as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the matrix A is upper or lower triangular.
! 51: * = 'U': Upper triangular
! 52: * = 'L': Lower triangular
! 53: *
! 54: * DIAG (input) CHARACTER*1
! 55: * Specifies whether or not the matrix A is unit triangular.
! 56: * = 'N': Non-unit triangular
! 57: * = 'U': Unit triangular
! 58: *
! 59: * N (input) INTEGER
! 60: * The order of the matrix A. N >= 0. When N = 0, ZLANTP is
! 61: * set to zero.
! 62: *
! 63: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
! 64: * The upper or lower triangular matrix A, packed columnwise in
! 65: * a linear array. The j-th column of A is stored in the array
! 66: * AP as follows:
! 67: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 68: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 69: * Note that when DIAG = 'U', the elements of the array AP
! 70: * corresponding to the diagonal elements of the matrix A are
! 71: * not referenced, but are assumed to be one.
! 72: *
! 73: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 74: * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 75: * referenced.
! 76: *
! 77: * =====================================================================
! 78: *
! 79: * .. Parameters ..
! 80: DOUBLE PRECISION ONE, ZERO
! 81: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 82: * ..
! 83: * .. Local Scalars ..
! 84: LOGICAL UDIAG
! 85: INTEGER I, J, K
! 86: DOUBLE PRECISION SCALE, SUM, VALUE
! 87: * ..
! 88: * .. External Functions ..
! 89: LOGICAL LSAME
! 90: EXTERNAL LSAME
! 91: * ..
! 92: * .. External Subroutines ..
! 93: EXTERNAL ZLASSQ
! 94: * ..
! 95: * .. Intrinsic Functions ..
! 96: INTRINSIC ABS, MAX, SQRT
! 97: * ..
! 98: * .. Executable Statements ..
! 99: *
! 100: IF( N.EQ.0 ) THEN
! 101: VALUE = ZERO
! 102: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 103: *
! 104: * Find max(abs(A(i,j))).
! 105: *
! 106: K = 1
! 107: IF( LSAME( DIAG, 'U' ) ) THEN
! 108: VALUE = ONE
! 109: IF( LSAME( UPLO, 'U' ) ) THEN
! 110: DO 20 J = 1, N
! 111: DO 10 I = K, K + J - 2
! 112: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 113: 10 CONTINUE
! 114: K = K + J
! 115: 20 CONTINUE
! 116: ELSE
! 117: DO 40 J = 1, N
! 118: DO 30 I = K + 1, K + N - J
! 119: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 120: 30 CONTINUE
! 121: K = K + N - J + 1
! 122: 40 CONTINUE
! 123: END IF
! 124: ELSE
! 125: VALUE = ZERO
! 126: IF( LSAME( UPLO, 'U' ) ) THEN
! 127: DO 60 J = 1, N
! 128: DO 50 I = K, K + J - 1
! 129: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 130: 50 CONTINUE
! 131: K = K + J
! 132: 60 CONTINUE
! 133: ELSE
! 134: DO 80 J = 1, N
! 135: DO 70 I = K, K + N - J
! 136: VALUE = MAX( VALUE, ABS( AP( I ) ) )
! 137: 70 CONTINUE
! 138: K = K + N - J + 1
! 139: 80 CONTINUE
! 140: END IF
! 141: END IF
! 142: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 143: *
! 144: * Find norm1(A).
! 145: *
! 146: VALUE = ZERO
! 147: K = 1
! 148: UDIAG = LSAME( DIAG, 'U' )
! 149: IF( LSAME( UPLO, 'U' ) ) THEN
! 150: DO 110 J = 1, N
! 151: IF( UDIAG ) THEN
! 152: SUM = ONE
! 153: DO 90 I = K, K + J - 2
! 154: SUM = SUM + ABS( AP( I ) )
! 155: 90 CONTINUE
! 156: ELSE
! 157: SUM = ZERO
! 158: DO 100 I = K, K + J - 1
! 159: SUM = SUM + ABS( AP( I ) )
! 160: 100 CONTINUE
! 161: END IF
! 162: K = K + J
! 163: VALUE = MAX( VALUE, SUM )
! 164: 110 CONTINUE
! 165: ELSE
! 166: DO 140 J = 1, N
! 167: IF( UDIAG ) THEN
! 168: SUM = ONE
! 169: DO 120 I = K + 1, K + N - J
! 170: SUM = SUM + ABS( AP( I ) )
! 171: 120 CONTINUE
! 172: ELSE
! 173: SUM = ZERO
! 174: DO 130 I = K, K + N - J
! 175: SUM = SUM + ABS( AP( I ) )
! 176: 130 CONTINUE
! 177: END IF
! 178: K = K + N - J + 1
! 179: VALUE = MAX( VALUE, SUM )
! 180: 140 CONTINUE
! 181: END IF
! 182: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 183: *
! 184: * Find normI(A).
! 185: *
! 186: K = 1
! 187: IF( LSAME( UPLO, 'U' ) ) THEN
! 188: IF( LSAME( DIAG, 'U' ) ) THEN
! 189: DO 150 I = 1, N
! 190: WORK( I ) = ONE
! 191: 150 CONTINUE
! 192: DO 170 J = 1, N
! 193: DO 160 I = 1, J - 1
! 194: WORK( I ) = WORK( I ) + ABS( AP( K ) )
! 195: K = K + 1
! 196: 160 CONTINUE
! 197: K = K + 1
! 198: 170 CONTINUE
! 199: ELSE
! 200: DO 180 I = 1, N
! 201: WORK( I ) = ZERO
! 202: 180 CONTINUE
! 203: DO 200 J = 1, N
! 204: DO 190 I = 1, J
! 205: WORK( I ) = WORK( I ) + ABS( AP( K ) )
! 206: K = K + 1
! 207: 190 CONTINUE
! 208: 200 CONTINUE
! 209: END IF
! 210: ELSE
! 211: IF( LSAME( DIAG, 'U' ) ) THEN
! 212: DO 210 I = 1, N
! 213: WORK( I ) = ONE
! 214: 210 CONTINUE
! 215: DO 230 J = 1, N
! 216: K = K + 1
! 217: DO 220 I = J + 1, N
! 218: WORK( I ) = WORK( I ) + ABS( AP( K ) )
! 219: K = K + 1
! 220: 220 CONTINUE
! 221: 230 CONTINUE
! 222: ELSE
! 223: DO 240 I = 1, N
! 224: WORK( I ) = ZERO
! 225: 240 CONTINUE
! 226: DO 260 J = 1, N
! 227: DO 250 I = J, N
! 228: WORK( I ) = WORK( I ) + ABS( AP( K ) )
! 229: K = K + 1
! 230: 250 CONTINUE
! 231: 260 CONTINUE
! 232: END IF
! 233: END IF
! 234: VALUE = ZERO
! 235: DO 270 I = 1, N
! 236: VALUE = MAX( VALUE, WORK( I ) )
! 237: 270 CONTINUE
! 238: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 239: *
! 240: * Find normF(A).
! 241: *
! 242: IF( LSAME( UPLO, 'U' ) ) THEN
! 243: IF( LSAME( DIAG, 'U' ) ) THEN
! 244: SCALE = ONE
! 245: SUM = N
! 246: K = 2
! 247: DO 280 J = 2, N
! 248: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
! 249: K = K + J
! 250: 280 CONTINUE
! 251: ELSE
! 252: SCALE = ZERO
! 253: SUM = ONE
! 254: K = 1
! 255: DO 290 J = 1, N
! 256: CALL ZLASSQ( J, AP( K ), 1, SCALE, SUM )
! 257: K = K + J
! 258: 290 CONTINUE
! 259: END IF
! 260: ELSE
! 261: IF( LSAME( DIAG, 'U' ) ) THEN
! 262: SCALE = ONE
! 263: SUM = N
! 264: K = 2
! 265: DO 300 J = 1, N - 1
! 266: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
! 267: K = K + N - J + 1
! 268: 300 CONTINUE
! 269: ELSE
! 270: SCALE = ZERO
! 271: SUM = ONE
! 272: K = 1
! 273: DO 310 J = 1, N
! 274: CALL ZLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
! 275: K = K + N - J + 1
! 276: 310 CONTINUE
! 277: END IF
! 278: END IF
! 279: VALUE = SCALE*SQRT( SUM )
! 280: END IF
! 281: *
! 282: ZLANTP = VALUE
! 283: RETURN
! 284: *
! 285: * End of ZLANTP
! 286: *
! 287: END
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